A branch and bound method is presented for evaluating alternative regional wastewater treatment systems, taking into account economies of scale in constructing treatment plants and interceptor sewers. A branch and bound tree is 'grown' by using an algorithm which is very efficient computationally because it uses a powerful inspection step and a network algorithm to solve subproblems. Each infeasible solution found by using the method is converted to a feasible'regional configuration of plants and interceptors. The alternative plans can be compared to examine tradeoffs between cost and other qualitative and quantitative planning objectives. Also the tree itself can be extended to generate additional planning alternatives. Rather than to find mathematically optimal solutions, the principal uses of the method are to generate systematically attractive alternative plans and potentially to assist in evaluating tradeoffs between different planning objectives. ' INTRODUCTION Planning regional wastewater systems is a current major problem in the United States and throughout the world. Regional planning activities usually consider joint, or regional, facilities for treating wastes piped from several sources. Since joint facilities are larger than the individual treatment facilities that they supplant, they offer economies of scale and the potential for better management. Additional costs are, of course, incurred for the interceptor sewers used to pipe the wastes to these regional facilities. In addition, in planning regional systems, many factors other than economic efficiency come into play.A branch and bound method is presented here for evaluating alternative regional wastewater systems, taking into account economies of scale in constructing treatment plants and interceptor sewers. Because there is a wide array of important planning factors, the method has been designed to generate alternative regional plans which can be evaluated in more detail as part of the planning process. Furthermore, the method is relatively easy to use, and the branch and bound tree can be 'grown' by computer or, if desired, by the analyst, a capability which is desirable in generating alternative plans and comparing them. For a discussion of how general planning processes can be viewed in terms of branch and bound approaches, see the work of Harris [1970].The branch and bound method presented here works as follows. Given a set of constraints which describe the physical requirements (such as wastewater treatment) and the large number of alternative locations and sizes of plants and interceptors, feasible solutions are generated and examined in sequence. Each feasible solution specifies a configuration of treatment plants and interceptors. The procedure can be followed to find the least costly configuration (under the assumed cost functions) or even extended beyond that point to examine additional alternative plans. The branch and bound algorithm presented is relatively powerful because it is specially designed for this problem; as described later...
