An integrated plant loading model with economies of scale and scope

This paper presents a new formulation of a class of plant product mix-loading problems which are characterized by fixed facility costs, concave production costs and an integrated network structure which encompasses inbound supply and outbound distribution flows. In particular, the authors are interested in assigning product lines and volumes to a set of capacitated plants. Fixed costs are incurred when a product line is assigned to a plant. The production cost function also exhibits concavity with respect to each product line volume. Thus both scale and scope economies are considered explicitly in the model. The problem formulation leads to a concave mixed-integer mathematical program. The authors develop an optimization algorithm within the framework of Benders decomposition for the case of a piecewise linear concave cost function. The present algorithm generates optimal solutions efficiently. The problem solutions also illustrate how the model is effective in evaluating tradeoffs between inbound, production and outbound costs. Finally the model is used to illustrate the impact of various cost factors (logistics, scale and complexity) on optimal product mix solutions.