The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of SDVRP, in which multiple vehicles start from multiple depots and return to their original depots at the end of their assigned tours. The MDVRP is NP-hard, therefore, the development of heuristic algorithms for this problem class is of primary interest. This paper solves Multi-Depot Vehicle Routing Problem with Cellular Ant A...

We consider the following two deterministic inventory optimization problems over a finite planning horizon T with non-stationary demands. • Submodular Joint Replenishment Problem. This involves multiple item types and a single retailer who faces demands. In each time step, any subset of item-types can be ordered incurring a joint ordering cost which is submodular. Moreover, items can be held in...

In the vehicle routing problem with time window (VRPTW), the objective is to minimize the number of vehicles and then minimize the total time travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced ...

This paper presents a meta-heuristic, which is based on the Threshold Accepting combined with modified Nearest Neighbor and Exchange procedures, to solve the Vehicle Routing Problem with Backhauls and Time Windows (VRPBTW). The VRPBTW assumes that trucks initially start from the depot, deliver goods to the linehaul customers, successively pickup goods from the backhaul consumers, and finally re...

The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the sum of all tour lengths, and existing literature handles this problem with a variety of assumptions and...

The aim of the study is to apply a Genetic Algorithm (GA) to solve a Vehicle Routing Problem (VRP) for a specific bakery company. This VRP application consists of 1 depot with 32 customers in 6 delivery zones. In the study, the GA is chosen to solve this vehicle routing problem as compared with an existing method currently used by the company, which resembles to the Nearest Neighbor Heuristic (...

The Ant System is a distributed metaheuristic that combines an adaptive memory with a local heuristic function to repeatedly construct solutions of hard combina-torial optimization problems. We present in this paper an improved ant system algorithm for the Vehicle Routing Problem with one central depot and identical vehicles. Computational results on fourteen benchmark problems from the literat...

the heterogeneous fixed fleet open vehicle routing problem (hffovrp) is one of the most significant extension problems of the open vehicle routing problem (ovrp). the hffovrp is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. in this problem, the vehicle doesn’t return to the depot after se...

The multi-depot fleet size and mix vehicle routing problem, also known as the multi-depot routing with heterogeneous vehicles, is investigated. A mathematical formulation is given and lower as well as upper bounds are produced using a three hour execution time of CPLEX. An efficient implementation of variable neighborhood search that incorporates new features in addition to the adaptation of se...

We address in this paper a distribution real case problem facing the fuel supplying companies. The cost of acquiring vehicles is often more significant than the routing cost. The goal is to minimise the number of required vehicles. We deal with a vehicle routing problem with double time windows for the depot and multiple use of vehicles (VRPDM). There is a single depot with double time windows,...