Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distrib
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ORIGINAL ARTICLE
Parameter estimation and optimization of multi‑objective capacitated stochastic transportation problem for gamma distribution Srikant Gupta1 · Harish Garg2 · Sachin Chaudhary3 Received: 30 March 2020 / Accepted: 13 May 2020 © The Author(s) 2020
Abstract The transportation problem in real life is an uncertain problem with multi-objective decision-making. In particular, by considering the conflicting objectives/criteria such as transportation costs, transportation time, discount costs, labour costs, damage costs, decision maker searches for the best transportation set-up to find out the optimum shipment quantity subject to certain capacity restrictions on each route. In this paper, capacitated stochastic transportation problem is formulated as a multi-objective optimization model along with some capacitated restrictions on the route. In the formulated problem, we assume that parameters of the supply and demand constraints’ follow gamma distribution, which is handled by the chance constrained programming approach and the maximum likelihood estimation approach has been used to assess the probabilistic distributions of the unknown parameters with a specified probability level. Furthermore, some of the objective function’s coefficients are consider as ambiguous in nature. The ambiguity in the formulated problem has been presented by interval type 2 fuzzy parameter and converted into the deterministic form using an expected value function approach. A case study on transportation illustrates the computational procedure. Keywords Multi-objective optimization · Capacitated transportation problem · Stochastic programming · Interval type-2 fuzzy number · Gamma distribution · Maximum likelihood estimation
Introduction The problem of transportation is a very interesting method of management sciences, which can be conceived and solved as a problem of linear programming (LP). Transport problem (TP) is seen as a logistics issue where the primary aim is to determine how and when to transport goods from distinct sources to distinct destinations with a minimum price or maximum profit. Also, today’s decision maker (DM) seeks to reduce the shipping expenses but simultaneously seeks to reduce the distribution system’s transportation time. We have been able to observe in recent years that for many of the real-world situations, a classic mathematical programming * Harish Garg [email protected] 1
Jaipuria Institute of Management, Jaipur, India
2
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, Punjab, India
3
Department of Community Medicine, Government Medical College, Kannauj, UP, India
model is insufficient. The nature of these problems requires, on the one hand, taking into account multiple goals and, on the other, different types of uncertainty. These uncertainties in the problem is represented by either with fuzziness or multi-choices or by probabilistic variables. Stochastic programming (SP) discusses situations under which random va
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