Optimal Capacity Expansion with Inventory

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Abstract
In a given region over a finite time horizon, a known nondecreasing demand for a single commodity has to be satisfied by production in that period and/or by inventory from the previous period. There is no initial production capacity or inventory, but the capacity and production may be increased at the beginning of each discrete time period. We assume that the capacity and production are nondecreasing over the time periods. The total time discounted costs to be minimized include the capacity expansion, production, inventory carrying, and idle capacity costs, which are assumed to be concave. The problem is to determine an optimal capacity expansion and production schedule, together with the associated inventory carrying and idle capacity schedules. Based on some interesting properties of an optimal solution, we devise an efficient dynamic programming algorithm to solve this problem.

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