A mathematical model for in-plant Milk-Run routing

Milk-run is one of the lean logistics implementations defined as a cyclic materials delivering system. In-plant milk-run system, a variant of milkrun, runs for the delivering materials within the plant from warehouse to assembly stations in a cyclic manner. It is implemented using Automated Guided Vehicles (AGV), which provide automated materials handling in plant. In this study, in-plant milk-run system is discussed and the importance of determining milk-run routes and period is emphasized. A mixed integer mathematical model is proposed for the determination of milk-run routes and its period simultaneously for AGVs. Besides, the mathematical model allows split deliveries for assembly stations. The proposed model is coded using GAMS software and the success of this model is shown on randomly generated test problems. The proposed model obtains the optimal solution approximately in 1 second for generated two test problems. This points out the advantage and practicability of the proposed mathematical model for in-plant milk-run system.