A net present value approach in developing optimal replenishment policies for a product life cycle

Abstract In this paper, a net present value approach is developed for a decision maker to determine the optimal number of inventory replenishments and the corresponding optimal inventory replenishment time points in the finite planning horizon. Also, the demand function considered in this paper follows the product-life-cycle shape to characterize more practical and realistic situation. The objective function of the net present value for the total relevant costs considered in our model is mathematically formulated as a mixed-integer nonlinear programming problem. A complete search procedure is provided to find the optimal solution by employing the properties derived in this paper and the Nelder–Mead algorithm. Moreover, several numerical examples and the corresponding sensitivity analyses are carried out to illustrate the features of our model by utilizing the search procedure developed in this paper.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  Kun-Jen Chung,et al.  Optimal inventory replenishment models for deteriorating items taking account of time discounting , 2000, Comput. Oper. Res..

[3]  Graham K. Rand,et al.  An eclectic algorithm for inventory replenishment for items with increasing linear trend in demand , 1990 .

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

[5]  Edward A. Silver,et al.  A Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand , 1979 .

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

[7]  Sheng-Pen Wang,et al.  On inventory replenishment with non-linear increasing demand , 2002, Comput. Oper. Res..

[8]  Suresh Kumar Goyal,et al.  A simple rule for determining replenishment intervals of an inventory item with linear decreasing demand rate , 2003 .

[9]  J. Buzacott.  Economic Order Quantities with Inflation , 1975 .

[10]  R. J. Henery,et al.  Inventory Replenishment Policy for Increasing Demand , 1979 .

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

[12]  Suresh Kumar Goyal,et al.  Determining economic replenishment intervals for linear trend in demand , 1994 .

[13]  Jinn-Tsair Teng,et al.  A deterministic inventory replenishment model with a linear trend in demand , 1996, Oper. Res. Lett..

[14]  Brian G. Kingsman,et al.  Ordering and Inventory Policies for Step Changes in the Unit Item Cost: A Discounted Cash Flow Approach , 2004, Manag. Sci..

[15]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[16]  Roger M. Hill,et al.  Batching policies for a product life cycle , 1996 .

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

[18]  Maurice Queyranne,et al.  Production and Inventory Model Using Net Present Value , 2002, Oper. Res..

[19]  Graham K. Rand,et al.  Heuristics for replenishment with linear decreasing demand , 2001 .

[20]  Graham K. Rand,et al.  Comparison of several heuristics using an analytic procedure for replenishment with non-linear increasing demand , 1999 .

[21]  M. Chandra,et al.  The effects of inflation and the time value of money on some inventory systems , 1985 .

[22]  Bibhas Chandra Giri,et al.  Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting , 2005, Eur. J. Oper. Res..

[23]  Louis Brosseau.  An Inventory Replenishment Policy for The Case of a Linear Decreasing Trend in Demand , 1982 .

[24]  Jinn-Tsair Teng,et al.  A forward recursive algorithm for inventory lot-size models with power-form demand and shortages , 2002, Eur. J. Oper. Res..

[25]  Chih-Hung Tsai,et al.  Exact solution of inventory replenishment policy for a linear trend in demand - two-equation model , 2002 .

[26]  Moncer Hariga.  Comparison of heuristic procedures for the inventory replenishment problem with a linear trend in demand , 1995 .

[27]  Leroy B. Schwarz.  Economic Order Quantities for Products with Finite Demand Horizons , 1972 .