Declarative Modeling of a Milk-Run Vehicle Routing Problem for Split and Merge Supply Streams Scheduling

A flow production system with concurrently executed supply chains providing material handling/transportation services to a given set of workstations is analyzed. The considered streams of split and merge supply chains representing all the stages at which value is added to a manufacturing product (including the delivery of raw materials and intermediate components are scheduled under constraints imposed by the solution to an associated milk-run vehicle routing problem. A declarative model of the investigated milk-run delivery principle makes it possible to formulate a vehicle routing and scheduling problem, the solution to which determines the route, the time schedule, and the type and number of parts that different trucks must carry to fulfill orders from various customers/recipients. The goal is to find solutions that minimize both vehicle downtime and the takt time of the production flow. The approach proposed allows to view the above trade-off-like problem as a constraint satisfaction problem and to solve it in the Oz Mozart constraint programming environment.