In this paper, we assume that not only the demand function but alsothe unit purchase cost is fluctuating with time. We then prove thatthe optimal production schedule not only exists but is also unique . Inaddition, we also show that the total cost associated with theproposed inventory system is a convex function of the number ofreplenishments. Consequently, the search for the optimal number ofreplenishments is simplified to find a local minimum. We furtherprovide an accurate starting value for searching the optimalreplenishment number. Next, we characterize the influences of bothdemand and unit purchase cost over the length of production run timeand the economic production quantity. Finally, a numerical example isprovided not only to illustrate the proposed algorithms but also toverify the theoretical results.
2002年管理科學國際學術研討會論文集=Proceedings of the 2002 International Conference in Management Science, pp.405-422