A net present value approach in developing optimal replenishment policies for a product life cycle. (English) Zbl 1162.90305

Chen, Cheng-Kang; Hung, Ta-Wei; Weng, Tzu-Chun

Appl. Math. Comput. 184, No. 2, 360-373 (2007).

Summary: 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.

MSC:

90B05	Inventory, storage, reservoirs
90C90	Applications of mathematical programming

Keywords:

net present value; inventory replenishment; product life cycle; Nelder-Mead algorithm

Software:

fminsearch

References:

[1]	Schwarz, L.B., Economic order quantities for products with finite demand horizons, AIIE transactions, 4, 234-237, (1972)
[2]	Donaldson, W.A., Inventory replenishment policy for a linear trend in demand – an analytical solution, Operational research quarterly, 28, 663-670, (1977) · Zbl 0372.90052
[3]	Silver, E.A., A simple inventory replenishment decision rule for a linear trend in demand, Journal of the operational research, 30, 71-75, (1979) · Zbl 0397.90035
[4]	Henery, R.J., Inventory replenishment policy for increasing demand, Journal of the operational research society, 30, 611-617, (1979) · Zbl 0424.90019
[5]	Ritchie, E., The E.O.Q. for linear increasing demand: a simple optimal solution, Journal of the operational research, 35, 949-953, (1984) · Zbl 0546.90028
[6]	Amrani, M.; Rand, G.K., An eclectic algorithm for inventory replenishment for items with increasing linear trend in demand, Engineering costs and production economics, 19, 261-266, (1990)
[7]	Yang, J.; Rand, G.K., An analytic eclectic heuristic for replenishment with linear increasing demand, International journal of production economics, 32, 261-266, (1993)
[8]	Teng, J.T., A note on inventory replenishment policy for increasing demand, Journal of the operational research, 45, 1335-1337, (1994) · Zbl 0819.90030
[9]	Goyal, S.K., Determining economic replenishment intervals for linear trend in demand, International journal of production economics, 34, 115-117, (1994)
[10]	Teng, J.T., A deterministic inventory replenishment model with a linear trend in demand, Operations research letters, 19, 33-41, (1996) · Zbl 0865.90038
[11]	Brosseau, L.J.A., An inventory replenishment policy for the case of a linear decreasing trend in demand, Infor, 20, 252-257, (1982) · Zbl 0503.90034
[12]	Hariga, M., Comparison of heuristic procedures for the inventory replenishment problem with a linear trend in demand, Computers & industrial engineering, 28, 245-258, (1995)
[13]	Lo, W.Y.; Tsai, C.H.; Li, R.K., Exact solution of inventory replenishment policy for a linear trend in demand – two equation model, International journal of production economics, 76, 111-120, (2002)
[14]	Zhao, G.Q.; Yang, J.; Rand, G.K., Heuristics for replenishment with linear decreasing demand, International journal of production economics, 69, 339-345, (2001)
[15]	Goyal, S.K.; Giri, B.C., A simple rule for determining replenishment intervals of an inventory with linear decreasing demand rate, International journal of production economics, 83, 139-142, (2003)
[16]	Yang, J.; Zhao, G.Q.; Rand, G.K., Comparison of several heuristics using an analytical procedure for replenishment with nonlinear increasing demand, International journal of production economics, 58, 49-55, (1999)
[17]	Wang, S.P., On inventory replenishment with non-linear increasing demand, Computers & operations research, 29, 1819-1825, (2002)
[18]	Yang, H.L.; Teng, J.T.; Chern, M.S., A forward recursive algorithm for inventory lot-size models with power-form demand and shortages, European journal of operational research, 137, 394-400, (2002) · Zbl 1029.90011
[19]	Roger, M.H., Batching policies for a product life cycle, International journal of production economics, 45, 421-427, (1996)
[20]	Buzacott, J.A., Economics order quantities with inflation, Operational research quarterly, 26, 553-558, (1975)
[21]	Chandra, M.J.; Bahner, M.L., The effects of inflation and the time value of money on some inventory systems, International journal of production economics, 23, 723-730, (1985)
[22]	Chung, K.J.; Lin, C.N., Optimal inventory replenishment models for deteriorating items taking account of time discounting, Computers & operations research, 28, 67-83, (2001) · Zbl 0976.90005
[23]	Sun, D.; Queyranne, M., Production and inventory model using net present value, Operations research, 50, 528-537, (2002) · Zbl 1163.90350
[24]	Grubbstrom, R.W.; Kingsman, B.G., Ordering and inventory policies for step changes in the unit item cost: a discounted cash flow approach, Management science, 50, 253-267, (2004) · Zbl 1232.91386
[25]	Moon, I.; Giri, B.C.; Ko, B., Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European journal of operational research, 162, 773-785, (2005) · Zbl 1067.90004
[26]	Nelder, J.A.; Mead, R., A simplex method for function minimization, Computer journal, 7, 308-313, (1965) · Zbl 0229.65053
[27]	Lagarias, J.C.; Reeds, J.A.; Wright, M.H.; Wright, P.E., Convergence properties of the nelder – mead simplex method in low dimensions, SIAM journal of optimization, 9, 112-147, (1998) · Zbl 1005.90056