Multi depot simultaneously pick up and delivery vehicle routing problem with stochastic pick up demand

Vehicle Routing Problem (VRP) is the problem of determining the routes of vehicles moving from one or more depots at minimum cost to satisfy the distribution/ collection demands of customers in different locations. Today, competing companies have to reduce their costs in order to get a share from the market. Companies attempting to reduce their costs try to minimize logistics costs, thud VRP is becoming an increasingly important issue for companies. Companies can serve customers from more than one depot and satisfy their distribution and collection requests with the same vehicle in order to reduce their logistics costs. When we examine the real-life problems, it is seen that Stochastic Vehicle Routing Problems (SVRP) whose demands, customer locations or customer service times are not known exactly, are encountered more frequently than the classical VRP. When the studies in the literature are examined, it is noteworthy that the Vehicle Routing Problem with Stochastic Demand (VRP_SD) is mostly studied by the researchers. In this study, Multi Depot Simultaneous Pick up and Delivery Vehicle Routing Problem with Stochastic Pick up Demand (MD_SPDVRP_SP) was investigated. In this study, it was assumed that the pick up demands of the customers came from the normal distribution. Firstly, the mathematical model was proposed for the Multi Depot Simultaneous Pick Up and Delivery Vehicle Routing Problem (MD_SPD_VRP) where deterministic demand is present and the effctivenes of this model is tested in this study. Subsequently, the stochastic programming mode is developed for MD_SPDVRP_SP by using a chance constrained programming approach. Since the developed model contains nonlinear constraints, the stochastic model is linearized using the linear transformation method firstly. Then, the effectiveness of the model is tested by using randomly generated test problems.