A simple heuristic for perishable item inventory control under non-stationary stochastic demand

In this paper, we study the single-item single-stocking location non-stationary stochastic lot sizing problem for a perishable product. We consider fixed and proportional ordering cost, holding cost and penalty cost. The item features a limited shelf life, therefore we also take into account a variable cost of disposal. We derive exact analytical expressions to determine the expected value of the inventory of different ages. We also discuss a good approximation for the case in which the shelf-life is limited. To tackle this problem, we introduce two new heuristics that extend Silver’s heuristic and compare them to an optimal Stochastic Dynamic Programming policy in the context of a numerical study. Our results demonstrate the effectiveness of our approach.

[1]  Ruud H. Teunter,et al.  Review of inventory systems with deterioration since 2001 , 2012, Eur. J. Oper. Res..

[2]  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 .

[3]  Steven Nahmias,et al.  Perishable Inventory Theory: A Review , 1982, Oper. Res..

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

[5]  Eligius M. T. Hendrix,et al.  Order quantities for perishable inventory control with non-stationary demand and a fill rate constraint , 2016 .

[6]  Qing Li,et al.  Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems , 2014, Manuf. Serv. Oper. Manag..

[7]  Ş. Tarim,et al.  The cost of using stationary inventory policies when demand is non-stationary , 2011 .

[8]  E. Silver.  Inventory control under a probabilistic time-varying, demand pattern , 1978 .

[9]  Yi Yang,et al.  Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs , 2012, Oper. Res..

[10]  Stefan Minner,et al.  Periodic review inventory-control for perishable products under service-level constraints , 2010, OR Spectr..

[11]  Min Wang,et al.  Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs , 2015, Oper. Res..

[12]  Xin Chen,et al.  Coordinating Inventory Control and Pricing Strategies for Perishable Products , 2014, Oper. Res..

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

[14]  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 .

[15]  Yi Yang,et al.  Coordinating Inventory Control and Pricing Strategies Under Batch Ordering , 2014, Oper. Res..

[16]  H. Chestnut.  International Federation of Automatic Control , 2013, Nature.

[17]  Roberto Rossi,et al.  Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times , 2010 .

[18]  Srinivas Bollapragada,et al.  A Simple Heuristic for Computing Nonstationary (s, S) Policies , 1999, Oper. Res..

[19]  Eligius M. T. Hendrix,et al.  On Computing Order Quantities for Perishable Inventory Control with Non-stationary Demand , 2015, ICCSA.

[20]  Itir Z. Karaesmen,et al.  Managing Perishable and Aging Inventories: Review and Future Research Directions , 2011 .

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

[22]  Roberto Rossi,et al.  Periodic Review for a Perishable Item under Non Stationary Stochastic Demand , 2013, MIM.

[23]  Eligius M. T. Hendrix,et al.  An MILP approximation for ordering perishable products with non-stationary demand and service level constraints , 2014 .

[24]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[25]  Eligius M. T. Hendrix,et al.  On Solving a Stochastic Programming Model for Perishable Inventory Control , 2012, ICCSA.