A mathematical model for perishable products with price- and displayed-stock-dependent demand

We consider perishable products under shelf and backroom storage capacity constraints.We propose an order quantity model with assortment, pricing and shelf space allocation decisions.We propose a metaheuristic approach that would maximize the retailer's profit.We compare the performance of our algorithm with well-known MINLP solvers. We introduce an economic order quantity model that incorporates product assortment, pricing and space-allocation decisions for a group of perishable products. The goal is to maximize the retailer's profit under shelf-space and backroom storage capacity constraints. We assume that the demand rate of a product is a function of the selling prices and the displayed stock levels of all the products in the assortment. We propose a Tabu Search based heuristic method to solve this complex problem.

[1]  Yigal Gerchak,et al.  Supply Chain Coordination when Demand Is Shelf-Space Dependent , 2000, Manuf. Serv. Oper. Manag..

[2]  Abdulrahman Al-Ahmari,et al.  A joint optimisation model for inventory replenishment, product assortment, shelf space and display area allocation decisions , 2007, Eur. J. Oper. Res..

[3]  Danny Segev,et al.  Near-Optimal Algorithms for the Assortment Planning Problem Under Dynamic Substitution and Stochastic Demand , 2015, Oper. Res..

[4]  Tzong-Ru Tsai,et al.  Inventory models with stock- and price-dependent demand for deteriorating items based on limited shelf space , 2010 .

[5]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[6]  Nikolaos V. Sahinidis,et al.  A polyhedral branch-and-cut approach to global optimization , 2005, Math. Program..

[7]  Hesham K. Alfares Maximum-Profit Inventory Model with Stock-Dependent Demand, Time-Dependent Holding Cost, and All-Units Quantity Discounts , 2015 .

[8]  Glen L. Urban,et al.  A Mathematical Modeling Approach to Product Line Decisions , 1969 .

[9]  P. Naert,et al.  SH.A.R.P.: Shelf Allocation for Retailers' Profit , 1988 .

[10]  Hardik N. Soni,et al.  Optimal ordering policy for stock-dependent demand under progressive payment scheme , 2008, Eur. J. Oper. Res..

[11]  Jinn-Tsair Teng,et al.  Economic production quantity models for deteriorating items with price- and stock-dependent demand , 2005, Comput. Oper. Res..

[12]  A. Goswami,et al.  An inventory model for deteriorating items with stock-dependent demand rate , 1996 .

[13]  Timothy L. Urban,et al.  The location and allocation of products and product families on retail shelves , 2010, Ann. Oper. Res..

[14]  Luis A. San-José,et al.  Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate , 2012, Int. J. Syst. Sci..

[15]  I. Grossmann,et al.  A combined penalty function and outer-approximation method for MINLP optimization : applications to distillation column design , 1989 .

[16]  S. K. Goyal,et al.  Recent trends in modeling of deteriorating inventory , 2001, Eur. J. Oper. Res..

[17]  Ralf W. Seifert,et al.  Joint Product Assortment, Inventory and Price Optimization to Attract Loyal and Non-loyal Customers , 2014 .

[18]  P. Larson,et al.  Psychic Stock: An Independent Variable Category of Inventory , 1990 .

[19]  Timothy L. Urban,et al.  Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns , 1997 .

[20]  Hark Hwang,et al.  A model for shelf space allocation and inventory control considering location and inventory level effects on demand , 2005 .

[21]  Martin A. Koschat Store inventory can affect demand: Empirical evidence from magazine retailing , 2008 .

[22]  Ming-Hsien Yang,et al.  A study on shelf space allocation and management , 1999 .

[23]  Yi-Chih Hsieh,et al.  An EOQ model with stock and price sensitive demand , 2007, Math. Comput. Model..

[24]  M. Corstjens,et al.  A Model for Optimizing Retail Space Allocations , 1981 .

[25]  G. Padmanabhan,et al.  An EOQ model for items with stock dependent consumption rate and exponential decay , 1990 .

[26]  L. Ouyang,et al.  An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging , 2006 .

[27]  Timothy L. Urban An Inventory Model with an Inventory-Level-Dependent Demand Rate and Relaxed Terminal Conditions , 1992 .

[28]  J. Eliashberg,et al.  Marketing-production joint decision-making , 1993 .

[29]  Guillaume Roels,et al.  Competing for Shelf Space , 2007 .

[30]  Ignacio E. Grossmann,et al.  An outer-approximation algorithm for a class of mixed-integer nonlinear programs , 1987, Math. Program..

[31]  T. Datta,et al.  An inventory system with stock-dependent, price-sensitive demand rate , 2001 .

[32]  Prashant Chintapalli,et al.  Simultaneous pricing and inventory management of deteriorating perishable products , 2015, Ann. Oper. Res..

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

[34]  Philip M. Wolfe,et al.  An inventory model for deteriorating items , 1991 .

[35]  Timothy L. Urban,et al.  A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate , 1988 .

[36]  M. Goh EOQ models with general demand and holding cost functions , 1994 .

[37]  Timothy L. Urban Production , Manufacturing and Logistics Inventory models with inventory-level-dependent demand : A comprehensive review and unifying theory , 2004 .

[38]  Yu-Chung Tsao,et al.  A piecewise linearization framework for retail shelf space management models , 2012, Eur. J. Oper. Res..

[39]  Liang-Yuh Ouyang,et al.  An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging , 2005, Eur. J. Oper. Res..

[40]  Hesham K. Alfares,et al.  Inventory model with stock-level dependent demand rate and variable holding cost , 2007 .

[41]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[42]  Hark Hwang,et al.  An optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime , 2000, Eur. J. Oper. Res..

[43]  S.-L. Yang,et al.  An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy , 2003, J. Oper. Res. Soc..

[44]  Anantaram Balakrishnan,et al.  "Stack Them High, Let 'em Fly": Lot-Sizing Policies When Inventories Stimulate Demand , 2004, Manag. Sci..

[45]  Wansheng Tang,et al.  Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand , 2015 .

[46]  Heinrich Kuhn,et al.  An efficient algorithm for capacitated assortment planning with stochastic demand and substitution , 2016, Eur. J. Oper. Res..

[47]  Timothy L. Urban An inventory-theoretic approach to product assortment and shelf-space allocation , 1998 .

[48]  Wansheng Tang,et al.  Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand , 2016, Int. J. Syst. Sci..