A bilevel game model for ascertaining competitive target prices for a buyer in negotiation with multiple suppliers

¹ Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi 110042, India
² Department of Mathematics, Arignar Anna Government Arts & Science College, Karaikal, Puducherry 609602, India
³ Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India

^* Corresponding author: akhilesh.maths@gmail.com

Received: 26 January 2021
Accepted: 16 December 2021

Abstract

In this paper, a decision-support is developed for a strategic problem of identifying target prices for the single buyer to negotiate with multiple suppliers to achieve common goal of maintaining sustained business environment. For this purpose, oligopolistic-competitive equilibrium prices of suppliers are suggested to be considered as target prices. The problem of identifying these prices is modeled as a multi-leader-single-follower bilevel programming problem involving linear constraints and bilinear objective functions. Herein, the multiple suppliers are considered leaders competing in a Nash game to maximize individual profits, and the buyer is a follower responding with demand-order allocations to minimize the total procurement-cost. Profit of each supplier is formulated on assessing respective operational cost to fulfill demand-orders by integrating aggregate-production-distribution-planning mechanism into the problem. A genetic-algorithm-based technique is designed in general for solving large-scale instances of the variant of bilevel programming problems with multiple leaders and single follower, and the same is applied to solve the modeled problem. The developed decision support is appropriately demonstrated on the data of a leading FMCG manufacturing firm, which manufactures goods through multiple sourcing.