The capacitated distribution and waste disposal problem

We study the problem of the simultaneous design of a distribution network with plants and waste disposal units, and the coordination of product flows and waste flows within this network. The objective is to minimize the sum of fixed costs for opening plants and waste disposal units, and variable costs related to product and waste flows. The problem is complicated by (i) capacity constraints on plants and waste disposal units, (ii) service requirements (i.e. production must cover total demand) and (iii) waste, arising from production, to be disposed of at waste disposal units. We discuss alternative mathematical model formulations for the two-level distribution and waste disposal problem with capacity constraints. Lower bounding and upper bounding procedures are analyzed. The bounds are shown to be quite effective when embedded in a standard branch and bound algorithm. Finally, the results of a computational study are reported.