An Optimization Framework for Combining the Petroleum Replenishment Problem with the Optimal Bidding in Combinatorial Auctions

We address in this paper a periodic petroleum station replenishment problem (PPSRP) that aims to plan the delivery of petroleum products to a set of geographically dispatched stations. It is assumed that each station is characterized by its weekly demand and by its frequency of service. The main objective of the delivery process is to minimize the total travelled distance by the vailable trucks over an extended planning horizon. The problem configuration is described through a set of trucks with several compartments each and a set of stations with demands and prefixed delivery frequencies. Given such input data, the minimization of the total distance is subject to assignment and routing constraints that express the capacity limitations of each truck's compartment in terms of the frequency and the pathway's restrictions. In this paper, we develop and solve the full space mathematical formulation for the PPSRP with application to the Omani context. Our ultimate aim is to include such a model into an integrated framework having the objective of advising petroleum distribution companies on how to prepare bids in case of participation in combinatorial auctions of the transportation procurement.