Solving the minsum product rate variation problem as an assignment problem

In this paper, we consider the Minimum Product Rate Variation Problem (PRVP), which consists in sequencing parts of different types so that the sum of discrepancy functions between actual and ideal productions is minimal. Such a problem can be reduced to an Assignment problem (AP) with a matrix of a special structure. Following this approach, the efficiency of different algorithms for an AP applied to the minsum PRVP case was compared. As a result, a new algorithm that exploits specific PRVP matrix properties is presented. Computational experiments are presented, including both types of objective functions, symmetric, as described in the literature, and asymmetric. The proposed approach allows, for the first time, obtaining optimal solutions for instances of dimensions up to 10,000 parts of different types to be produced.