An economic order quantity model with partial backlogging under general backorder cost function

In this work, we study a single-item inventory model where shortages are allowed. A known constant fraction of the demand during the stockout period is backlogged, and the rest are lost sales. Usually, in the literature on inventory control, the unit backorder cost is considered to be a linear function of the waiting time until the customer gets the item. However, in some real-world situations, the unit cost of a backorder may not be linear. To model this situation, we develop a new approach by considering that the backlogging unit cost is a nondecreasing, continuous, and positive function of the amount of time the customers wait before receiving the item. Our objective is to maximize the average profit per unit time. An effective solution procedure to determine the optimal policy and the maximum average profit is developed. Numerical examples, which help us to understand the theoretical results, are also presented.

[1]  David W. Pentico,et al.  The deterministic EOQ with partial backordering: A new approach , 2009, Eur. J. Oper. Res..

[2]  Kaj Rosling,et al.  Inventory Cost Rate Functions with Nonlinear Shortage Costs , 2002, Oper. Res..

[3]  Prakash L. Abad,et al.  Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale , 2000 .

[4]  Suresh Kumar Goyal,et al.  Some notes on the optimal production stopping and restarting times for an EOQ model with deteriorating items , 2001, J. Oper. Res. Soc..

[5]  John R. Grabner,et al.  Marketing Notes and Communications: Stockout Cost Models: Empirical Tests in a Retail Situation , 1975 .

[6]  S. Çetinkaya,et al.  Nonlinear Programming Analysis to Estimate Implicit Inventory Backorder Costs , 1998 .

[7]  Kit-Nam Francis Leung,et al.  Technical note: A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of backorders and lost sales , 2008 .

[8]  Fangruo Chen,et al.  Inventory models with general backorder costs , 1993 .

[9]  L. Zurich,et al.  Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[10]  Peter Chu,et al.  The sensitivity of the inventory model with partial backorders , 2004, Eur. J. Oper. Res..

[11]  Gino K. Yang.  Note on sensitivity analysis of inventory model with partial backorders , 2007, Eur. J. Oper. Res..

[12]  Juan García Laguna,et al.  A new perspective on the partial backlogging EOQ model , 2003 .

[13]  Arnoldo C. Hax,et al.  Production and inventory management , 1983 .

[14]  Ford W. Harris,et al.  How Many Parts to Make at Once , 1990, Oper. Res..

[15]  Benjamin L. Schwartz,et al.  A New Approach to Stockout Penalties , 1966 .

[16]  Arnold Reisman,et al.  On the Evaluation of Shortage Costs for Inventory Control of Finished Goods , 1972 .

[17]  B. L. Schwartz.  Optimal Inventory Policies in Perturbed Demand Models , 1970 .

[18]  T.C.E. Cheng,et al.  Optimal production stopping and restarting times for an EOQ model with deteriorating items , 1998, J. Oper. Res. Soc..

[19]  H. Wee,et al.  An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation , 2007 .

[20]  Reza Tavakkoli-Moghaddam,et al.  An economic production lot size model with deteriorating items, stock-dependent demand, inflation, and partial backlogging , 2006, Appl. Math. Comput..

[21]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[22]  Patrick S. Chen,et al.  A note on inventory replenishment policies for deteriorating items in an exponentially declining market , 2002, Comput. Oper. Res..

[23]  Kyung S. Park,et al.  Inventory model with partial backorders , 1982 .

[24]  S. K. Goyal,et al.  The production-inventory problem of a product with time varying demand, production and deterioration rates , 2003, Eur. J. Oper. Res..

[25]  D. Montgomery,et al.  INVENTORY MODELS WITH A MIXTURE OF BACKORDERS AND LOST SALES. , 1973 .

[26]  K. S. Chaudhuri,et al.  An economic production lot size model with increasing demand, shortages and partial backlogging , 2005, Int. Trans. Oper. Res..

[27]  H. Wee.  Deteriorating inventory model with quantity discount, pricing and partial backordering , 1999 .

[28]  Avijit Banerjee,et al.  An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time , 2009, Eur. J. Oper. Res..

[29]  John R. Grabner,et al.  Stockout Cost Models: Empirical Tests in a Retail Situation , 1975 .

[30]  Z T Balkhi.  On the optimal production stopping and restarting times for an EOQ model with deteriorating items , 2000, J. Oper. Res. Soc..

[31]  David Rosenberg,et al.  A new analysis of a lot‐size model with partial backlogging , 1979 .

[32]  Luis A. San-José,et al.  A general model for EOQ inventory systems with partial backlogging and linear shortage costs , 2009, Int. J. Syst. Sci..