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A process control approach to tactical inventory management in production-inventory systems
Abstract
Supply chain management (SCM) is concerned with the efficient movement of goods through a network of suppliers and retailers. As delayed and uncertain dynamical systems, supply chains provide an excellent opportunity for demonstrating the benefits of control engineering principles to what is traditionally perceived as a "business" problem. This paper presents a fundamental yet practical approach for applying control-theoretic principles to tactical inventory management problem in a production-inventory system, the basic unit in a supply chain. Beginning with the use of a fluid analogy, we present internal model control (IMC) and model predictive control (MPC) as means for generating a series of increasingly sophisticated decision policies for inventory management. A combined feedback-feedforward multi-degree-of-freedom IMC policy is shown to properly adjust factory starts in the presence of inventory target changes, forecasted shifts in customer demand, and stochastic changes in demand. The MPC policy displays equivalent performance, but incorporates the added functionality of managing inventory in the presence of constraints, an important practical consideration. The MPC policy shows improved performance, greater flexibility, and higher functionality relative to an advanced order-up-to policy based on control engineering principles found in the literature.
... Another interesting approach rests on the application of Internal Model Control (IMC) based on H 2 -optimal tracking set point, unmeasured and measured disturbance (demand) rejection. These controllers allow successfully to deal with tactical decision making as demonstrated in [25] and [26]. The same control strategy enriched by an identification method was proposed by [11] for the inventory control and the estimation of the lead time. ...
... Section III recalls the main principles of model-free control. Section IV, presents an application of MFC and IMC one to a semiconductor manufacturing supply chain borrowed for comparative study from [25]. Finally, some concluding remarks and discussions are provided in Section V. ...
... A. Mathematical modeling of production-inventory system Without loss of generality, consider, for numerical simulations purposes, the production-inventory system borrowed from [25] and depicted in Fig.1. A fluid representation of a three-nodes (or three echelons) semiconductor manufacturing supply chain is consisting of one fabrication/test1, one assembly/test2 and one finish node. ...
In the frame of supply chain networks, several approaches stemming from control theory seem to be more adapted to deal with dynamic inventory management. Nevertheless , the used methods, until today, are model-based control strategies where supply chain models play a major role. Due to the increasing complexity of such systems, the modeling of supply chains becomes more difficult and fails to capture all the dynamic behavior of the supply chain networks. This paper proposes as an alternative to these approaches a model-free control method and its corresponding intelligent controllers for inventory control in supply chain. Several concrete numerical simulations and comparative studies mainly with the internal model control show the efficiency of the approach and promising future of the obtained results even in the presence of various disturbances.
... presenting the characteristics of the hybrid system. 23 So far, the operation of discrete manufacturing industry 24 has been widely studied by scholars in various countries [1], 25 which has further developed in theory, and many kinds of 26 inventory control strategies have been practiced. There are 27 less results on either hybrid supply chain or multi-echelon 28 inventory control strategy of process industry, which is dis- 29 proportionate to the development of process industry. ...
... It is a good choice to use the control theory 123 to analyze the material balance in supply chain. Some schol-124 ars likened the inventory control system of supply chain to 125 the level control system [24], [25], adopted various advanced 126 control methods to solve the uncertainty in the inventory 127 system, and improved the flexibility and stability of supply 128 chain. 129 Jay and Daniel introduced the control theory to the 130 inventory management problems. ...
... 129 Jay and Daniel introduced the control theory to the 130 inventory management problems. They proposed internal 131 model control and model predictive control(MPC) meth-132 ods combined with the feedforward-feedback control under 133 the change of inventory target and customer order [24]. 134 Riddalls and Bennett [27] developed expressions and formu-135 las based on control theory, and designed controller to imple-136 ment inventory control strategy. ...
Multi-echelon inventory control is the main form of the management of supply chain inventory, and it has been paid extensive attention by scholars because of its importance in supply chain management. Process industries, represented by metallurgy, petrochemical and pharmaceutical industry, have typical characteristics such as high investment, high costs, and high resource utilization, they play a key role for industrialization. In this paper, the simulation model of multiproduct three-echelon inventory control system is established for the hybrid supply chain of process industry. Based on the idea of control engineering, a feedback control law is designed for inventory control. Several mixed inventory control strategies were applied to the model. The proportional plus integral control algorithm is used to modify the inventory control strategies. Based on this simulation model, a simulation-based optimization method is applied to the three-echelon inventory control system. The results show that the reciprocal of total entropy ratio and customer satisfaction are optimized by the mixed inventory control strategies, when the hybrid supply chain is affected by order uncertainty.
... Therefore, the efficiency of supply chain performance has been considered as a competitive strategy for many companies to save money ( White and Censlive, 2013b). It also provides many social benefits such as reducing the waste (by minimising the unsold items) and improving the environment (by reducing the energy consumptions) ( Schwartz and Rivera, 2010). One of the very significant features of supply chain literature is the problem of inventory control. ...
... 3. General description of production-inventory control system A production-inventory system is a basic unit in a supply chain ( Schwartz and Rivera, 2010) integrating inventory control policy with the production process (Evans and Naim, 1994). Production-inventory systems have been modelled using both discrete time and continuous time based on the way the inventory status is reviewed and neither modelling process is superior ( ). ...
... The efficiency of a production-inventory system frequently depends on decisions which are often based on intuition and experience (Sarimveis et al., 2008). However, the aim of a controller strategy is to generate a sophisticated decision for production-inventory systems ( Schwartz and Rivera, 2010). The control strategy within a production-inventory system is usually based on average sales, a fraction of the inventory discrepancy and a fraction of the WIP discrepancy. ...
Purpose
The purpose of this study is to propose a new dynamic model of a production-inventory control system. The objective of the new model is to maximise the flexibility of the system so that it can be used by decision makers to design inventory systems that adopt various strategies that provide a balance between reducing the bullwhip effect and improving the responsiveness of inventory performance.
Design/methodology/approach
The proposed production-inventory control system is modelled and analysed via control theory and simulations. The production-inventory feedback control system is modelled through continuous time differential equations. The simulation experiments design is conducted by using the state-space model of the system. The Automatic Pipeline Inventory and Order-Based Production Control System (APIOBPCS) model is used as a benchmark production-inventory control system.
Findings
The results showed that the Two Automatic Pipelines, Inventory and Order-Based Production Control System (2APIOBPCS) model outperforms APIOBPCS in terms of reducing the bullwhip effect. However, the 2APIOBPCS model has a negative impact on Customer Service Level. Therefore, with careful parameter setting, it is possible to design control decisions to be suitably responsive while generating smooth order patterns and obtain the best trade-off of the two objectives.
Research limitations/implications
This research is limited to the dynamics of single-echelon production-inventory control systems with zero desired inventory level.
Originality/value
This present model is an extension and improvement to Towill’s (1982) and John et al.’s (1994) work, since it presents a new dynamic model of a production-inventory control system which utilises an additional flow of information to improve the efficiency of order rate decisions.
... This suggests that patients can be seen as units in a queue, with arrivals and departures akin to inventory inflows and outflows. This perspective allows for the application of established inventory management techniques as in [6], [24], [27], [30], [31], in order to improve ED operations. From this point of view, in the hospital inventory system, patients are viewed as inventory, and demand which is non-homogeneous by time of day and day of week are considered as disturbances. ...
... Decisions from the controller u i (t) are represented with knobs that are manipulated with the objective of achieving a goal, and time-varying arrival rates are shown with a generic input arrival pattern (D A (t) and D ED (t)) (See e.g., Fig. 3, for a fluid representation of the ED). From a straightforward conservation principle in different nodes i, a more or less analogous to delay model's system (see [27], [25], [23] for more explanations) reads, Decision to transfer an ED patient from the ED queue into ED WIP to be serviced Manip var. ...
The paper addresses a critical issue in healthcare management - the effective management of the emergency department (ED) within a hospital. It acknowledges the com- plexity of the hospital environment, which grapples with a mul- titude of challenges, including high demand for services, soaring costs, budgetary limitations, and finite healthcare resources. The proposed solution leverages a two-stage control approach to tackle the occupancy rate management in the ED. This strategy combines differential flatness as a tool for open-loop control and trajectory planning. This approach is valuable for modeling and controlling dynamic systems, as it helps in designing efficient trajectories for patients in the ED. Additionally, the paper introduces model-free control, which is a powerful technique to handle model inaccuracies, uncertainties, and unexpected demands for patient care. This approach allows for real-time adjustments in trajectory planning, ensuring that the system responds effectively to changing conditions. The simulations conducted on a real emergency department at Barner Hospital validate the effectiveness of the proposed framework. This is a significant achievement, demonstrating the adaptability and robustness of the system even in scenarios involving random demands and high-pressure care situations.
... The effectiveness of any enterprise is measured by its capability to deliver the desired product to customers at the correct time, to the right place, and in sufficient quantity. Therefore, the production decisions must be fast, reactive and robust to the different uncertainties in the business environment and at the same time optimized to reach key supply chain objectives [35]. The improvement of inventory management successfully contributes to better customer satisfaction while ensuring high revenues and lower costs in addition to the positive environmental impact of the production process (minimization of raw materials and energy consumption). ...
... The developed adaptive model-free control policy is validated and compared to the internal model control (IMC) approaches (IMC with 2 degree of freedom and 3 degree of freedom 2DoF and 3DoF) of a single node of semiconductors manufacturing supply chain. The data are borrowed from [35] with the IMC parameters: n r = 2, n d = n F = 3, λ r = λ F = 2, λ d = 4. The main objective is to keep the inventory level y(t) at a desired value y ⋆ (t) = 800 Mega Tonne (MT). ...
This paper examines the application of model- free control as introduced by Fliess and Join, to tactical inventory control in a supply chain system. The presence of the unavoidable delay which is inherent to such system requires a compensation action. Here, the delay compensation is achieved via a forecasting method stemming from the new advances of time series. The conducted simulations and comparative studies of a real industrial example show improved performance, greater flexibility, and higher functionality of the proposed framework even in the presence of various disturbances and sever constraints.
... The standard inventory management policies based on traditional Economic Order Quantity (EOQ) approaches with a judiciouslydesigned PID controller in the case of a single inventory in a supply chain has been illustrated in (Rivera & Pew, 2005). It is also claimed that a well-tuned PID-based policy is able to generate effective decisions on orders that ultimately reduce the need for safety stock by eliminating backorders. 2 The application of the control theory in inventory-production systems has been illustrated in different studies, see (Azarskov et al., 2013(Azarskov et al., , 2017Salcedo et al., 2013;Hasani et al., 2018;Neck, 1984;Schwartz & Rivera, 2010;Sourirajan et al., 2008;Tao et al., 2017;White & Censlive, 2016). Uncertainty in the dynamic-stochastic P/I control system has been the focus of different studies in the literature, see (Pishvaee et al., 2011;Tang et al., 2019;Van Landeghem & Vanmaele, 2002). ...
... where is the response (output) at time domain 0 ≤ ≤ and is the desired setpoint for the response of the model. A good implementation of the control theory applied to production-inventory control has been presented by (Dejonckheere et al., 2003;Schwartz & Rivera, 2010;White, 1999;Wikner, 1994). In the mentioned studies, an exponential smoothing has been used to obtain the average sales consumption as a function of the sales (demand) rate in optimal control of dynamic P/I system (see Fig. 1). ...
In production/inventory control systems, the goal of the controller is to generate sophisticated decisions by controlling the order rate and inventory level. This paper aims at modeling a dynamic-stochastic production/inventory control system under two sources of variability (uncertainty) including uncertainties on demand rate and frustrating rate. The study deals with obtaining a robust optimal design of a Proportional-Integral-Derivative (PID) controller in in the stochastic control system. For this purpose, a new robust simulation-optimization method in the class of computational intelligence is proposed. To cope with the unknown distribution of uncertainty, the crossing weighted uncertainty scenarios are combined with the proposed method. Within this study, a new sequential robust efficient global optimization is proposed to make a trade-off between optimal and robustness terms in final optimization results. Finally, a numerical case with simulation experiments is conducted to demonstrate the advantages of the proposed policy in terms of optimal result, robustness, and computational cost.
... Dolgui et al. [8] presented some of the existing literature of supply planning tools 91 Information Technology and Control 2020/1/49 under uncertainty of lead times. Schwartz and Rivera [28] gave a practical approach for applying control-theoretic principles to tactical inventory management problem in a production-inventory system, the basic unit in a supply chain. Janušauskaitė [14] investigated two mathematical models of multistage inventory control processes with continuous and discrete density functions of demands. ...
... Dolgui et al. [8] presented some of the existing literature of supply planning tools under uncertainty of lead times. Schwartz and Rivera [28] gave a practical approach for applying control-theoretic principles to tactical inventory management problem in a production-inventory system, the basic unit in a supply chain. Janušauskaitė [14] investigated two mathematical models of multistage inventory control processes with continuous and discrete density functions of demands. ...
In this paper we solve a problem of optimization and production planning using the optimal control methods and Pontryagin Maximum Principle. We propose an economic model and find an optimal plan of production for n products, to ensure the required quantity at specified delivery data with minimum cost of inventory and production. We prove that the economic system is not controllable, in the sense that we cannot reach any final stock quantity. Finally, we justify this construction with a numerical example.
... Unavoidable dead times, often called lead times or throughput times, are due to phenomena like transport and production. Delay differential equations play therefore an increasing rôle (see, e.g., [1], [27], [20], [21], [36], [41], [42], [51], [55], [56], [62], [63], [64], [67], [79], and the references therein). Several previous publications use a model, that is more or less analogous to the following delay system, which is derived via a straightforward conservation principle, ...
... This last quantity is obtained thanks to the forecastd(t + L) of the customer demand via the techniques sketched in Section II-A.2. Figure 1 displays excellent results with K p = 0.1. The data are borrowed from [62]. The customer demand is represented in Figure 1-(c): note that after the constant portion at the beginning a corrupting uniform white noise n, −1 ≤ n ≤ 1, has been added. ...
Supply chain management and inventory control provide most exciting examples of control systems with delays. Here, Smith predictors, model-free control and new time series forecasting techniques are mixed in order to derive an efficient control synthesis. Perishable inventories are also taken into account. The most intriguing "bullwhip effect" is explained and attenuated, at least in some important situations. Numerous convincing computer simulations are presented and discussed.
... Unavoidable dead times, often called lead times or throughput times, are due to phenomena like transport and production. Delay differential equations play therefore an increasing rôle (see, e.g., [1], [27], [20], [21], [36], [41], [42], [51], [55], [56], [62], [63], [64], [67], [79], and the references therein). Several previous publications use a model, that is more or less analogous to the following delay system, which is derived via a straightforward conservation principle, ...
... This last quantity is obtained thanks to the forecastd(t + L) of the customer demand via the techniques sketched in Section II-A.2. Figure 1 displays excellent results with K p = 0.1. The data are borrowed from [62]. The customer demand is represented in Figure 1-(c): note that after the constant portion at the beginning a corrupting uniform white noise n, −1 ≤ n ≤ 1, has been added. ...
Supply chain management and inventory control pro- vide most exciting examples of control systems with delays. Here, Smith predictors, model-free control and new time series forecasting techniques are mixed in order to derive an efficient control synthesis. Perishable inventories are also taken into account. The most intriguing “bullwhip effect” is explained and attenuated, at least in some important situations. Numerous convincing computer simulations are presented and discussed.
... Unavoidable dead times, often called lead times or throughput times, are due to phenomena like transport and production. Delay differential equations play therefore an increasing rôle (see, e.g., [1], [27], [20], [21], [36], [41], [42], [51], [55], [56], [62], [63], [64], [67], [79], and the references therein). Several previous publications use a model, that is more or less analogous to the following delay system, which is derived via a straightforward conservation principle, ...
... This last quantity is obtained thanks to the forecastd(t + L) of the customer demand via the techniques sketched in Section II-A.2. Figure 1 displays excellent results with K p = 0.1. The data are borrowed from [62]. The customer demand is represented in Figure 1-(c): note that after the constant portion at the beginning a corrupting uniform white noise n, −1 ≤ n ≤ 1, has been added. ...
Demand forecasting plays an important role for supply chains decision making. It also represents a basis step for activity planning in response to customer demand. In this paper, recent advances in times series allow a new robust and easy approach for demand forecasting. Such technique which is based on algebraic methods of estimation seems to be more adequate for such supply chains task. Several computer simulations and comparative studies demonstrate the relevance of the proposed approach.
... 2. Aspects of production-inventory systems A production-inventory system is an integrated system that models the inventory control policy with the production process (Evans and Naim, 1994). It is a basic unit in a supply chain (Schwartz and Rivera, 2010). The efficiency of a production-inventory system mostly depends on decisions which are often based on intuition and experience . ...
... The efficiency of a production-inventory system mostly depends on decisions which are often based on intuition and experience . However, the aim of the control system is to generate sophisticated decisions for production-inventory systems (Schwartz and Rivera, 2010). A production-inventory system is typically characterised by a forward flow of materials and a backward flow of information. ...
Purpose
This paper examines the impact of applying two classical controller strategies, including two proportional (P) controllers with two feedback loops and one proportional-integral-derivative (PID) controller with one feedback loop, on the order and inventory performance within a production-inventory control system.
Design/methodology/approach
The simulation experiments of the dynamics behaviour of the production-inventory control system are conducted using a model based on control theory techniques. The Laplace transformation of an Order-Up-To (OUT) model is obtained using a state-space approach, and then the state-space representation is used to design and simulate a controlled model. The simulations of each model with two control configurations are tested by subjecting the system to a random retail sales pattern. The performance of inventory level is quantified by using the Integral of Absolute Error (IAE) whereas the bullwhip effect is measured by using the Variance ratio (Var).
Findings
The simulation results show that one PID controller with one feedback loop outperforms two P controllers with two feedback loops at reducing the bullwhip effect and regulating the inventory level.
Originality/value
The production-inventory control system is broken down into three components, namely: the forecasting mechanism, controller strategy and production-inventory process. A state-space approach is adopted to design and simulate the different controller strategy.
... This research paper addressed two problems in the context of high-volume supply chain, by applying infinite and finite dimensional mathematical approaches. Several research works have presented the use of PDEs for production systems [35][36], whereas the use of ODEs in the mathematical modeling for production-inventory systems was more common [37][38]. In this work, infinite and finite dimensional systems incorporate dynamic pricing into the description of a dynamical system while taking demand fluctuations into account. ...
This research work aims to develop the mathematical modeling for a class of dynamic supply chains. Demand fluctuation corresponds to product demand volatility, which increases or decreases over a given time frame. Industrial engineering practitioners should consider the function that applied mathematical modeling plays in providing approximations of solutions that may be used in simulations and technical implementations at the strategic, tactical, and operational levels of an organization. In order to achieve proper results, two mathematical models are presented in this paper: In addition to a finite-dimensional system of Ordinary Differential Equations (ODEs) for coupled dynamic pricing, production rate, and inventory level, which properly integrates Lyapunov stability analysis of the dynamical system and simulations, there is an infinite-dimensional Partial Differential Equation (PDE) production level modeling system available. Infinite and finite-dimensional systems incorporate a dynamic pricing approach in the mathematical modeling. The main research goal of this work is to explore the dynamic nature of supply chains applying PDE and ODE methods, with proper analytical analysis and simulations for both systems.
... Several approaches from operations research or control theory have been proposed to address the various aspects of supply chains problems. Tactical inventory management in production-inventory system, which is the basic unit in supply chain has recently gained several attention and several interesting contributions have been reported in literature ranging from deterministic to highly complex stochastic methods (See e.g., [5], [21], [26], [27], [30], [31], [32], [33], [35], [40], [41], [45], [46], [47] and the references therein). It is important to emphasize that most of the approaches to dynamic inventory management are model-based one. ...
... Just to cite a few contributions, we mention the following ones: an adaptive MPC scheme for the simultaneous identification and control of production-inventory systems has been proposed in Aggelogiannaki et al. (2008), the same authors consider a similar problem in Doganis et al. (2008) using a neural network time series forecasting method, the stock replenishment policy defined in Alessandri et al. (2011) deals with the uncertainty affecting the future customer demand using a worst case approach. A comparison between MPC and Internal Model Control strategies is made in Schwartz and Rivera (2010), and the case of multiple supply sources is considered in Xie et al. (2021). CONTACT Valentina Orsini vorsini@univpm.it ...
This paper deals with the inventory control in supply chains under the following assumptions: (1) perishable goods with uncertain deteriorating factor, (2) a future uncertain customer demand that, over a limited prediction horizon, belongs to a known compact set. The problem is to define a smooth control policy maximising the fulfilled customer demand and minimising the inventory level. This problem is here solved through a new Robust Model Predictive Control (RMPC) approach. This implies solving a min-max optimisation problem with hard constraints on the control effort (i.e. the sequence of replenishment orders). To drastically reduce the numerical complexity of this problem, the control signal is sought in the space of B-spline functions, which are known to be universal approximators admitting a parsimonious parametric representation. This allows us: (1) to reduce the number of both decision variables and constraints involved in the optimisation procedure, (2) to reformulate the numerically demanding minimisation of the worst case cost functional as a simpler Weighted Constrained Robust Least Squares (WCRLS) estimation problem. The WCRLS algorithm can be efficiently solved using interior point methods. A rigorous analysis of stability and feasibility conditions is provided. ARTICLE HISTORY
... Without an efficient RSC and strong inventory management strategies, it is becoming more difficult to achieve this target and gain a competitive advantage (Christopher & Jüttner, 2000). Improved inventory management contributes to lower costs, increased revenue and greater customer satisfaction (Schwartz & Rivera, 2010). (Azadivar, 1999). ...
It is often taken for granted that the right products will be available to buy in retail outlets seven days a week, 52 weeks a year. Consumer perception is that of a simple service requirement, but the reality is a complex, time sensitive system - the retail supply chain (RSC). Due to short product life-cycles with uncertain supply and demand behaviour, the RSC faces many challenges and is very vulnerable to disruptions. In addition, external risk events such as BREXIT, extreme weather, the financial crisis, and terror attacks mean there is a need for effective RSC risk management (RSCRM) processes within organisations. Literature shows that although there is an increasing amount of research in RSCRM, it is highly theoretical with limited empirical evidence or applied methodologies. With an active enthusiasm coming from industry practitioners for RSCRM methodologies and support solutions, the RSCRM research community have acknowledged that the main issue for future research is not tools and techniques, but collaborative RSC system wide implementation.
The implementation of a cross-organisational initiative such as RSCRM is a very complex task that requires real-world frameworks for real-world practitioners. Therefore, this research study attempts to explore the business requirements for developing a three-stage integrated RSCRM framework that will encourage extended RSC collaboration. While focusing on the practitioner requirements of RSCRM projects and inspired by the laws of Thermodynamics and the philosophy of System Thinking, in stage one a conceptual reference model, The 𝑃6 Coefficient, was developed building on the formative work of supply chain excellence and business process management. The 𝑃6 Coefficient reference model has been intricately designed to bridge the theoretical gap between practitioner and researcher with the aim of ensuring practitioner confidence in partaking in a complex business process project. Stage two focused on a need for a standardised vocabulary, and through the SCOR11 reference guide, acts as a calibration point for the integrated framework, ensuring easy transfer and application within supply chain industries. In their design, stages one and two are perfect complements to the final stage of the integrated framework, a risk assessment toolbox based on a Hybrid Simulation Study capable of monitoring the disruptive behaviour of a multi-echelon RSC from both a macro and micro level using the techniques of System Dynamics (SD) and Discrete Event Simulation (DES) modelling respectively.
Empirically validated through an embedded mixed methods case study, results of the integrated framework application are very encouraging. The first phase, the secondary exploratory study, gained valuable empirical evidence of the barriers to successfully implementing a complex business project and also validated using simulation as an effective risk assessment tool. Results showed certain high-risk order policy decisions could potentially reduce total costs (TC) by over 55% and reduce delivery times by 3 days. The use of the 𝑃6 Coefficient as the communication/consultation phase of the primary RSCRM case study was hugely influential on the success of the overall hybrid simulation study development and application, with significant increase in both practitioner and researcher confidence in running an RSCRM project. This was evident in the results of the hybrid model’s macro and micro assessment of the RSC. SD results effectively monitored the behaviour of the RSC under important disruptive risks, showing delayed effects to promotions and knowledge loss resulted in a bullwhip effect pattern upstream with the FMCG manufacturer’s TC increasing by as much as €50m. The DES analysis, focusing on the NDC function of the RSC also showed results of TC sensitivity to order behaviour from retailers, although an optimisation based risk treatment has reduced TC by 30%. Future research includes a global empirical validation of the 𝑃6 Coefficient and enhancement of the application of thermodynamic laws in business process management. The industry calibration capabilities of the integrated framework application of the integrated framework will also be extensively tested.
... The identified values are then used to adjust the delay compensation in a decentralized IMC. Schwartz and Rivera (2010) have introduced two and three degrees of freedom feedback feedforward IMC as well as model predictive control as a novel inventory replenishment policy in supply chain and its applications to the control of a single echelon. Centralized IMC approaches (two-degrees of freedom) where inventory target tracking and disturbance (demand) rejection in the inventory control, treated separately, have been developed by Salcedo et al. (2013). ...
Inventory control in the frame of supply chain systems represents a challenging problem due to their dynamical behavior, ranging from fast changing demand, transport and delivery delays and production phenomena like bullwhip effect. Nevertheless, modeling such systems in order to capture all its components and to design a robust and dynamic management, remains an open problem. In this paper, a model-free control which permits to design several control strategies without need to any exact model, is proposed. Several numerical simulations as well as the conducted comparative studies show the relevance of the proposed approach. In addition, the paper considers the case of a poor knowledge of the supply chain model and introduce an exact and fast deterministic method which is of a algebraic flavor in order to estimate the parameters of the model.
... It is seen that (27)-(29) define a problem of the kind (3), (5). Hence, according to Section II.B, each WCRLS estimation problem (27)- (29) can be formulated as ...
This paper deals with the inventory control in supply
chains under the following assumptions: 1) highly perishable
goods with uncertain decay factor, 2) a future customer demand
belonging to a known compact uncertainty set. The problem is
to define a control policy keeping the on hand stock level as close
as possible to a desired level despite the above uncertainties. The
contribution of this paper focuses on a Robust Model Predictive
Control (RMPC) approach. This implies solving a min-max
optimization problem with hard constraints on some physical
variables. To drastically reduce the numerical complexity of this
problem, the control signal (i.e. the sequence of replenishment
orders) is sought in the space of B-spline functions, which are
known to be universal approximators admitting a parsimonious
parametric representation. This allows us: 1) to reduce the
number of both decision variables and constraints involved
in the optimization procedure, 2) to reformulate the numerically
involved minimization of the worst case cost functional
as a Weighted Constrained Robust Least Squares (WCRLS)
estimation problem. The WCRLS algorithm can be efficiently
implemented using second order cone programming. A rigorous
analysis of stability and feasibility conditions is provided.
... La figura 2 presenta un sistema PI adaptado a partir de modelos matemáticos publicados previamente en [28]- [29] para el sistema dinámico muelle-masa-amortiguador, y de trabajos que analizan sistemas de producción-inventario mediante analogías de fluidos [30] con aplicaciones en la fabricación de semiconductores en [31]- [32] y enfoques orientados a la modelización de la demanda para la gestión de inventarios presentados en [33]- [34]. ...
This research work presents an optimal control approach for a class of sustainable production-inventory system (PI). Modeling, analysis, and control for a PI system are present. For systems modeling purposes, a mixed capacity/third order PI is to analyze, dynamic approaches for production-inventory systems which are valuable in order to maximize profits and minimize costs over the PI. Optimality, robustness, and stability are the top-level characteristics which encompass a suitable control. Optimal control formulation is conducted via Pontryagin maximum principle, with a present value-Hamiltonian approach (PVH)
Keywords: Mathematical modeling, Optimal control, Production-inventory systems, Resilience, Sustainability.
... In [20], MPC control is used to demonstrate that safety stock levels can be significantly reduced and financial benefits achieved while maintaining satisfactory operating performance in supply chain. Concret applications of MPC and Internal Model Control (IMC) have been developed in [21], [22], [23]. ...
Abstact-Although dynamic supply chain management is nowadays quite widely studied, several problems related to their control remain a challenging task. Indeed, most of the methods are model-based control strategies where supply chain models play a major role. The increasing complexity of these systems makes their representation more difficult and fails to capture all the dynamic behavior of the supply chain networks. This paper proposes a new efficient and easy implementable framework for tactical management in supply chain systems. The developed approach rests on the use of model-free control in order to deal with the inventory control of supply chains. The provided numerical simulations of a petrochemical example shows the effectiveness and robustness of model-free controllers against the classic controllers.
... The identified values are then used to adjust the delay compensation in a decentralized IMC. Schwartz and Rivera (2010) have introduced two and three degrees of freedom feedback feedforward IMC as well as model predictive control as a novel inventory replenishment policy in supply chain and its applications to the control of a single echelon. Centralized IMC approaches (two-degrees of freedom) where inventory target tracking and disturbance (demand) rejection in the inventory control, treated separately, have been developed by Salcedo et al. (2013). ...
Inventory control in the frame of supply chain systems represents a challenging problem due to their dynamical behavior, ranging from fast changing demand, transport and delivery delays and production phenomena like bullwhip effect. Nevertheless, modeling such systems in order to capture all its components and to design a robust and dynamic management, remains an open problem. In this paper, a model-free control which permits to design several control strategies without need to any exact model, is proposed. Several numerical simulations as well as the conducted comparative studies show the relevance of the proposed approach. In addition, the paper considers the case of a poor knowledge of the supply chain model and introduce an exact and fast deterministic method which is of a algebraic flavor in order to estimate the parameters of the model.
... In paper [18] Li and Wang proposed an integrated replenishment and production control policy under inventory inaccuracy and time-delay, while Li and Arreola-Risa investigated in [19] optimization of a production-inventory system under a cost target. Schwartz and Rivera [28] described a process control approach to tactical inventory management in production-inventory systems, and Towill, Evans and Cheema [29] proposed an analysis and design of an adaptive minimum reasonable inventory control system. ...
A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
... This methodology will result in a work drift and asset management device that is optimized to the organizations. As stated by Schwartz & Rivera (2010) [13] the inventory management system as a technique or process begins with the acquisition of an inventory or stocks, then maintains with the redeployment of property, and ends while an asset is terminated. It interfaces with many employees performing distinct systems of management and control disciplines related to asset or item implementation, guide, and protection features within the organization in addition to finance and corporate management areas all throughout the organizations. ...
Worldwide several firms have suffered a lot of problems in inventory management which concerns their operational achievement. Good inventory management is a means to improve customer service and reduce stock. The objective of inventory management is to handle it in a most reasonable cost and remove the constant accumulations for continuous developments. This paper brings out how to assess the effect of integrated inventory management practices on organizations representation of some selected universities in Amhara region, Ethiopia. To remain competitive, inventory accounts needs a huge capital of an organization and must have a good management in the overall flow of resource from the initial purchase to final usage. Generally, the goal of every business is to hold little inventory and keep their business running. So, those universities in this region have hold a little inventory and make their organizations run well, even determine how much they do have in their store and determine for how long it will serve them.
... Knowing what kind of competitive advantages that might be generated through the alignment of business strategy along with IT strategy is utmost important and strategically significant since very few studies have been addressed the effects of IT business strategic alignment on SCA. In the end, this research intends to draw a new path between IT business strategic alignment and multiple dimensions of SCA among Algerian high-tech i Dynamic capability theory regards IT-business strategic alignment as firm-unique internal competencies that allow them to align IT strategy with a business strategy which in turn lead to superior performance ( Schwartz and Rivera, 2010). Several studies have examined the role of IT business strategic alignment on organization performance ( Croteau and Bergeron, 2001;Kearns and Lederer, 2003;Huang, 2010) industry ). ...
Understanding the relationship between IT Business Strategic Alignment (ITBSA), IT Personnel Capabilities (ITPC), and Intangible IT Resources (IITR) is utmost important. Strategic scholars and professionals looks to these three strategic resources as the main driver of generating distinctive competencies which in turn become the main source of creating sustainable competitive advantages (SCA). The aim of this study is to establish and understand a new path between three strategic inputs on the SCA which overlooked in the literature and thereby there is a need to cover this critical gap. The main objective of this paper is to determine whether IT personnel capability will influence directly and/or indirectly (moderating role) on the relationship between IT business strategic alignment and intangible IT resources towards creating SCA. Hence, this paper question to what extent capability of IT personnel is able to strengthen the relationship between ITBSA and ITPC on the SCA. Applying, Resources-based View (RBV) and Dynamic Capability View (DCV), this paper intended to investigate the role of IT personnel capability on enabling firm’s strategic resources such as ITBSA and IITR on SCA achievement. Therefore, in order to achieve the proposed objectives and answering the questions of this study, the author will apply cross sectional survey for collecting appropriate data from IT managers among Algerian high-tech industry. Implications and suggestions will be discussed.
... Based on fluid analogy methodology (Schwartz and Rivera, 2010;, the manufacturing system, or one of the key process in a supply chain, is illustrated in Figure3. This model considers a single-item product procedure in the factory. ...
The inventory management of supply chain is concerned with an efficient transportation of materials and products through supply chain members. In this paper, a series of linear models have been presented with lag
time uncertainty for improving inventory management. In addition, a fluid analogy has been used for a single-product manufacturing system, or the basic unit of a supply chain. Robust control synthesis, which has been proven to cope with its ability for the system with high uncertainty, is utilised in optimising the inventory management and guaranteeing high performance of complete system. In addition, this control scheme aims to ensure the customer satisfaction by tracking and keeping the actual inventory close to target inventory under the influence of uncertainty. The extensive numerical simulations have been carried out to validate the proposed approach against disturbances. Finally, the simulation results show that the robust control system ensures good ability on keeping the target inventory under uncertainty.
... In Schwartz, Wang, and Rivera (2006), a simulation-based optimisation is presented to decide, optimally, the internal parameters of internal model control and the model's predictive control policies for inventory management in supply chains under uncertainties are supply and demand. An approach for applying control strategies to inventory management problem in a production-inventory system is presented in Schwartz and Rivera (2010), which uses an internal model control and model predictive control to calculate decision policies for inventory management. In Subramanian, Rawlings, Maravelias, Flores-Cerrillo, and Megan (2013), a distributed model predictive control is proposed to optimise supply chains, particularly cooperative model predictive control. ...
In this paper, we present experimental results from the application of model predictive control (MPC) to inventory management in a real hospital. In particular, the stock levels of ten different drugs that belong to the same laboratory have been controlled by using an MPC policy. The results obtained after four months show that the adopted approach outperforms the method employed by the hospital and reduces both the average stock levels and the work burden of the pharmacy department. This paper also paper presents some practical insights regarding the application of advanced control methods in this context.
... Beginning with the first study published on using calculus of variations to solve production-inventory problems by Holt et al. (1960), integrated production-inventory problems with lot-size and capacity optimization have been extensively considered (Axsaeter, 1985;Feichtinger and Hartl, 1985;Axsäter and Rosling, 1993;Grubbström and Wikner, 1996;Ortega and Lin, 2004;Schwartz and Rivera, 2010). With the help of linear classical control theory, Disney and Towill (2002) and Hoberg et al. (2007) recently investigated the effects of inventory control policies on order and inventory variability. ...
In this Chapter, we analyze state-of-the-art research streams on managing operational and disruption risks in supply chain design and planning. It structures and classifies existing research and practical applications of different quantitative methods subject to recently derived empirical frameworks. We identify gaps in current research and delineate future research avenues. The results of this literature analysis are twofold. Supply chain managers can observe which quantitative tools are available for different applications. On the other hand, from the point of view of operational research, limitations and future research needs can be identified for decision-supporting methods in supply chain risk management domains.
... Tanthatemee and Phruksaphanrat [22] propose a fuzzy logic control approach to continuous inventory control system with uncertain demand and supply. Schwartz and Rivera [23] present a process control approach to inventory management in stochastic environments. The supply chain is modeled using a fluid analogy with uncertainty in both customer demand and factory production. ...
In the last decade, global competition has forced manufacturers to optimize logistics. The implementation of collapsible containers provides a new perspective for logistics cost savings, since using collapsible containers reduces the frequency of shipping freight. However, optimization of logistic cost is complicated due to the interactions in a system, such as market demand, inventory, production throughput, and uncertainty. Therefore, a systematic model and accurate estimation of the total cost and system performance are of great importance for decision making. In this paper, a mathematical model is developed to describe deterministic and stochastic scenarios for a closed-loop container dynamic flow system. The uncertainties in a factory and a supplier are considered in the model. The performance evaluation of the collapsible container system and total cost estimation are provided through model analysis. Furthermore, fuzzy control method is proposed to monitor the processing rate of the supplier and the factory and to adjust the rate of the supplier operation then further reduce the logistic cost. A case study with a matlab simulation is presented to illustrate the accuracy of the mathematical model and the effectiveness of the fuzzy controller.
... Such similarity gave raise to The management of generalised flow-based networks is a complex task and has become a research subject worldwide. Strategical and tactical decisions in physical network operation can be addressed by different methods proposed within the supply-chain theory (Papageorgiou, 2009), but the mathematical tools available in control systems theory have shown to be more suitable to handle the problem consisting of time variance, uncertainties, delays, dimensionality and lack of system information (see, e.g., Ortega and Lin, 2004;Sarimveis et al., 2008;Schwartz and Rivera, 2010;Subramanian et al., 2013). Most of the approaches developed in the aforementioned references for the control of dynamic networks are mainly focused on performance and robustness, and the control strategy is often implemented in a multi-layer control architecture. ...
This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalised flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamical allocation of safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the case study considered.
... At the stage of the production process definition, one of the steps is to define the resources necessary for its implementation [7], i.e. their types and specific instances. For example, a resource may be an employee or more specifically an employee at a defined position or with the appropriate privileges or powers. ...
The paper proposes the Unified Process Management for Service and Manufacture (UPM-Srv-Mnf), the intent of which is to constitute integrated platform for modelling and exchange of information in the field of production processes. The UPM-Srv-Mnf consists of a theoretical basis, formal notation, modeling language, algorithms, and methods of processing information as well as modeling methodology. This article focuses on the passage concerning the most theoretical foundations in the identification of selected categories and relations such as generalization-specialization, part–whole, class-feature, class-instance, and property-instance. The platform used to build UPM-Srv-Mnf is the Semantic Knowledge Base (SKB), which is the result of a research project on methods of representation and processing of knowledge.
... Similar applications are used in industry in the monitoring of the production of chemicals. Schwartz and Rivera (2010) applied transfer function modelling to solving problems of production inventory management. ...
Monitoring and control is very important in maintaining quality outputs, reducing downtimes and improving operation's efficiency of processes. Transfer function modelling has been the heart of process monitoring and control. This study surveys the past, present and future of transfer function modelling. The survey found that continuous transfer function models used in modelling engineering control systems have the widest applications. Similarly, the discrete transfer function models are applied mostly in forecasting and have wide application in econometrics and the social sciences and to a little extent in the physical and life sciences. The current efforts by researchers in extending the frontiers of discrete transfer function modelling to fault diagnosis, improvement of maintenance and operation's efficiency, determination of production process capability etc were highlighted. Finally, the future directions of research in transfer function modelling which include but not limited to: leak detection and failure prediction, improved modelling software tools, performance evaluation and improvement in chemical industries, power systems, oil and gas industries, economic and management systems etc was suggested. Our findings show that transfer function would be very important in solving manufacturing dysfunction.
... Following the effective forecasting illustrated above, the inventory optimization tool also provides suggestions regarding the schedules for optimal restocking while also providing thresholds on a unit levels for the automated replenishment and ordering of inventory within companies (Schwartz & Rivera, 2010, pp. 113-115). ...
The purpose of this study is to carry out research to analyse factors involved in inventory control decision process and its implementation for company’s growth. The research is to be carried out through secondary data available in the perspective of the topic. The research centered on the concepts of inventory control decision-making process, and a detailed reports of different businesses implications of inventory control decision making process and its influence in company’s growth and survivals in competitive environment. The theoretical details of the research assess some examples of some companies that have successfully achieved inventory control, which leads to minimum cost implications for holding inventory.
Supply chain networks undergo transformations on the scale unlike any seen before. Extensive technology adoptions in supply chain networks render changes in network structures entailing multi-structural dynamics (i.e., new technologies such as Industry 4.0 and additive manufacturing lead to creating more dynamic and reconfigurable supply chains). This chapter presents an introduction to the book on supply network dynamics and control with chapters devoted to theory, methods, and applications in manufacturing, service, supply chain, and Industry 4.0 systems.KeywordsSupply chainDynamicsControlIndustry 4.0Cloud supply chainDigital twinReconfigurable supply chain
Today, most manufacturing control systems are complex and expensive, so they are limited to employ a small number of function evaluations for optimal design. Yet, looking for optimization methods with the less-computational cost is an open issue in engineering control systems. This paper aims to propose an effective adaptive optimization approach by integrating Kriging surrogate and Particle Swarm Optimization (PSO). In this method, a novel iterative adaptive approach is utilized using two sets of training samples including initial training and adaptive sample points. The initial training points are designed by space-filling design, while the adaptive points are generated using a new jackknife resampling approach. The proposed approach can effectively convergence towards the global optimal point using a small number of function evaluations. The efficiency and applicability of the proposed algorithm are evaluated using the optimal design of the fractional-order PID (FOPID) controller for some benchmark transfer functions. Then, the introduced approach is applied for tuning the parameters and the sensitivity analysis of the FOPID controller for a dynamic production-inventory control system. The results are in good agreement with the results reported in the literature, while the proposed approach is executed with a lower computational burden.
This paper investigates the signaling role of stocking for new experience products in a two‐period setting. The seller privately observes the product quality information, which cannot be resolved until the second selling period. We show that the stocking plays a pivotal role in signaling the quality information, and the equilibrium strategy depends highly on ordering cost and the consumer prior belief about the seller type. If the seller is unable to dynamically decide the retail prices, separating equilibrium arises more frequently and such a fixed pricing may result in a win‐win situation for both seller and consumers.
No contexto da inovação empresarial, a gestão do estoque tem se destacado em virtude da sua importância para a lucratividade, retorno sobre o capital investido e como estratégia para suportar a definição de vantagem competitiva para a organização. Diante desse cenário, o objetivo desta pesquisa é identificar as principais características dos artigos publicados sobre gestão de estoques e inovação no Brasil entre 2010 e 2018, sob o ponto de vista do método de controle abordado. Para se atingir o objetivo, utilizou-se como metodologia a pesquisa bibliométrica com abordagem quantitativa e a coleta de dados foi realizada através da plataforma SPELL. Os principais resultados demonstram que a maioria dos artigos sobre gestão de estoques foram publicados em 2016, possuem dois autores, a Instituição de Ensino que mais autores estão afiliados foi a USP, os métodos mais abordados foram o LEC, Just in time e Curva ABC que abordam a gestão de estoque de forma tradicional sem acréscimo de inovação. Já os que abordam aspectos inovadores, estão relacionados à tecnologia da informação. O estudo contribuiu para a definição do perfil de publicações sobre o tema, auxiliando na definição de trabalhos futuros.
Inventory control can be broadly defined as "the activity of checking a shop’s stock." However, a more focused definition takes into account the more science-based, methodical practice of not only verifying a business' inventory but also focusing on the many related facets of inventory management "within an organisation to meet the demand placed upon that business economically. “Other facets of inventory control include supply chain management, production control, financial flexibility, and customer satisfaction.
Chapter Outline: After going through this chapter students will be able to understand about
• Cost Factors In Inventory Control
• Inventory Carrying Cost
• Ordering Cost
• EOQ, Lead Time
• Safety Stock
• Reorder Level
• Minimum Level, Max. Level
• Types of Inventory Control Systems
• Perpetual Inventory Control System
• ABC Method Etc.
• Valuation Of Materials Issued From Store
• FIFO, LIFO, etc.
This paper deals with adaptive super-twisting (STW) sliding mode control (SMC) algorithm to manage chaotic supply chain system. A multi-echelon supply chain system having parametric perturbations and disturbances is presented to demonstrate chaotic nonlinear dynamical behaviours. When changing input variables slightly in the supply chain system, the predicted outputs will be completely different due to chaotic behaviours with bifurcation. In addition, various uncertainties along with exogenous disturbances make the system dynamics more complex to manage as they propagate both upstream and downstream of the supply chain networks. Particularly, the adaptive STW SMC algorithm has been designed for chaos suppression and synchronisation of the supply chain system. Next, the robust control algorithm with adaptive law for the closed-loop system has been proved by using Lyapunov stability theorem. Then, extensive numerical simulations are conducted to demonstrate the validity of the active control synthesis for optimal operations management of chaotic supply chain networks. The control algorithm based on system theory provides satisfactory performance on achieving chaos suppression and synchronisation of the chaotic supply system. The control system theory can be expanded into new integration software applications for operations management of supply chain networks. Finally, the presented control synthesis with dynamical analysis is essential for strategic decision-makers in the modern supply chain management.
Modern production and logistics systems, supply chains, and Industry 4.0 networks are challenged by increased uncertainty and risks, multiple feedback cycles, and dynamics. Control theory is an interesting research avenue which contributes to further insights concerning the management of the given challenges in operations and supply chain management. In this paper, the applicability of control theory to engineering and management problems in supply chain operations is investigated. Our analysis bridges the fundamentals of control and systems theory to supply chain and operations management. This study extends our previous survey in the Annual Reviews in Control (Ivanov et al. 2012) by including new literature published in 2012–2018, identifying two new directions of control theory applications (i.e., ripple effect analysis in the supply chains and scheduling in Industry 4.0) and analysis towards the digital technology use in control theoretic models. It describes important issues and perspectives that delineate dynamics in supply chains, operations, and Industry 4.0 networks and identifies and systemizes different streams in the application of control theory to operations and supply chain management and engineering in the period from 1960–2018. It updates the existing applications and classifications, performs a critical analysis, and discusses further research avenues. Further development of interdisciplinary approaches to supply chain optimization is argued. An extended cooperation between control engineers and supply chain experts may have the potential to introduce more realism to dynamic planning and models, and improve performance in production and logistics systems, supply chains, and Industry 4.0 networks. Finally, we analyze the trends towards the intellectualization of control and its development towards supply chain control analytics.
This paper presents a centralised model predictive control strategy applied to biomass inventory control in sugarcane industries. Sugarcane industries are important renewable energy producers and an adequate inventory control of their feed material (biomass) can improve energy production. Simple linear discrete-time models with dead-time are developed to predict the controlled variable behaviour. Two layers are used in the controller, in the upper one performance is optimised by an linear programming (LP) algorithm and a multivariable generalised predictive controller (GPC) or multivariable generalised predictive controller with dead-time compensation (DTC-GPC) is used in the lower level. Simulation results in general show that the proposed controllers globally optimise the system behaviour and find an optimal ordering amount for keeping stock levels. In cases of plant/model mismatch DTC-GPC can have a significant and positive impact on the control of stock levels adding one more parameter for achieving minimised oscillatory performances (bullwhip effect).
The item fill rate – defined as the fraction of demand that is immediately satisfied from on-hand stock – is commonly used as a performance measure in service level agreements between customers and suppliers. Under such agreements, the fill rate is measured over a finite horizon (the performance review period) and the supplier faces a financial penalty if an agreed target is not met. The distribution of the item fill rate (fill rate) determines the probability of exceeding the agreed target, it is therefore a point of interest in SLA coordination. The average finite horizon fill rate decreases with an increase in performance review period length. However, the impact of performance review period length on the shape of the fill rate distribution is not well understood. Past studies of finite horizon fill rate only consider a single customer in the supply chain. In this study, we analyze fill rate distributions for a supplier that has multiple customers each with their own service level agreement. We examine the effects of performance review period length, choice of demand fulfillment (service) policy and correlation between customers’ demands on both the average fill rate and the probability of achieving the target fill rate. This study provides new insights into service level agreement coordination between suppliers and customers. For instance, the results show that a supplier with multiple customers must take care with choosing a service policy, as rationing will affect the fill rate distribution and hence the realized service level.
This research reports on the application of transfer function in performance assessment of power distribution facilities of utility companies: Shell and PHCN. It involves taking input-output data from transformers over a 1-year period and developing transfer functions of the bimonthly transformation processes for the period. The results indicate that the distribution facility of Shell had higher coefficients of performance (COP) than PHCN facilities. The average efficiencies of Shell's distribution facility were well within 90-98 percent recommended by the IEC while that of PHCN's facility were below. Generally, there were correlation between coefficient of performance and efficiency, but in some cases a high efficiency corresponded to low COP, a paradox confirming the superiority of COP as a metric for performance assessment.
Sometimes is not possible to dispose enough area to store raw materials and finished products on a shared area. In order to reduce costs in this restricted area, it must apply phase shifting between start production and raw material arrival but not any quantity of phase shifting if system stability is required. Considering inventory-production system as a closed loop system controlled by phase, this paper demonstrate that phase shifting allowed is obtained through applying the phase locked loop (PLL) of telecommunication theory as an alternative to analytical (maximum-minimum) with restrictions method.
A time series is a set of observations that are generated sequentially in time. This article considers discrete-time series, where observations are made at some fixed interval h. A time series can also be considered as a possible realization of a stochastic process, which is a statistical phenomenon that evolves in time according to probabilistic laws. This article presents a set of three interactive software tools for time series analysis education (ITTSAE) written in Sysquake [17], a language similar to that used in Matlab, and that generates tools with interactive graphics that have simple interfaces. The interactive tool set ITTSAE is distributed free of charge [18] in the form of executable files for different platforms. As such, they are readily available to any user (student or instructor) who may want to use them.
Focus on the complex logistic structure of modern hybrid process work shop, the optimization inventory model is set up with the objective is not only to meet the content limit, but also to minimize the warehousing costs and ensure the supply-demand balance of each machine unit. On this basis, the application software system for inventory prediction and simulation is developed and the effectiveness of the system is illustrated at last.
The development of control-oriented decision policies for inventory management in supply chains has received considerable interest in recent years, and demand modeling to supply forecasts for these policies is an important component of an effective solution to this problem. Drawing from the problem of control-relevant parameter estimation, this paper presents an approach for demand modeling in a production-inventory system that relies on a control-relevant weight to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecast signals tactical inventory management policies based on internal model control. The formulation is multi-objective in nature, allowing the user to emphasize inventory variation, starts change variation, or a weighted combination. By integrating the demand modeling and inventory control problems, it is possible to obtain reduced-order demand models that exhibit superior performance. A systematic approach for generating these weights is presented and the benefits resulting from their use demonstrated on a representative production-inventory system case study.
Demand amplification, now frequently referred to as “bullwhip”, is potentially a very costly phenomenon. It can lead to stock-outs, large and expensive capacity utilisation swings, lower quality products, and considerable production/transport on-costs as deliveries are ramped up and down at the whim of the supply chain. However, the detection of bullwhip depends on which “lens” is used. This in turn depends on the background and requirements of various “players” within the value stream. To gain insight into this scenario we exploit a relatively simple replenishment model. Because new and novel analytic solutions have been derived for all important performance metrics, comparison of the competing bullwhip measures is thereby greatly streamlined. In the complex real world the likelihood is that supply chains will generate even greater inconsistency between alternative variance, shock, and filter lens viewpoints.
This paper introduces and elucidates the concept of model-based predictive control (MBPC) used as a decision-making tool for handling complex integrated production planning problems within a stochastic environment. First, a functional overview of the MBPC methodology is provided, then the framework under which the MBPC approach is used as a decision-making tool is given. Simulation experiments have strongly indicated the flexibility and effectiveness of the proposed approach. (C) 1997 Elsevier Science B.V.
An important contributory factor to the bullwhip effect (i.e. the variance amplification of order quantities observed in supply chains) is the replenishment rule used by supply chain members. First the bullwhip effect induced by the use of different forecasting methods in order-up-to replenishment policies is analysed. Variance amplification is quantified and we prove that the bullwhip effect is guaranteed in the order-up-to model irrespective of the forecasting method used. Thus, when production is inflexible and significant costs are incurred by frequently switching production quantities up and down, order-up-to policies may no longer be desirable or even achievable. In the second part of the paper a general decision rule is introduced that avoids variance amplification and succeeds in generating smooth ordering patterns, even when demand has to be forecasted. The methodology is based on control systems engineering and allows important insights to be gained about the dynamic behaviour of replenishment rules.
The well-known “Bullwhip Effect” concerns the increasing variance of orders as they proceed through the supply chain. In the continuous time representation we solve the delay-differential equation for the inventory balance, which is coupled to the ordering policy. The time domain evolution of the system emerges. We calculate the Bullwhip Effect and compare it to known results for the discrete time representation. The discrete and continuous Bullwhip Effect expressions have similar structures. We show that the two domains are managerially equivalent so that in practice either domain can be used to study a supply chain.
The present paper analyses the bullwhip problem generated by exponential smoothing algorithms in both 'stand alone' passing-on-orders mode, and within inventory controlled feedback systems. Results are predicted from transfer function analysis, and then confirmed by simulation via the Explorer supply chain software. A novel feature of the paper is the introduction of the 'matched filter' concept into the exponential smoothing algorithm. This adjusts the value of the smoothing constant depending on whether the Constant, Linear, or Quadratic forecasting model is used. It is shown that matching the filter via noise bandwidth equalises the output variance when the demand is a random signal. Hence some of the unwanted effects of using the Linear and Quadratic forecasting models are attenuated. We show that 'matching the filter' is a very valuable concept for controlling bullwhip both in stand alone mode as in inventory controlled feedback systems. However, there is little benefit obtained by using sophisticated forecasting methods within the inventory controlled feedback systems as their tracking ability is not substantially improved.
Supply chain management (SCM) in semiconductor manufacturing poses significant challenges that arise from the presence of long throughput times, unique constraints, and stochasticity in throughput time, yield, and customer demand. To address these concerns, a model predictive control (MPC) algorithm is developed which relies on a control-oriented formulation to generate daily decisions on starts of factories. A multiple-degree-of-freedom observer formulated for ease of tuning is implemented to achieve robustness and performance in the presence of nonlinearity and stochasticity in both supply and demand. The control algorithm is configured to meet the requirements of meeting customer demand (both forecasted and unforecasted), and track inventory and starts targets provided by higher level decision policies. Unique features of semiconductor manufacturing, such as capacity limits, packaging, and product reconfiguration, are formally addressed by imposing different constraints related to starts and inventories. This functionality contrasts that of standard approaches to MPC and makes this controller suitable as a tactical decision tool for semiconductor manufacturing and similar forms of high-volume discrete-parts manufacturing problems. Two representative case studies are examined under diverse realistic conditions with this flexible formulation of MPC. It is demonstrated that system robustness, performance, and high levels of customer service are achieved with proper tuning of the filter gains and weights, as well as the presence of adequate capacity in the supply chain.
The development of control-oriented decision policies for inventory management in supply chains has received considerable interest in recent years, and demand modeling to supply forecasts for these policies is an important component of an effective solution to this problem. Drawing from the problem of control-relevant identification, we present an approach for demand modeling based on data that relies on a control-relevant prefilter to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecast signals to a tactical inventory management policy based on Model Predictive Control. Integrating the demand modeling and inventory control problems offers the opportunity to obtain reduced-order models that exhibit superior performance, with potentially lower user effort relative to traditional "open-loop" methods. A systematic approach to generating these prefilters is presented and the benefits resulting from their use are demonstrated on a representative production/inventory system case study.
For a single product, single-stage capacitated production-inventory model with stochastic, periodic (cyclic) demand, we find the optimal policy and characterize some of its properties. We study the finite-horizon, the discounted infinite-horizon and the infinite-horizon average cases. A simulation based optimization method is provided to compute the optimal parameters. Based on a numerical study, several insights into the model are also provided.
Solutions for Chapter 1.- Solutions for Chapter 2.- Solutions for Chapter 3.- Solutions for Chapter 4.- Solutions for Chapter 5.- Solutions for Chapter 6.- Solutions for Chapter 7.- Solutions for Chapter 8.- Solutions for Chapter 9.- Solutions for Chapter 10.- Solutions for Chapter 11.- Solutions for Chapter 12.
Optimal inventory policy is first derived for a simple model in which the future (and constant) demand flow and other relevant quantities are known in advance. This is followed by the study of uncertainty models — a static and a dynamic one — in which the demand flow is a random variable with a known probability distribution. The best maximum stock and the best reordering point are determined as functions of the demand distribution, the cost of making an order, and the penalty of stock depletion.
Mathematical models based on average or steady-state conditions are insufficient when dealing with dynamic situations faced by production–inventory systems in current business environments. Therefore, the use of mathematical tools based on control theory to handle time-varying phenomena has been reinvigorated in order to accommodate these new needs. Given the variety of research approaches in the field over several decades, there is a need to provide a review of this work. This review identifies some major research efforts for applying control theoretic methods to production–inventory systems. It is shown that in general, control theory is applied to reduce inventory variation, reduce demand amplification and optimize ordering rules. Some control theory tools applied are block diagram algebra, Mason's gain formula, Bode plots, Laplace transform, Z transform and optimal control. Basic approaches are classified within stochastic control theory and deterministic control theory. Two important issues are then identified within the deterministic models. First, separate efforts to integrate systems horizontally (i.e. supply chain) or vertically (i.e. hierarchical approach) are identified. Second, none of the reviewed models implemented a systematic way to calculate all the required model parameters. Some authors presented suggestions to optimize some parameters, but no reference was found that tried to obtain these parameter values from a real system.
The paper deals with the modelling and control of aggregated production-inventory systems as described by differential equations. Hitherto, research in the area has been characterized by the approximation of production delays by first-order lags rather than more realistic pure delays. We demonstrate the substantial qualitative differences between these two approaches and thus generate the motivation for the rest of the paper, which tackles pure delay systems. The application of some relatively new design methodologies for delay systems yields four design choices that are tested for their performance over a range of criteria including stability robustness. The investigation is then extended to the model of a supply chain comprising many such productioninventory systems. The mechanism by which disturbances can be transmitted along the supply chain causing disruption and incurring costs to other supply chain echelons is elucidated. A heuristic feedback policy designed adaptively to tune the individual system designs in response to such disturbances is presented.
In this paper, a new systematic approach to the design of feedforward-feedback (FF-FB) control systems is proposed, applicable in cases where bounds on plant and disturbance uncertainties are known. The robust performance of this control scheme is compared with that of two alternative feedback designs, on the basis of a test case in which the superiority of pure feedforward control is guaranteed for perfect models. On the basis of the results, the limits to the advantages of a combined feedforward-feedback controller over the optimal feedback compensator are determined as a function of plant and disturbance uncertainties. Design guidelines are laid for both FB and FB-FF designs where the significant disturbance can be measured and where model and disturbance uncertainties can be quantified.
For a large number of single input-single output (SISO) models typically used in the process industries, the Internal Model Control (IMC) design procedure is shown to lead to PID controllers, occasionally augmented with a first-order lag. These PID controllers have as their only tuning parameter the closed-loop time constant or, equivalently, the closed-loop bandwidth. On-line adjustments are therefore much simpler than for general PID controllers. As a special case, PI- and PID-tuning rules for systems modeled by a first-order lag with dead time are derived analytically. The superiority of these rules in terms of both closed-loop performance and robustness is demonstrated.
The development of control-oriented decision policies for inventory management in supply chains has received considerable interest in recent years, and demand modeling to supply forecasts for these policies is an important component of an effective solution to this problem. Drawing from the problem of control-relevant identification, we present an approach for demand modeling based on data that relies on a control-relevant prefilter to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecast signals to a tactical inventory management policy based on Model Predictive Control. Integrating the demand modeling and inventory control problems offers the opportunity to obtain reduced-order models that exhibit superior performance, with potentially lower user effort relative to traditional "open-loop" methods. A systematic approach to generating these prefilters is presented and the benefits resulting from their use are demonstrated on a representative production/inventory system case study.
Effective management of inventories in large-scale production and distribution systems requires methods for bringing model solutions closer to the complexities of real systems. Motivated by this need, we develop simulation-based methods for estimating sensitivities of inventory costs with respect to policy parameters. These sensitivity estimates are useful in adjusting optimal parameters predicted by a simplified model to complexities that can be incorporated in a simulation.
We consider capacitated, multiechelon systems operating under base-stock policies and develop estimators of derivatives with respect to base-stock levels. We show that these estimates converge to the correct value for finite-horizon and infinite-horizon discounted and average cost criteria. Our methods are easy to implement and experiments suggest that they converge quickly. We illustrate their use by optimizing base-stock levels for a subsystem of the PC assembly and distribution system of a major computer manufacturer.
A quadratic model for production-inventory planning was made famous by Holt, Modigliani, Muth, and Simon in 1960 in (Holt, C. C., F. Modigliani, J. F. Muth, H. A. Simon. 1960. Planning Production, Inventories, and Work Force. Prentice-Hall, Englewood Cliffs, New Jersey.), especially for its application to a paint factory. A discrete control version of a related quadratic production-inventory model was studied by Kleindorfer, Kriebel, Thompson, and Kleindorfer in (Kleindorfer, P. R., C. H. Kriebel, G. L. Thompson, G. B. Kleindorfer. 1975. Discrete optimal control of production plans. Management Sci. 22 261–273.).
In the present paper we solve a continuous version of the model in Kleindorfer, Kriebel, Thompson, and Kleindorfer (Kleindorfer, P. R., C. H. Kriebel, G. L. Thompson, G. B. Kleindorfer. 1975. Discrete optimal control of production plans. Management Sci. 22 261–273.) in complete detail. The reason we are able to obtain a complete solution (which can rarely be done in control models) is that the linear decision rule, which is optimal here as in other quadratic models, permits the elimination of the adjoint function from the state variable equation after one differentiation of the latter. Thus the difficult two-point boundary value problem which usually arises in control problems is converted into an ordinary second order differential equation, which is readily solved.
One advantage of having a complete solution to the problem is that it is possible to determine turnpike horizon points. These correspond to zeros of the adjoint function, and have the property that if they are known exactly, then a production-inventory plan which is optimal up to the next horizon point also forms part of the overall optimal plan. In the case of cyclic demand these turnpike horizon points usually occur every half cycle. Similar horizons are likely to exist in real production-inventory problems. A planning procedure for a real problem which extends only as far as a suspected horizon has a good chance of producing an optimal or near optimal solution for that period of time.
A second advantage of having the complete solution available is that it is possible to develop a practical production-inventory system which intermingles a prediction procedure (such as the use of a finite Fourier series) with the solution procedure so that a comparison between predicted and actual inventories can be made continuously. Whenever the discrepancy between these two becomes sufficiently large, the model suggests proper corrective actions to be taken.
Forecasting highly uncertain demand signals is an important component for successfully managing inventory in semiconductor supply chains. We present a control-relevant approach to the problem that tailors a forecasting model to its end-use purpose, which is to provide forecast signals for a tactical inventory management policy based on model predictive control (MPC). The success of the method hinges on a control-relevant prefiltering operation applied to demand estimation data that emphasizes a goodness-of-fit in regions of time and frequency most important for achieving desired levels of closed-loop performance. A multiobjective formulation is presented that allows the supply-chain planner to generate demand forecasts that minimize inventory deviation, starts change variance, or their weighted combination when incorporated in an MPC decision policy. The benefits obtained from this procedure are demonstrated on a case study drawn from the final stage of a semiconductor manufacturing supply chain.
Supply chains are complicated dynamical systems triggered by customer demands. Proper selection of equipment, machinery, buildings and transportation fleets is a key component for the success of such systems. However, efficiency of supply chains mostly depends on management decisions, which are often based on intuition and experience. Due to the increasing complexity of supply chain systems (which is the result of changes in customer preferences, the globalization of the economy and the stringy competition among companies), these decisions are often far from optimum. Another factor that causes difficulties in decision making is that different stages in supply chains are often supervised by different groups of people with different managing philosophies. From the early 1950s it became evident that a rigorous framework for analyzing the dynamics of supply chains and taking proper decisions could improve substantially the performance of the systems. Due to the resemblance of supply chains to engineering dynamical systems, control theory has provided a solid background for building such a framework. During the last half century many mathematical tools emerging from the control literature have been applied to the supply chain management problem. These tools vary from classical transfer function analysis to highly sophisticated control methodologies, such as model predictive control (MPC) and neuro-dynamic programming. The aim of this paper is to provide a review of this effort. The reader will find representative references of many alternative control philosophies and identify the advantages, weaknesses and complexities of each one. The bottom line of this review is that a joint co-operation between control experts and supply chain managers has the potential to introduce more realism to the dynamical models and develop improved supply chain management policies.
This paper examines the application of model predictive control (MPC), an advanced control technique originating from the process industries, to supply chain management (SCM) problems arising in semiconductor manufacturing. The main goal of this work is to demonstrate the usefulness of MPC as a tactical decision policy that is an integral part of a comprehensive hierarchical decision framework aimed at achieving operational excellence. A fluid analogy is used to describe the dynamics of the supply chain. Compared to traditional flow control problems, challenges of SCM in semiconductor manufacturing result from high stochasticity and nonlinearity in throughput times, yields and customer demands. The advantages of the control-oriented receding horizon formulation behind MPC are presented for three benchmark problems which highlight distinguishing features of semiconductor manufacturing. The effects of tuning, model parameters, and capacity are shown by comparing system robustness and multiple performance metrics in each case study.
In this article we model standard inventory ordering rules in terms of control systems theory. A differential equation is designed describing the development of a system in which an input signal reaching a predefined level triggers an output. The reorder point of inventory control systems may be interpreted as such a level triggering a replenishment. Systems using this kind of control are frequent in a variety of applications. Apart from inventory, domestic heat and pressure control are but two examples.
In this paper, an adaptive model predictive control (MPC) configuration is proposed for the identification and control of production–inventory systems. The time-varying dynamic behavior of the production process is approximated by an adaptive Finite Impulse Response (FIR) model. The well-known recursive least-squares (RLS) method is used for the online identification of the model coefficients. The adapted model along with a smoothed estimation of the future customer demand are used to predict inventory levels over the optimization horizon. The efficiency of the proposed scheme is evaluated regarding its capability to eliminate the inventory drift. The performance of the method with respect to the bullwhip effect is also considered and studied in the paper. Comparison with non-adaptive control approaches illustrates the advantages of the proposed method.
We refer to Model Predictive Control (MPC) as that family of controllers in which there is a direct use of an explicit and separately identifiable model. Control design methods based on the MPC concept have found wide acceptance in industrial applications and have been studied by academia. The reason for such popularity is the ability of MPC designs to yield high performance control systems capable of operating without expert intervention for long periods of time. In this paper the issues of importance that any control system should address are stated. MPC techniques are then reviewed in the light of these issues in order to point out their advantages in design and implementation. A number of design techniques emanating from MPC, namely Dynamic Matrix Control, Model Algorithmic Control, Inferential Control and Internal Model Control, are put in perspective with respect to each other and the relation to more traditional methods like Linear Quadratic Control is examined. The flexible constraint handling capabilities of MPC are shown to be a significant advantage in the context of the overall operating objectives of the process industries and the 1-, 2-, and ∞-norm formulations of the performance objective are discussed. The application of MPC to non-linear systems is examined and it is shown that its main attractions carry over. Finally, it is explained that though MPC is not inherently more or less robust than classical feedback, it can be adjusted more easily for robustness.
This paper describes a model predictive control strategy to find the optimal decision variables to maximize profit in supply chains with multiproduct, multiechelon distribution networks with multiproduct batch plants. The key features of this paper are: (1) a discrete time MILP dynamic model that considers the flow of material and information within the system; (2) a general dynamic optimization framework that simultaneously considers all the elements of the supply chain and their interactions; and (3), a rolling horizon approach to update the decision variables whenever changes affecting the supply chain arise. The paper compares the behavior of a supply chain under centralized and decentralized management approaches, and shows that the former yields better results, with profit increases of up to 15% as shown in an example problem.
Model Predictive Control (MPC) is presented as a robust, flexible decision framework for dynamically managing inventories and meeting customer requirements in demand networks (a.k.a. supply chains). As a control-oriented framework, an MPC-based planning scheme has the advantage that it can be tuned to provide acceptable performance in the presence of significant uncertainty, forecast error, and constraints on inventory levels, production and shipping capacity. The translation of the supply chain problem into a formulation amenable to MPC implementation is initially developed for a single-product, two-node example. Insights gained from this problem are used to develop a partially decentralized MPC implementation for a six-node, two-product, three-echelon demand network problem developed by Intel Corporation that consists of interconnected assembly/test, warehouse, and retailer entities. Results demonstrating the effectiveness of this Model Predictive Control solution under conditions of demand forecast error, constraints on capacity, shipping and release, and discrepancies between actual and reported production throughput times (i.e. plant-model mismatch) are presented. The Intel demand network problem is furthermore used to evaluate the relative merits of various information sharing strategies between controllers in the network. Both the two-node and Intel problems show the potential of Model Predictive Control as an integral component of a hierarchical, enterprise-wide planning tool that functions on a real-time basis, supports varying levels of information sharing and centralization/decentralization, and relies on combined feedback–feedforward control action to enhance the performance and robustness of demand networks. These capabilities ultimately mitigate the “bullwhip effect” in the supply chain while reducing safety stocks to profitable levels and improving customer satisfaction.
A simulation-based optimization framework involving simultaneous perturbation stochastic approximation (SPSA) is presented as a means for optimally specifying parameters of internal model control (IMC) and model predictive control (MPC)-based decision policies for inventory management in supply chains under conditions involving supply and demand uncertainty. The effective use of the SPSA technique serves to enhance the performance and functionality of this class of decision algorithms and is illustrated with case studies involving the simultaneous optimization of controller tuning parameters and safety stock levels for supply chain networks inspired from semiconductor manufacturing. The results of the case studies demonstrate that safety stock levels can be significantly reduced and financial benefits achieved while maintaining satisfactory operating performance in the supply chain.
A two-layered optimisation-based control approach for multi-product, multi-echelon supply chain networks with independent production lines is presented. The control strategy applies multivariable model-predictive control principles to the entire network. The optimisation-based control scheme aims at adjusting the decision variables in the supply chain (e.g. transportation loads, product inventory) to satisfy the customer orders with the least operating cost over a specified rolling time horizon using a detailed difference model of the system. A move suppression term that penalises the rate of change in the transported quantities through the network increases the robustness of the control system. Dedicated feedback controllers are utilised to maintain product inventory at all nodes of the supply chain network within pre-specified target levels that are subsequently embedded within the optimisation-based control framework. Simulated results exhibit good dynamic performance under both stochastic and deterministic demand variations. The effects of transportation time delays, size of control horizons and demand forecast models on the control performance are investigated.
This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.
Thesis (Ph. D.)--Arizona State University, 2006. Includes bibliographical references (leaves [152]-156).
For a single product, single-stage capacitated production-inventory model with stochastic, periodic (cyclic) demand, we find the optimal policy and characterize some of its properties. We study the finite-horizon, the discounted infinite-horizon and the infinite-horizon average cases. A simulation based optimization method is provided to compute the optimal parameters. Based on a numerical study, several insights into the model are also provided.
After describing the general supply chain management problem with examples from the semiconductor industry, attention is restricted to the core manufacturing problem. Using a control-oriented approach for this nonlinear stochastic combinatorial optimization problem, an outer loop for addressing the planning parts of the problem and an inner loop to manage the execution aspects are proposed. The outer loop provides a material release plan generated by a linear programming formulation (LP) and inventory safety stock targets generated by a dynamic programming formulation (DP) to the inner loop to guide execution. Portions of the nonlinearity and stochasticity inherent in the problem are addressed by the outer loop that requires iterative convergence between the LP and the DP. The inner loop is formulated from the perspective of model predictive control (MPC) and integrates optimal control and stochastic control. Initial results are presented to demonstrate the ability of the inner loop to track material release and safety stock targets while improving delivery performance in the face of both supply and demand stochasticity. A simulation module is also described that supports the other components of the system by validating their efficacy before application in the real world. This component has to address the integrated flows of materials, information, and decisions through the supply chain, and employs innovative approaches combining a number of specialized models to do so quickly and accurately.
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Dynamic version of the economic lot size model
- Wagner