A mathematical model for a multi-commodity, two-stage transportation and inventory problem

Abstract

This paper presents a mathematical model for two-stage planning of transportation and inventory for many sorts of products (multi-commodity). The situation considered in this paper, which happens in a local furniture manufacturing firm, is that the total supply in origins exceeds the current-stage's total demand from all destinations (markets). Therefore, the problem is how to arrange the current-stage's shipping in consideration of next-stage's (that is, future's) inventory in both origins and destinations. A mathematical model is proposed for the problem with the objective of minimizing the total cost of both shipping and inventory for all products within two stages. Meanwhile, since the next-stage's shipping costs usually are unknown, this paper presents a new concept of rational unit shipping cost: a forecasted average cost with weight of nextstage's shipping amount. Finally, a numerical example extracted from the furniture manufacturing company with 4 origins, 4 destinations and 4 commodities is illustrated in the paper.