A column generation algorithm for vehicle scheduling and routing problems

Abstract

During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks.One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them to the affected people. To successfully deliver these items to the people in need, the organization needs to make decisions that range from the quick acquisition of vehicles from the local market, to the preparation of pickup and delivery schedules and vehicle routes. During crises, the supply of vehicles is often limited, their acquisition cost is steep, and special rental periods are imposed. At the same time, the affected area needs the aid materials as fast as possible, and deliveries must be made within due time. Therefore, it is imperative that the decisions of acquiring, scheduling, and routing of vehicles are made optimally and quickly. In this paper, we consider a variant of a truckload open vehicle routing problem with time windows, which is suitable for modeling vehicle routing operations during a humanitarian crisis.We present two integer linear programming models to formulate the problem. The first one is an arc-based mixed integer linear programming model that is solved using a general purpose solver. The second one, on the other hand, is based on a path-based formulation, for which we design a column generation framework so as to solve it. Finally, we perform numerical experiments and compare the performance of the two models. The comparison shows that the latter path-based formulation outperforms the former without sacrificing solution quality when employing our column generation framework.

Vehicle Routing Optimisation in Humanitarian Operations: A Survey on Modelling and Optimisation Approaches

“…Ref. [46] addressed the scheduling and open vehicle routing of pick up and drop off aid delivery problem through the perspective of a humanitarian coordinator. The coordinator as the decision maker is to decide how many vehicles should be rented from the third party logistics service provider while taking into consideration the limited duration of the rent in the aftermath of a hurricane.…”

“…From these models, various interesting and complex problems are addressed. As a general trend, it could be seen that most work addressed split delivery, such as in [34,42,46,47,[49][50][51]61,71,73,75,76,78,81,83,85,87,94,96,102,116,123,128,158] and multi-trip VRP that can be seen in [31,47,50,61,76,88,90,94,97,98,124,126,129], ref. [134,149,159] normally stressed on the problem of vehicle limitations such as the numbers of vehicle or the fuel limitation.…”

Towards Real-Time Energy Management of Multi-Microgrid Using a Deep Convolution Neural Network and Cooperative Game Approach

“…As the number of coalitions and players increases, it becomes inefficient and difficult to solve; thus, CGA resolves this problem by reducing the number of enumerations. CGA is studied to solve the vehicle scheduling problem [49], sea traffic scheduling problem [50], location routing problems [51], job scheduling problem [52], and fleet designing problem [53]. However, the CGA method is underexplored in the field of MMG.…”

A Pointer Neural Network for the Vehicle Routing Problem with Task Priority and Limited Resources

“…As mentioned above, exact algorithms and heuristic algorithms are the primary classes of operation re-search methods. In some instances, exact algorithms, such as dynamic programming [20], column generation [8] and the branch-and-price [2] method, have been used. Yu et al [32] propose an improved branchand-price (BAP) algorithm to precisely solve the heterogeneous fleet green vehicle routing problem with time windows, and a multi-vehicle approximate dynamic programming algorithm was designed to speed up the pricing problem in BAP.…”