Balancing the arrival times of users in a two-stage location problem

There has been a number of facility location problems dealing with the introduction of the equity issue in the travel distances distribution. In this paper we analyze a new aspect of equity concerning the distribution of the arrival times of customers. Given a depot and a set of demand points generating flow which also represent potential locations, we consider a discrete two-stage location problem whose aim is to locate a given number of facilities and to allocate the demand points to a facility. We assume as objective the maximization of the minimum difference between two consecutive arrival times of flows to the depot through the patronized facility. This particular equity measure is introduced in order to reduce risks of congestion in the dynamic of flow arrivals at the common destination. The problem is described through two Integer Programming formulations. Computational results for solution methods based on both formulations are then shown and analyzed

An elliptical cover problem in drone delivery network design and its solution algorithms

Given n demand points in a geographic area, the elliptical cover problem is to determine the location of p depots (anywhere in the area) so as to minimize the maximum distance of an economical delivery trip in which a delivery vehicle starts from the nearest depot to a demand point, visits the demand point and then returns to the second nearest depot to that demand point. We show that this problem is NP-hard, and adapt Cooper’s alternating locate-allocate heuristic to find locally optimal solutions for both the point-coverage and area-coverage scenarios. Experiments show that most locally optimal solutions perform similarly well, suggesting their sufficiency for practical use. The one-dimensional variant of the problem, in which the service area is reduced to a line segment, permits recursive algorithms that are more efficient than mathematical optimization approaches in practical cases. The solution also provides the best-known lower bound for the original problem at a negligible computational cost

A computer graphics approach to logistics strategy modelling

This thesis describes the development and application of a decision support system for logistics strategy modelling. The decision support system that is developed enables the modelling of logistics systems at a strategic level for any country or area in the world. The model runs on IBM PC or compatible computers under DOS (disk operating system). The decision support system uses colour graphics to represent the different physical functions of a logistics system. The graphics of the system is machine independent. The model displays on the screen the map of the area or country which is being considered for logistic planning. The decision support system is hybrid in term of algorithm. It employs optimisation for allocation. The customers are allocated by building a network path from customer to the source points taking into consideration all the production and throughput constraints on factories, distribution depots and transshipment points. The system uses computer graphic visually interactive heuristics to find the best possible location for distribution depots and transshipment points. In a one depot system it gives the optimum solution but where more than one depot is involved, the optimum solution is not guaranteed. The developed model is a cost-driven model. It represents all the logistics system costs in their proper form. Its solution very much depends on the relationship between all the costs. The locations of depots and transshipment points depend on the relationship between inbound and outbound transportation costs. The model has been validated on real world problems, some of which are described here. The advantages of such a decision support system for the formulation of a problem are discussed. Also discussed is the contribution of such an approach at the validation and solution presentation stages

Facility Location Problems: Models, Techniques, and Applications in Waste Management

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for e�ective and e�cient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP

Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper

When centers can fail: a close second opportunity

This paper presents the p-next center problem, which aims to locate p out of n centers so as to minimize the maximum cost of allocating customers to backup centers. In this problem it is assumed that centers can fail and customers only realize that their closest (reference) center has failed upon arrival. When this happens, they move to their backup center, i.e., to the center that is closest to the reference center. Hence, minimizing the maximum travel distance from a customer to its backup center can be seen as an alternative approach to handle humanitarian logistics, that hedges customers against severe scenario deteriorations when a center fails. For this extension of the p-center problem we have developed several different integer programming formulations with their corresponding strengthenings based on valid inequalities and variable fixing. The suitability of these formulations for solving the p-next center problem using standard software is analyzed in a series of computational experiments. These experiments were carried out using instances taken from the previous discrete location literature.Peer ReviewedPostprint (author’s final draft