Production and work force assignment problem: A bi-level programming approach

A home supplies manufacturer manufactures many products and each requires workers with different skills. The manufacturer invites a contracting company to supply workers with different skills for each phase of the production process. The problem becomes a production and work force assignment problem, which can be considered as a bi-level programming problem. The supplier, as the upper decision maker, aims to achieve the objective of maximizing gross revenue by making decisions concerning production levels. The contracting company, as the lower-level decision maker, regards the target to be maximizing profit by making decisions concerning the number of assigned workers. There are uncertainties during the production process and therefore the problem has random fuzzy coefficients. To deal with the uncertainties, a general linear bi-level model with random fuzzy variables is introduced and several properties and crisp equivalents are proposed. Then an interactive programming method is applied to deal with the derived expected bi-level programming problem; after several iterations, the interactive solutions converge to the optimal one. Lastly, a numerical example is also presented to demonstrate the proposed optimization methods.