We present a mathematical programming model for the combined vehicle routing and scheduling problem with time windows and additional temporal constraints. The temporal constraints allow for imposing pairwise synchronization and pairwise temporal precedence between customer visits, independently of the vehicles. We describe some real world problems where the temporal constraints, in the literature, usually are remarkably simplified in the solution process, even though these constraints may significantly improve the solution quality and/or usability. We also propose an optimization based heuristic to solve real size instances. The results of numerical experiments substantiate the importance of the temporal constraints in the solution approach. We also make a computational study by comparing a direct usage of a commercial solver against the proposed heuristic where the latter approach can find high quality solutions within distinct time limits.
In this paper we present a branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. The synchronization constraints are used to model situations when two or more customers need simultaneous service. The synchronization constraints impose a temporal dependency between vehicles, and it follows that a classical decomposition of the vehicle routing and scheduling problem is not directly applicable. With our algorithm, we have solved 44 problems to optimality from the 60 problems used for numerical experiments. The algorithm performs time window branching, and the number of subproblem calls is kept low by adjustment of the columns service times.
A cost-efficient use of harvesting resources is important in the forest industry. The main planning is carried out in an annual resource plan that is continuously revised. The harvesting operations are divided into harvesting and forwarding. The harvesting operation fells trees and puts them in piles in the harvest areas. The forwarding operation collects piles and moves them to storage locations adjacent to forest roads. These operations are conducted by machines (harvesters, forwarders and harwarders), and these are operated by crews living in cities/villages that are within some maximum distance from the harvest areas. Machines, harvest teams and harvest areas have different characteristics and properties and it is difficult to find the best possible match throughout the year. The aim of the planning is to find an annual plan with the lowest possible cost. The total cost is based on three parts: production cost, traveling cost and moving cost. The production cost is the cost for the harvesting and forwarding. The traveling cost is the cost for driving back and forwards (daily) from the home base to the harvest area and the moving cost is associated with moving the machines and equipment between harvest areas. The Forest Research Institute of Sweden (Skogforsk), together with a number of Swedish forest companies, has developed a decision support platform for the planning. One important element of this platform is that it should find high-quality plans within short computational times. One central element is an optimization model that integrates the assignment of machines to harvest areas and schedules the harvest areas during the year for each machine. The problem is complex and we propose a two-phase solution method where, first, we solve the assignment problem and, second, the scheduling. In order to be able to control the scheduling in phase 1 as well, we have introduced an extra cost component that controls the geographical distribution of harvest areas for each machine in phase 1. We have tested the solution approach on a case study from one of the larger Swedish forest companies. This case study involves 46 machines and 968 harvest areas representing a log volume of 1.33 million cubic meters. We describe some numerical results and experience from the development and tests.
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