A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand

Askin, Ronald G.

doi:10.1080/05695558108974545

Cited by 54 publications

(54 citation statements)

References 4 publications

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“…Early works in this area adopted heuristic strategies such as those proposed by Silver [16], Askin [2] and Bookbinder and Tan [4]. Under some mild assumptions the first complete solution method for this problem was introduced by Tarim and Kingsman [20], who proposed a deterministic equivalent Mixed Integer Programming (MIP) formulation for computing (R n , S n ) policy parameters.…”

Section: Introductionmentioning

confidence: 99%

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

et al. 2008

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This paper1 considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all.

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Section: Introductionmentioning

confidence: 99%

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

et al. 2008

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“…The shortest path in this reduced network has a cost of 403. The order periods and the order quantities are respectively [1,2,3,4] and [149, 138, −25, 83]. This assignment is infeasible for the non-relaxed problem since the expected order quantity in period 3 is −25, therefore its cost is a lower bound for the optimal solution cost of our original problem.…”

Section: An Examplementioning

confidence: 99%

“…As Silver points out, computing replenishment cycle policy parameters under non-stationary stochastic demand is a computationally hard task [17]. Early works in this area adopted heuristic strategies such as those proposed by Silver [17], Askin [1] and Bookbinder & Tan [5]. Under some mild assumptions, the first complete solution method for this problem was introduced by Tarim & Kingsman [22], who proposed a deterministic equivalent Mixed Integer Programming (MIP) formulation for computing (R n , S n ) policy parameters.…”

Section: Introductionmentioning

confidence: 99%

A state space augmentation algorithm for the replenishment cycle inventory policy

Rossi

Tarim

Hnich

et al. 2011

International Journal of Production Economics

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In this work we propose an efficient Dynamic Programming approach for computing Replenishment Cycle policy parameters under non-stationary stochastic demand and service level constraints. The Replenishment Cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of State Space Relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using Dynamic Programming in order to produce a solution for the original problem.

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“…Early works in stochastic inventory control area adopted heuristic strategies such as those proposed by Silver [25], Askin [2] and Bookbinder and Tan [7]. The first complete (MIP) solution method, which operates under mild assumptions, was introduced for this problem by Tarim and Kingsman [29].…”

Section: Existing Approachesmentioning

confidence: 99%

“…Our objective is to minimize the expected total cost under a service level constraint, that is the probability that at the end of every time period the net inventory will not be negative. Early works in the area were heuristic (Silver [25] and Askin [2]). Bookbinder and Tan [7] proposed another heuristic, under the staticdynamic uncertainty strategy.…”

Section: Introductionmentioning

confidence: 99%

A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints

et al. 2008

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We consider a class of production/inventory control problems that has a single product and a single stocking location, for which a stochastic demand with a known non-stationary probability distribution is given. Under the widely-known replenishment cycle policy the problem of computing policy parameters under service level constraints has been modeled using various techniques. Tarim and Kingsman introduced a modeling strategy that constitutes the state-of-the-art approach for solving this problem. In this paper we identify two sources of approximation in Tarim and Kingsman's model and we propose an exact stochastic constraint programming approach. We build our approach on a novel concept, global chance-constraints, which we introduce in this paper. Solutions provided by our exact approach are employed to analyze the accuracy of the model developed by Tarim and Kingsman.

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A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand

Cited by 54 publications

References 4 publications

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

A state space augmentation algorithm for the replenishment cycle inventory policy

A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints

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