Multi-objective two-stage grey transportation problem using utility function with goals

Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.

[1]  H. Pastijn.  Handbook of critical issues in goal programming: Carlos Romero Pergamon Press, Oxford, 1990, xi + 124 pages, £25.00, ISBN 008 0406610 , 1992 .

[2]  S. K. Roy,et al.  Multi-Objective Interval-Valued Transportation Probabilistic Problem Involving Log-Normal , 2017 .

[3]  Shiang-Tai Liu,et al.  The total cost bounds of the transportation problem with varying demand and supply , 2003 .

[4]  Sankar Kumar Roy,et al.  Multi-choice stochastic transportation problem involving Weibull distribution , 2014 .

[5]  Sifeng Liu,et al.  Study on GSOM model based on interval grey number , 2007, IEEE International Conference on Grey systems and Intelligent Services.

[6]  Peter L. Hammer,et al.  Time‐minimizing transportation problems , 1969 .

[7]  Prabhjot Kaur,et al.  An iterative algorithm for two level hierarchical time minimization transportation problem , 2015, Eur. J. Oper. Res..

[8]  Honghua Wu,et al.  Aggregation Operators of Interval Grey Numbers and Their Use in Grey Multi-Attribute Decision-Making , 2013 .

[9]  Lei Sun,et al.  Transportation cost allocation on a fixed route , 2015, Comput. Ind. Eng..

[10]  Wlodzimierz Szwarc,et al.  Some remarks on the time transportation problem , 1971 .

[11]  Gerhard-Wilhelm Weber,et al.  Transportation interval situations and related games , 2016, OR Spectr..

[12]  Gerhard-Wilhelm Weber,et al.  Special Issue on International Aspects of OR , 2016 .

[13]  Alexander Schrijver,et al.  Handbook of Critical Issues in Goal Programming , 1992 .

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

[15]  A. Charnes.  Management Model And Industrial Application Of Linear Programming , 1961 .

[16]  Y. Aneja,et al.  BICRITERIA TRANSPORTATION PROBLEM , 1979 .

[17]  Ruiyou Zhang,et al.  A reactive tabu search algorithm for the multi-depot container truck transportation problem , 2009 .

[18]  Gurupada Maity,et al.  Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand , 2016 .

[19]  Zhigeng Fang,et al.  General grey numbers and their operations , 2012 .

[20]  Mehrdad Tamiz,et al.  Goal programming for decision making: An overview of the current state-of-the-art , 1998, Eur. J. Oper. Res..

[21]  Jeffrey Forrest,et al.  On algorithm rules of interval grey numbers based on the “Kernel” and the degree of greyness of grey numbers , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[22]  Sankar Kumar Roy,et al.  Solving Single-Sink, Fixed-Charge, Multi-Objective, Multi-Index Stochastic Transportation Problem , 2014 .

[23]  Sankar Kumar Roy,et al.  Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal , 2017, Ann. Oper. Res..

[24]  Hsing-Pei Kao,et al.  Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming , 2010, Comput. Ind. Eng..

[25]  Turan Paksoy,et al.  Revised multi-choice goal programming for multi-period, multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing , 2010 .

[26]  Sankar Kumar Roy,et al.  Solving Solid Transportation Problem with Multi-Choice Cost and Stochastic Supply and Demand , 2014, Int. J. Strateg. Decis. Sci..

[27]  James P. Ignizio,et al.  Sequential linear goal programming: Implementation via MPSX , 1979, Comput. Oper. Res..

[28]  Sankar Kumar Roy,et al.  Solving multi-objective transportation problem with interval goal using utility function approach , 2016 .

[29]  Amy H. I. Lee,et al.  An evaluation framework for product planning using FANP, QFD and multi-choice goal programming , 2010 .

[30]  Ching-Ter Chang.  Revised multi-choice goal programming , 2008 .

[31]  Santanu S. Dey,et al.  On the transportation problem with market choice , 2015, Discret. Appl. Math..

[32]  Sankar Kumar Roy,et al.  Multi-choice stochastic transportation problem involving extreme value distribution , 2013 .

[33]  Naiming Xie,et al.  Novel methods on comparing grey numbers , 2010 .

[34]  Julian Scott Yeomans,et al.  Efficient generation of alternative perspectives in public environmental policy formulation: applying co-evolutionary simulation–optimization to municipal solid waste management , 2011, Central Eur. J. Oper. Res..

[35]  Pamela C. Nolz,et al.  Synchronizing vans and cargo bikes in a city distribution network , 2017, Central Eur. J. Oper. Res..

[36]  L. V. Kantorovich,et al.  Mathematical Methods of Organizing and Planning Production , 1960 .

[37]  Sankar Kumar Roy,et al.  Solving multi-choice multi-objective transportation problem: a utility function approach , 2014 .

[38]  Ching-Ter Chang,et al.  Multi-choice goal programming , 2007 .

[39]  Yu Lean,et al.  Time-dependent fuzzy random location-scheduling programming for hazardous materials transportation , 2015 .

[40]  S. Z. A. Gök,et al.  Cooperative grey games and the grey Shapley value , 2015 .