An Efficient Algorithm to Solve Transshipment Problem in Uncertain Environment
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An Efficient Algorithm to Solve Transshipment Problem in Uncertain Environment Ashok Kumar1
•
Ritika Chopra2 • Ratnesh Rajan Saxena3
Received: 19 February 2020 / Revised: 7 June 2020 / Accepted: 13 July 2020 Taiwan Fuzzy Systems Association 2020
Abstract Transshipment problems are special type of transportation problems in which goods are transported from a source to a destination through various intermediate nodes (sources/destinations), possibly to change the modes of transportation or consolidation of smaller shipments into larger or deconsolidation of shipments. These problems have found great applications in the era of e-commerce. The formulation of transshipment problems involves knowledge of parameters like demand, available supply, related cost, time, warehouse space, budget, etc. However, several types of uncertainties are encountered in formulating transshipment problem mathematically due to factors like lack of exact information, hesitation in defining parameters, unobtainable information or whether conditions. These types of uncertainty can be handled amicably by representing the related parameters as intuitionistic fuzzy numbers. In this article, a fully fuzzy transshipment problem is considered in which the related parameters (supply, demand and cost) are assumed to be represented as trapezoidal intuitionistic fuzzy numbers. The proposed
method is based on ambiguity and vagueness indices, thereby taking into account hesitation margin in defining the values precisely. These indices are then used to rank fuzzy numbers to derive a fuzzy optimal solution. The technique described in this paper has an edge as it directly produces a fuzzy optimal solution without finding an initial basic feasible solution. The method can easily be employed to fuzzy transshipment problems involving trapezoidal intuitionistic, triangular intuitionistic, trapezoidal, triangular, interval valued fuzzy numbers and real numbers. The proposed technique is supported by numerical illustrations and it has been shown that the method described in the paper is computationally much more efficient than already existing method and is applicable to a larger set of problems. Keywords Intuitionistic fuzzy set Intuitionistic fuzzy number Intuitionistic fuzzy optimal solution Fully intuitionistic fuzzy transshipment problem
1 Introduction & Ashok Kumar [email protected] Ritika Chopra [email protected] Ratnesh Rajan Saxena [email protected] 1
Department of Mathematics, University of Delhi, Delhi 110007, India
2
Department of Mathematics, Shaheed Rajguru College of Applied Sciences for Women University of Delhi, Delhi 110096, India
3
Department of Mathematics, Deen Dayal Upadhyaya College University of Delhi, Delhi 110078, India
In classical transportation problems (TP), goods are transferred from certain origins to some destinations. But in some cases, the goods may be shipped directly or through one or more intermediate nodes to a certain destination. Each of these nodes may behave as origin or destination. Su
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