Inventory model with stochastic demand, and no backorders: separate vs. joint cost minimisations

This paper develops an inventory model with stochastic demand, but no backorders. Three different ways to find the minimum cost are chosen. The first two involve minimising the sum of carrying cost and ordering cost separately from the sum of safety stock cost, and underage cost. The third way is to optimise the sum of the four individual costs jointly. The paper begins by comparing the subtotals. One notable result is that the two subtotal costs, and the grand total cost are immaterially different for the three ways. However, if one scrutinises the four individual costs there are significant disparities. For example, the carrying cost is much higher for the third optimisation method relative to the first two, but the ordering cost is much lower. Therefore, each one of the four individual costs should be closely monitored, not only the subtotals or the grand total.