MILP-based model for approximating non-stationary (R, S) policies with correlated demands

This paper addresses the single-item single-stock location stochastic lotsizing problem under (R,S) policy. We assume demands in different periods are dependent. We present a mixed integer linear programming (MILP) model for computing optimal (R,S) policy parameters, which is built upon the conditional distribution. Our model can be extended to cover time-series-based demand processes as well. Our computational experiments demonstrate the effectiveness and versatility of this model.

[1]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[2]  Roberto Rossi,et al.  Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing , 2013, ArXiv.

[3]  A. F. Veinott.  Optimal Policy for a Multi-product, Dynamic Non-Stationary Inventory Problem , 1965 .

[4]  James H. Bookbinder,et al.  Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints , 1988 .

[5]  H. Scarf.  THE OPTIMALITY OF (S,S) POLICIES IN THE DYNAMIC INVENTORY PROBLEM , 1959 .

[6]  Howard E. Thompson,et al.  Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes , 1975 .

[7]  Stergios B. Fotopoulos,et al.  Safety stock determination with correlated demands and arbitrary lead times , 1988 .

[8]  G. Reyman.  State reduction in a dependent demand inventory model given by a time series , 1989 .

[9]  Ş. Tarim,et al.  The stochastic dynamic production/inventory lot-sizing problem with service-level constraints , 2004 .

[10]  Roberto Rossi,et al.  A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints , 2008, Constraints.

[11]  Ronald G. Askin.  A Procedure for Production Lot Sizing with Probabilistic Dynamic Demand , 1981 .

[12]  Jing-Sheng Song,et al.  Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand , 2001, Oper. Res..

[13]  S. Sethi,et al.  OPTIMALITY OF STATE‐DEPENDENT (s, S) POLICIES IN INVENTORY MODELS WITH MARKOV‐MODULATED DEMAND AND LOST SALES , 2009 .

[14]  Roberto Rossi,et al.  An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints , 2011, Eur. J. Oper. Res..

[15]  Brian G. Kingsman,et al.  Production, Manufacturing and Logistics Modelling and computing (R n ,S n ) policies for inventory systems with non-stationary stochastic demand , 2005 .

[16]  Stephen C. Graves,et al.  A Single-Item Inventory Model for a Nonstationary Demand Process , 1999, Manuf. Serv. Oper. Manag..

[17]  Roberto Rossi,et al.  O C ] 1 3 A ug 2 01 3 Piecewise linear approximations of the standard normal first order loss function , 2013 .

[18]  Awi Federgruen,et al.  An Efficient Algorithm for Computing Optimal (s, S) Policies , 1984, Oper. Res..

[19]  Armagan Tarim,et al.  Constraint programming for computing non-stationary (R, S) inventory policies , 2008, Eur. J. Oper. Res..

[20]  Jing-Sheng Song,et al.  Inventory Control in a Fluctuating Demand Environment , 1993, Oper. Res..