Decentralized decision‐making involving multiple criteria: a multiple knapsack formulation

Abstract

There is a class of multiple criteria problems involving multiple decision‐makers which we call the multiple knapsack problem. Although difficult to solve in its original form, the problem may be readily solved by a different model structure whose elements are obtained from the original problem after decomposition via Lagrangean relaxation. The sub‐problems resulting from the decomposition involve multiple criteria utility functions of unknown form for single decision‐makers. The structure of the resulting sub‐problems is such that the set of feasible alternatives generated for each sub‐problem can, with little effort, be ranked by the decision‐maker and a utility value assigned to a suitable subset of the best alternatives. The subset of best alternatives for each decision‐maker is incorporated into the new model (a master problem) which can supply either optimal or very good solutions to the original problem.