Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution

¹ Department of Mathematics, Kishorenagar Sachindra Sikshasadan, 721401 Contai, West Bengal, India
² Department of Mathematics, Bengal Institute of Technology, 1, no. Govt. Colony, 700150 Kolkata, West Bengal, India
³ Kishore Bharati Bhagini Nivedita College, Ramkrishna Sarani, 700060 Kolkata, India

^* Corresponding author: shib_sankar@yahoo.com, shibsankarsana@gmail.com

Received: 28 December 2018
Accepted: 2 May 2019

Abstract

The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a transportation problem in a multi-choice environment containing the parameters in all constraints which follow the Logistic distribution and cost coefficients of objective function are also multiplicative terms of binary variables. Using the stochastic programming approach, the stochastic constraints are converted into an equivalent deterministic one. A transformation technique is introduced to manipulate cost coefficients of objective function involving multi-choice or goals for binary variables with auxiliary constraints. The auxiliary constraints depends upon the consecutive terms of multi-choice type cost coefficient of aspiration levels. A numerical example is presented to illustrate the whole idea.