The cyclic production routing problem

This paper introduces the Cyclic Production Routing Problem (CPRP). The CPRP is an extension of the well-known NP-hard Production Routing Problem (PRP), which is a hard-to-solve combinatorial optimisation problem with numerous practical applications in the field of freight transportation, logistics and supply chain management. Under the PRP setting, a manufacturer is responsible for determining production decisions, as well as the timing and quantity of replenishment services offered to a set of geographically dispersed customers over a multi-period time horizon. The problem calls for jointly optimising the production, inventory, distribution and routing decisions. In this paper, the basic PRP model is modified to generate repeatable cyclic production and delivery schedules. A two-commodity flow formulation is proposed along with valid inequalities. Extensive comparisons between the basic PRP and the proposed cyclic variant on well-known benchmark instances are provided. The new variant is significantly harder to solve, especially when the vehicle fleet is limited. From a managerial perspective, the generation of cyclic production-routing schedules significantly increases all costs, whereas the number of vehicle routes required to implement a cyclic schedule is higher.