A finite horizon lot-sizing problem with time-varying deterministic demand and waiting-time-dependent partial backlogging

Abstract This paper presents a general time-varying demand inventory lot-sizing model with waiting-time-dependent backlogging and a lot-size-dependent replenishment cost. It differs from many related trended inventory replenishment models in two directions. First, our model not only allows part of the backlogged demands to turn into lost sales, but this backlog-to-lost-sales conversion rate is modeled by a general continuously decreasing function of the remaining waiting time until the next replenishment delivery. Second, this paper considers the dependence of replenishment cost on lot size. We derive the model's cost function for a “shortages followed by inventory” replenishment policy. Some convenient mathematical properties of the cost function are identified, with which an effective numerical solution procedure is developed for determining the optimal replenishment policy. Numerical examples and some sensitive-analysis results are then reported.

[1]  Asoke Kumar Bhunia,et al.  An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand , 1999 .

[2]  Upendra Dave,et al.  A deterministic lot-size inventory model with shortages and a linear trend in demand , 1989 .

[3]  Upendra Dave.  On a Heuristic Inventory-replenishment Rule for Items with a Linearly Increasing Demand Incorporating Shortages , 1989 .

[4]  K. S. Chaudhuri,et al.  A note on a lot sizing heuristic for deteriorating items with time-varying demands and shortages , 2000, Comput. Oper. Res..

[5]  Manoranjan Maiti,et al.  Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon , 2001, Comput. Oper. Res..

[6]  R. Hill.  Inventory Models for Increasing Demand Followed by Level Demand , 1995 .

[7]  Hon-Shiang Lau,et al.  An economic lot-size model for deteriorating items with lot-size dependent replenishment cost and time-varying demand , 2000 .

[8]  S. Goyal.  A simple heuristic method for determining economic order interval for linear demand , 1987 .

[9]  J. Teng.  A Note on Inventory Replenishment Policy for Increasing Demand , 1994 .

[10]  R. I. Phelps.  Optimal Inventory Rule for a Linear Trend in Demand with a Constant Replenishment Period , 1980 .

[11]  Sheng-Pen Wang,et al.  An inventory replenishment policy for deteriorating items with shortages and partial backlogging , 2002, Comput. Oper. Res..

[12]  S. Goyal,et al.  An Alternative Procedure for Determining the Optimal Policy for an Inventory Item Having Linear Trend in Demand , 1995 .

[13]  E. Ritchie,et al.  The E.O.Q. for Linear Increasing Demand: A Simple Optimal Solution , 1984 .

[14]  Hui-Ming Wee,et al.  A deterministic lot-size inventory model for deteriorating items with shortages and a declining market , 1995, Comput. Oper. Res..

[15]  G. Rand,et al.  An analytic eclectic heuristic for replenishment with linear increasing demand , 1993 .

[16]  W. A. Donaldson.  Inventory Replenishment Policy for a Linear Trend in Demand An Analytical Solution , 1977 .

[17]  Tapan Kumar Datta,et al.  A Note on a Replenishment Policy for an Inventory Model with Linear Trend in Demand and Shortages , 1992 .

[18]  M. Hariga.  Optimal EOQ Models for Deteriorating Items with Time-Varying Demand , 1996 .

[19]  S. Goyal,et al.  The Finite Horizon Trended Inventory Replenishment Problem With Shortages , 1992 .

[20]  T. M. Murdeshwar.  Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages-An Optimal Solution , 1988 .

[21]  Chung-Yuan Dye,et al.  An EOQ model for deteriorating items with time varying demand and partial backlogging , 1999, J. Oper. Res. Soc..

[22]  Suresh Kumar Goyal,et al.  The Trended Inventory Lot Sizing Problem with Shortages Under a New Replenishment Policy , 1996 .