Fuzzy programming and profit and cost allocation for a production and transportation problem

• Published in: European Journal of Operational Research Vol. 131; no. 1; pp. 1 - 15
• Main Authors: Sakawa, Masatoshi, Nishizaki, Ichiro, Uemura, Yoshio
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.05.2001; Elsevier BV; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Cost allocation methods; Fuzzy logic; Fuzzy programming; Game theory; Mathematical models; Optimization; Production and transportation problem; Production management; Profit and cost allocation; Studies; Transportation; Production and transportation problem; Profit and cost allocation; Fuzzy programming; Optimization
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/S0377-2217(00)00104-1

In this paper, we deal with a real problem on production and transportation in a housing material manufacturer, and consider a production and transportation planning under the assumption that the manufacturer makes multiple products at factories in multiple regions and the products are in demand in each of the regions. First, we formulate mixed zero–one programming problems such that the cost of production and transportation is minimized subject to capacities of factories and demands of regions. Second, to realize stable production and satisfactory supply of the products in fuzzy environments, fuzzy programming for the production and transportation problem is incorporated. Finally, under the optimal planning of production and transportation, we show a profit and cost allocation by applying a solution concept from game theory. Using actual data, we show usefulness of the fuzzy programming and a rational allocation scheme of the profit and cost.