Cost Allocation Heuristics For Solving The Fixed Charge Problem

The fixed charge problem extends the linear programming problem by incorporating a discontinuity in the objective function at an activity level of zero. The objective function value is zero with an activity level of zero. Any activity level above zero has a finite non-variable component in the objective function plus a component which is proportional to the activity level. Other discontinuities in the objective function can be represented by different reformulations. These formulations are useful in approaching a number of managerial problems in areas such as facility location, production planning or manpower planning.;As fixed charge problems become large, various methods of obtaining the optimal solution have excessive computational requirements. As a result, a number of methods have been developed for obtaining good but not necessarily optimal solutions. These approximate methods are able to solve much larger problems.;Considerable success has been achieved with both optimizing and approximate algorithms for problems with a special structure. However, algorithms, both optimizing and approximate, capable of solving any fixed charge problem have been successful with much smaller problems. With many problems requiring a general formulation, there is a need for an effective method of solving large general fixed charge problems.;A new approximate solution technique will be introduced which will be based on necessary conditions which must be met by a solution plus quasi-sufficient conditions which will indicate either a good solution or an improvement which can be made. The new technique will use heuristics to incorporate the fixed charges into the objective function through a series of cost allocations.;The new solution technique will be evaluated on a number of large general fixed charge problems including test problems and a wide variety of actual applications. In addition, a comparative analysis is made with alternative solution methods. The results indicate that the new solution technique provides a significant improvement to existing methods for solving large fixed charge problems