Breakable Fuzzy Multi-stage Transportation Problem

In this paper, we investigate two new transportation models with breakability and restriction on transportation. Sometime in transportation process the items which are transported, have got damaged due to bad conditions of the road and vehicle. Here we consider the problem that there are so many plants and customers and the goods are transported in n-stages. We formulate two transportation models under crisp and fuzzy environment where we consider the transportation parameters are crisp and fuzzy in nature, respectively. We also consider the breakability (takes the deterministic value for the respective models) at each stages. For the fuzzy model, generalized triangular fuzzy number and mean of $$\alpha $$α-cut method are considered. Numerical illustration is provided to illustrate the developed models.

[1]  Hasan Pirkul,et al.  A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution , 1998, Comput. Oper. Res..

[2]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[3]  Manoranjan Maiti,et al.  Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment , 2013 .

[4]  Tapan Kumar Roy,et al.  Fuzzy multi-objective mathematical programming on reliability optimization model , 2006, Appl. Math. Comput..

[5]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[6]  M. Maiti,et al.  Solution of multi-item interval valued solid transportation problem with safety measure using different methods , 2014 .

[7]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[8]  K. Hindi,et al.  Efficient Solution of a Multi-commodity, Two-stage Distribution Problem with Constraints on Assignment of Customers to Distribution Centres , 1998 .

[9]  Shyi-Ming Chen,et al.  OPERATIONS ON FUZZY NUMBERS WITH FUNCTION PRINCIPAL , 1985 .

[10]  Jing-Shing Yao,et al.  A fuzzy stochastic single-period model for cash management , 2006, Eur. J. Oper. Res..

[11]  S. Mondal,et al.  A multi-item transportation problem with fuzzy tolerance , 2013, Appl. Soft Comput..

[12]  F. L. Hitchcock.  The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[13]  Ali Amiri,et al.  Production , Manufacturing and Logistics Designing a distribution network in a supply chain system : Formulation and efficient solution procedure , 2005 .

[14]  Mitsuo Gen,et al.  A genetic algorithm for two-stage transportation problem using priority-based encoding , 2006, OR Spectr..