Mixed Integer Programming Formulation for Time-Dependent Petrol Station Replenishment Problem: A Real-Life Case in İstanbul

Abstract

With the increase in the consumption of petroleum and petroleum products, these limited resources must be provided efficiently, accurately, and with minimal damage. Therefore, the accurate and effective distribution of petroleum, and related problems with petroleum distribution have attracted much attention among the practitioners and optimization working researchers over the years. The petroleum distribution problem, as a version of the Vehicle Routing Problem (VRP), deals with the planning of petroleum distribution from the depot(s) to the petrol stations safely and quickly. In this study, the petrol station replenishment problem (PSRP) is handled and a case study is presented for a public company located in İstanbul. The problem is considered as a time-dependent VRP with time windows. A novel mixed integer mathematical model is proposed for the problem. In order to handle the proposed time-dependent problem in a more realistic way, variable tanker speeds are considered based on traffic density. The optimum route is determined in which risks such as environment and marine pollution may occur in case of possible accidents, and these risks are minimized by the proposed mathematical model considering the factors as traffic, vehicle speed, road structure, the road's proximity to the sea and living areas