Order acceptance and scheduling in a parallel machine environment with weighted completion time

Abstract

This paper studies the order acceptance and scheduling (OAS) problem in an identical parallel machine environment where orders are characterised by their revenues, processing times and weights. A mixed integer linear programming (MILP) model is presented for the problem with the objective of maximising the revenue minus the scheduling cost. The problem is NP- hard and a branch and bound (B%B) algorithm is developed to solve the problem. An extension of the B%B algorithm is proposed to solve very large problem instances to obtain e-optimal solutions. The B%B algorithm and the extended B%B are evaluated for their performances against the solutions obtained by solving the MILP problem formulation using CPLEX solver through computational experiments. [Received 15 June 2017; Revised 2 February 2018; Accepted 10 March 2018]