Production, Inventory and Capacity Expansion Scheduling with Integer Variables

The combined production-inventory and capacity expansion problem is modeled as a linear, integer program. The model assumes constant returns to scale in the production function of a firm which must meet, at minimum cost, deterministic demands for a single product over N periods with no backordering. A linear transformation is used to obtain an equivalent form of the model which is then decomposed into fixed cost and variable cost parts. A global optimum is obtained by enumerating on the fixed cost variables and solving transportation sub-problems with the remaining variables. Special demand and cost structures and extensions are discussed, and computational experience presented.