Title: Solution of a sustainable bi-objective book-producers' problem using statistical approach

Authors: Snigdha Karmakar; Sujit Kumar De; Adrijit Goswami

Addresses: Department of Mathematics, IIT Kharagpur, West Bengal, India ' Department of Mathematics, Midnapore College (Autonomous), Pin-721101, West Bengal, India ' Department of Mathematics, IIT Kharagpur, West Bengal, India

Abstract: This article leads to statistical approach on bi-objective economic production quantity (EPQ) inventory problem especially on two book producers' problem under unit selling price and production run time dependent demand rate. The concept of 'early product-early demand' and 'low price-high demand' policy has been employed for developing this bi-objective inventory problem. The discounts on marked unit selling price have been offered at the time of selling the books on spot for both the producers also. In this model we are optimising the objective functions of both producers for this it is considered as bi-objective model. However, behind any computational process there might have the effects of extraneous variables for which we have used correlation approach to solve the model. In addition, we use goal attainment (GA) approach to solve the bi-objective problems first and then generate dataset from sensitivity analysis of the model. Moreover, we compute the correlation coefficients matrix for both joint and independent relations of the objective functions. The decision is made on the basis of testing of hypothesis over the decision maker's (DM) zone of intelligence. Finally, the dot plots are made for justification of the model.

Keywords: bi-objective inventory; extraneous variables; discounts; goal attainment method; Spearman's correlation coefficient; optimisation.

DOI: 10.1504/IJOR.2019.103121

International Journal of Operational Research, 2019 Vol.36 No.3, pp.310 - 336

Received: 23 May 2016
Accepted: 12 Nov 2016

Published online: 17 Oct 2019 *

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