Fixed Charge Facility Location Research Articles

Allocation of Distributed Energy Systems at District-Scale over Wide Areas for Sustainable Urban Planning with a MILP Model

An optimal allocation of centralized district-scale distributed energy resource (DER) systems with district heating and cooling network (DHCN) is studied. A generic mixed integer linear programming (MILP) model is constructed to increase the system efficiency and decrease costs by reducing energy distribution losses and transportation costs in energy distribution network. Initial investment costs based on size and type (co/trigeneration) of the facility and demand-weighted transportation costs are minimized by the capacitated fixed charge facility location (FCFL) model. However, unlike the standard FCFL model, by adding the maximum coverage distance in the set covering problem, a new method has been proposed. Thus, its aim is to avoid assigning a demand point to a candidate facility from a point farther than the predetermined distance. That means that the weakness of disregarding the distance between supply and demand points in the FCFL problem is eliminated. Additionally, this model, in which the annual inputs are used, has a generic framework suitable to form infrastructure needs in consideration of distributed energy systems in the general planning level for sustainable urban planning. For this purpose, the applications of the model, both case study and tests, have been made over wide areas, with annual demand and capacity values. Consequently, a case study with different coverage distances has been conducted to see the effect of coverage distance on the model, and also test problems with different sizes have been carried out to demonstrate the capability of the proposed model.

The Uncapacitated Battery Swapping Facility Location Problem with Localized Charging System Serving Electric Bus Fleet

Abstract This paper considers a refueling system for battery electric buses (BEBs) with battery swapping technology. The service capability of the battery swapping stations (BSSs) is restricted by localized charging system in terms of its charger type and the quantity of both chargers and batteries. The modelling intention is to answer four fundamental questions: How many BSSs should there be? Where should they be? Which BEBs should they serve? How big should they be? In this context, the problem has been formulated as a mixed-integer problem and decomposed into two subproblems. The first subproblem solves the uncapacitated fixed charge facility location problem (UFCFLP) to find the optimal BSSs location and the swapping demand assignment of BEBs. The optimal configuration of localized charging system is developed as integer linear programming problem to decide the charger type and battery inventory in the second subproblem. The solution method is tested on a small network under various parameter settings to investigate the BSS location and configuration and verify the feasibility and effectiveness of the proposed solution approach. Results shows that the battery capacity would affect the number of BSS to locate and the localized charging system configuration mainly depends on the charger and battery costs.

Exploring K-best solutions to enrich network design decision-making

In this paper, we explore alternative solutions to the Capacitated Fixed Charge Facility Location problem (CFCFL) that usually arises in Supply Chain Network Design problems. More specifically, we aim to investigate in which cases these solutions can be considered as good as the optimal one from the point of view of decision-making in real-world problems. A method, as well as four enhancement variations, based on a mixed-integer programming (MIP) model is proposed, which allows K-best alternative solutions to be obtained. The method and its variations were applied to two benchmark instance sets available in the literature and the computational times were evaluated. The results have shown that the gap between the optimal solutions and the 20-best alternative ones were, on average, less than 1%; more surprisingly, 63.8% of all these alternative solutions had a gap smaller than 0.5%. This suggests that our approach may be used to identify whether near-optimal alternative solutions can yield to a better overall solution from the point of view of the decision-maker, by allowing other qualitative attributes to be considered. We were also able to rate the robustness of some selected facilities since many candidates have appeared in all 20 best solutions. In addition, the results may also suggest a way to measure the difficulty of benchmark instances for combinatorial problems and thus enhance the comparison of different heuristics proposed to solve them; not to mention that the uncertainty in input data of such strategic problems may reduce the relevance of the effort to find the best solution in the contexts in which several high-quality solutions arise.

Multiple Approaches of Solving Allocation Problems on Postal Transportation Network in Conditions of Large Countries

Abstract The article deals with the optimizing the postal transportation network with two different optimizing methods. The research adopted in this article uses allocation models within graph theory to obtain results for addressed optimization problem. The article presents and compares two types of these models: p-median and uncapacitated fixed charge facility location model. The aim of p-median model is to find the location of P facilities in network, serving all demands in a way ensuring the average transport cost to be minimal. Fixed charge location model approach the issue of facility location based on minimizing the overall costs of implementation of selected variants. The latter this two models are subsequently applied on the postal network to determine the optimal location of postal facilities. These two models are adopted in the condition of large country with area above 300 000 km2. The Italy was chosen as a typical country that fits this condition. The underlying infrastructure of Italy is represented by simplified model of a postal network, abstracted by a graph G = (V, E, c, w). The results can serve as a basis for modification of the used models for the simulation of networks in the postal sector and as a key that compares the opportunities and results of application of these two models in the conditions large countries.

Planning charging infrastructure for plug-in electric vehicles in city centers

ABSTRACTInstalling charging facilities in existing parking lots in city centers is considered an effective measure to encourage the adoption of plug-in electric vehicles (PEV). This article is concerned with the problem of locating these facilities so as to minimize the total system cost. The problem is formulated as a fixed charge facility location model with charging capacity constraints. The proposed model extends the existing work by allowing unserved demands and considering drivers’ preference for familiar parking lots. Accordingly, inconvenience costs are introduced for unserved demands and for those who have to change their parking lots in order to charge at work. The proposed model is not only always feasible, but also introduces a pricing mechanism so that the level of service (measured by the cost of unserved demands) can be traded off with the infrastructure cost. In addition, a stochastic version of the proposed model is developed to address the effects of uncertain PEV market penetration rate on the planning of charging facilities. A case study is conducted to analyze the sensitivity of the models to different cost components, and to compare the results of the stochastic and deterministic models.

A bilevel fixed charge location model for facilities under imminent attack

We investigate a bilevel fixed charge facility location problem for a system planner (the defender) who has to provide public service to customers. The defender cannot dictate customer-facility assignments since the customers pick their facility of choice according to its proximity. Thus, each facility must have sufficient capacity installed to accommodate all customers for whom it is the closest one. Facilities can be opened either in the protected or unprotected mode. Protection immunizes against an attacker who is capable of destroying at most r unprotected facilities in the worst-case scenario. Partial protection or interdiction is not possible. The defender selects facility sites from m candidate locations which have different costs. The attacker is assumed to know the unprotected facilities with certainty. He makes his interdiction plan so as to maximize the total post-attack cost incurred by the defender. If a facility has been interdicted, its customers are reallocated to the closest available facilities making capacity expansion necessary. The problem is formulated as a static Stackelberg game between the defender (leader) and the attacker (follower). Two solution methods are proposed. The first is a tabu search heuristic where a hash function calculates and records the hash values of all visited solutions for the purpose of avoiding cycling. The second is a sequential method in which the location and protection decisions are separated. Both methods are tested on 60 randomly generated instances in which m ranges from 10 to 30, and r varies between 1 and 3. The solutions are further validated by means of an exhaustive search algorithm. Test results show that the defender's facility opening plan is sensitive to the protection and distance costs.

Variable capacity sizing and selection of connections in a facility layout

The variable capacity sizing and selection of connections in the facilities design context is discussed (to the best knowledge of the authors) for the first time in the open literature. A connection is defined as the connected part that links di1erent sets of departments through which some interdepartmental material flows must go. The goal of the problem is to select the location and capacity of the connections (and to assign the flows) so as to minimize the sum of the fixed connection installation costs and material movement cost in the material handing system. Mathematical programming formulations are presented for continuous and discrete capacity options. For the continuous unbounded capacity case, we prove that it can be reduced to the uncapacitated fixed charge facility location problem. For the discrete capacity case, a Lagrangian relaxation-based solution approach is developed. It provides a 'good' feasible solution as well as a lower bound for assessing the optimality gap. Computational results are reported. Our findings indicate that the discrete version of the problem can be e1ectively solved with the Lagrangian heuristic.

The fixed charge facility location problem with coverage restrictions

Abstract This paper develops a fixed charge facility location model with coverage restrictions, minimizing cost while maintaining an appropriate level of service, in identifying facility locations. Further, it discusses the insights that can be gained using the model. Two Lagrangian relaxation based heuristics are presented and tested. Both heuristics use a greedy adding algorithm to calculate upper bounds and subgradient optimization to calculate lower bounds. While both procedures are capable of generating good solutions, one is computationally superior.