AN INTEGER PROGRAMMING APPROACH TO CAPACITY EXPANSION AND PRODUCTION PLANNING

The combined capacity expansion, production-inventory problem Is modeled as a linear, integer program and then extended to also allow capacity de-crease. The models assume constant returns to scale in the production function of a firm which must meet deterministic demands for a single product over N periods, with no backordering, at minimum cost. A linear transformation is used to obtain equivalent forms of the models which are then decompos-ed into fixed cost and variable cost parts. Enumer-ation is done on the fixed cost variables and transpor-tation sub-problems are solved with the remaining var-iables. Special demand and cost structures are inves-tigated, one of which leads to formulation of the en-tire problem as a network. Extensions are made to include piecewise-linear, convex production costs and lumpiness in ca-pacity acquisition. A reinterpretation of the models to handle the employment smoothing problem is also pre-sented. Finally, computational results of a Fortran IV coding of the basic algorithms are presented