Fleet size planning when outside carrier services are available

The delivery of goods from a warehouse to local customers is a critical aspect of a material logistics system. A strategic decision must be made periodically (e.g., once a year) whether to maintain a private delivery fleet, to employ outside commercial carrier services, or to use a combination of both options. The authors seek to develop a methodology to address this long range planning decision. The present model considers a geographic area, with random daily demands, served by a single warehouse. The costs considered include the fixed and variable (per mile) costs of a private vehicle and the outside carriers’ delivery charges. A private vehicle is constrained by the length of the work-day, since it returns to the warehouse only after completing all its deliveries. Since actual customer locations change from day to day, for planning purposes the authors divide the geographic area into sectors and decide how best to serve each sector. The model determines the private fleet size and the specific assignment of each sector to a private vehicle or to an outside carrier. The centerpiece of the present solution approach consists of a single-source capacitated facility location formulation, in which each ‘customer’ (sector) is served by a single ‘facility’ (private vehicle or outside carrier). Computational results are reported.