Adaptation of the plant location model for regional environmental facilities and cost allocation strategy

This paper is divided into two parts. In the first part of the paper, the plant location model is adapted for the special case of siting wastewater treatment facilities when the wastewater sources and treatment facilities are arranged in a chain or linear configuration. In this problem, flows or shipments may be merged in common pipes that provide economies of scale in transport. In order to apply the plant location model, an appropriate definition of the additional cost incurred when a waste source joints a regional facility is required. In addition, sequential priority constraints are developed in the siting model in order to make possible proper accounting of transport costs. The new siting model can be conveniently solved by linear programming. In the second part of the paper, a dual of the plant location model is explored as a cost allocation method for the fixed charge facility siting problem. The constraint sets of the dual model can be shown to imply the core conditions of the related cost game; hence, a set of the dual variables from the dual problem can be regarded as rational cost allocations. The analysis places both facility siting and cost allocation in a common framework.