Resource allocation in parallel-series production systems with shared inputs and outputs: a data envelopment analysis approach

¹ Research Center of Performance & Productivity Analysis, Istinye University, Istanbul, Turkey
² Department of Mathematics, College of Science, Sultan Qaboos University, Al-Khod 123, Muscat, Oman
³ Department of Applied Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

^* Corresponding author: alireza.amirteimoori@istinye.edu.tr; aamirteimoori@gmail.com

Received: 27 May 2024
Accepted: 5 September 2025

Abstract

The problem of resource allocation and reallocation in management science and production theory has drawn much attention among researchers and decision-makers. In this contribution, we focus on this problem in production processes in which two parallel stages are serially connected to a third stage. We assume that in addition to stage-specific inputs, we have shared inputs between the two parallel stages. In this sense, a linear programming-based model is proposed to calculate the technical efficiency of the whole process along with an optimal split of shared resources. To demonstrate the real-world applicability of the proposed approach, a case study on 22 Indian insurance companies is conducted. The analysis reveals that only three companies are efficient across all scenarios. Furthermore, narrow bounds on shared resources and intermediate products lead to more accurate and reliable results compared to medium and wide bounds, highlighting the importance of precise resource allocation constraints.