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Multi-dimensional transportation problems in multiple environments: a simulation based heuristic approach

  • Soft computing in decision making and in modeling in economics
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Abstract

Here, a general methodology is proposed to formulate and solve any multidimensional balanced/unbalanced, constrained/unconstrained transportation problems(TP) in different environments(crisp/fuzzy/rough). To understand the general model easily, here, at first, a multi-item 5-dimensional fixed charge profit maximization TP under budget and time constraint is presented. A potential solution of the problem is coded as a permutation of the different cells of the allocation matrix. A general decoding rule is proposed to determine the actual allocation from this coded solution. A heuristic approach is applied on a set of randomly generated coded solution of the target problem to determine the marketing decision. Applying swap operations on the coded solutions, the perturbation rules of the heuristic Particle Swarm Optimization(PSO) are modified to solve the problem. In a particular case, the problem is analysed as a bi-criteria decision making problem with the maximization of the total profit as well as the minimization of the total shipment time under a budget constraint. The bi-criteria TP is formulated as a single objective optimisation problem using a proposed rule and the same heuristic is run for a finite number of times to determine the pareto optimal front. To formulate the problem in the fuzzy(rough) environment an approach is proposed using credibility(trust) measure of fuzzy(rough) events. Proper fuzzy(rough) simulation algorithms are also proposed to solve the problem for any type of fuzzy(rough) estimation. Using this approach no crisp equivalent of any imprecise parameters is used for the marketing decision. Due the unavailability of the test data in the literature, different hypothetical data sets are used for the illustration of the models.

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Authors and Affiliations

  1. Department of Computer Science, Yogoda Satsanga Palpara Mahavidyalaya, Palpara, Purba, Medinipur, West Bengal, 721458, India

    Sova Pal

  2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, Midnapore, West Bengal, 721102, India

    Prasenjit Pramanik

  3. Department of Mathematics, Raja Narendra Lal Khan Women’s College, Midnapore, West Bengal, 721102, India

    Ajoy Kumar Maiti

  4. Department of Mathematics, Mahishadal Raj College, Purba-Medinipur, Mahishadal, West Bengal, 721628, India

    Manas Kumar Maiti

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  1. Sova Pal
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  2. Prasenjit Pramanik
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  3. Ajoy Kumar Maiti
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  4. Manas Kumar Maiti
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Contributions

5-dimensional multi item TP under different constraints in both precise and imprecise environments: Discussion, mathematical formulation, solution methodology, numerical illustration. Multi-dimensional multi item TP: theoretical discussion, mathematical formulation, solution methodology. Fuzzy and Rough Simulation: Algorithm developed and used. Soft Computing technique: Swap sequence based PSO.

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Correspondence to Prasenjit Pramanik.

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Pal, S., Pramanik, P., Maiti, A.K. et al. Multi-dimensional transportation problems in multiple environments: a simulation based heuristic approach. Soft Comput 27, 11603–11628 (2023). https://doi.org/10.1007/s00500-023-08204-x

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