A profit-maximizing plant-loading model with demand fill-rate constraints

This paper discusses a new formulation of a class of plant product-mix loading problems which are characterized by capacitating production facilities, demand fill-rate requirements, fixed facility costs, concave variable production costs and an integrated network structure which encompasses inbound supply and outbound distribution flows. In particular, the paper is interested in assigning product lines and volumes to a set of capacitated plants under the demand fill-rate constraints. Fixed costs are incurred when a product line is assigned to a plant. The variable production-cost function also exhibits concavity with respect to each product-line volume. Thus both scale economies and plant focus effect are considered explicitly in the model. The model also can be used to determine which market to serve in order to best allocate the firm’s resources. The problem formulation leads to a concave mixed-integer mathematical programme. Given the state of the art of non-linear programming techniques, it is often not possible to find global optima for reasonably sized problems. The paper develops 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.