Uncapacitated Fixed-charge Location Problem Research Articles

Reliable Facility Systems Design Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

The reliability of facility location problem has aroused wide concern recently. Many researchers focus on reliable and robust facility systems design under component failures and have obtained promising performance. However, the target and reliability of a facility system are to a large degree adversely affected by the edge failures in the network, which remains a deep study. In this paper, we focus on facility systems’ reliability subject to edge failures. For a facility location system, we formulate two models based on classical uncapacitated fixed-charge location problem under deterministic and stochastic cases. For a specific example, location decisions and the comparison of reliability under different location models are given. Extensive experiments verify that significant improvements in reliability can be attained simply by increasing the amount of operating cost.

An Efficient Approach for Solving Reliable Facility Location Models

We consider reliable facility location models in which facilities are subject to unexpected failures, and customers may be reassigned to facilities other than their regular facilities. The objective is to minimize the total expected costs in normal and failure scenarios. We allow facilities to have different failure rates and do not limit the number of facilities that might be assigned to a customer. Lower bounds for reliable uncapacitated fixed-charge location problem (RUFLP) are derived and used to introduce a class of efficient algorithms for solving the RUFLP problem.

Critical supply network protection against intentional attacks: A game-theoretical model

A crucial issue in today's critical supply chains is how to protect facilities against intentional attacks, since it has become unacceptable to ignore the high impact of low probability disruptions caused by these attacks. This article develops a game-theoretical model to deal with the protection of facilities, in the context of the uncapacitated fixed-charge location problem. Given a set of investment alternatives for protecting the facilities against identified threats, the objective is to select the optimal defence strategy. The attacker is considered as a player who tries to maximise the expected damage while weighing against the attacks expenditures. The conflict on facilities vulnerability is modelled using the concept of contest. The vulnerability of a facility is defined by its destruction probability. Contest success functions determine the vulnerability of each facility dependent on the relative investments of the defender and the attacker on each facility, and on the characteristics of the contest. A method is developed to evaluate the utilities of the players (i.e., the defender and the attacker). This method evaluates many expected costs, including the cost needed to restore disabled facilities, the backorder cost, and the cost incurred because of the increase in transportation costs after attacks. In fact, when one or several facilities are unavailable, transportation costs will increase since reassigned customers may receive shipments from facilities which are farther away. The model considers a non-cooperative two-period game between the players, and an algorithm is presented to determine the equilibrium solution and the optimal defence strategy. An illustrative example is presented. The approach is compared to other suggested strategies, and some managerial insights are provided in the context of facility location.

Reliable Facility Location Design Under Uncertain Correlated Disruptions

Most of the previous studies on reliable facility location design assume that disruptions at different locations are independent. In this paper, we present a model that allows disruptions to be correlated with an uncertain joint distribution, and apply distributionally-robust optimization to minimize the expected cost under the worst-case distribution with the prespecified marginal disruption probabilities. We find this robust model to be advantageous in several aspects. First, the worst-case disruption distribution reflects a practical situation, known as the “ripple effect”, where a disastrous event at one source affects facilities within an impact region. Second, the structure of the worst-case distribution allows reformulating this seemingly much more complicated problem as a much easier stochastic program. Third, in a numerical study for the uncapacitated fixed-charge location problem, we find that failing to consider correlation could lead to excessive loss, which is also increasing in important factors such as disruption probability, propagation effect, and service interruption penalty. On the other hand, the robust model results in much lower regret even when disruptions are actually independent. Thus, we believe the robust optimization model could serve as an alternative approach for solving reliable facility location problems. Compared to the traditional approach, it better captures disruption propagation, requires much less computational effort, and delivers more favorable designs.

Reliable facility location design under disruptions

Distribution networks have been facing an increased exposure to risk of unpredicted disruptions causing significant economic forfeitures. At the same time, the existing literature features very few studies which examine the impact of facility fortification for improving network reliability. In this paper, we present two related models for design of reliable distribution networks: a reliable P-median problem (RPMP) and a reliable uncapacitated fixed-charge location problem (RUFL). Both models consider heterogenous facility failure probabilities, one layer of supplier backup, and facility fortification within a finite budget. Both RPMP and RUFL are formulated as nonlinear integer programming models and proved to be NP-hard. We develop Lagrangian relaxation-based (LR) solution algorithms and demonstrate their computational efficiency. We compare the effectiveness of the LR-based solutions to that of the solutions obtained by a myopic policy which aims to fortify most reliable facilities regardless of the demand topology. Finally, we discuss an alternative way to assess the effectiveness of the design solutions by using the rate of return on fortification investment.

Reliability Analysis of Systems Based on the UFLP under Facility Failure and Conditional Supply Cases

The reliability of facility location problems has been received wide attention for several decades. Researchers formulate varied models to optimize the reliability of location decisions. But the most of such studies are not practical since the models are too ideal. In this paper, based on the classical uncapacitated fixed-charge location problem (UFLP) and some supply constraints from the reality, we distinguish deterministic facility failure and stochastic facility failure cases to formulate models to measure the reliability of a system. The computational results and reliability envelopes for a specific example are also given.

Reliability Analysis of Facility Systems Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. Such failures may be caused by various natural disasters or terrorist attacks. In this paper, we consider facility systems’ reliability analysis based on the classical uncapacitated fixed-charge location problem when subject to edge failures. For an existing facility system, we formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.

Reliable Facility Location Design Under the Risk of Disruptions

Reliable facility location models consider unexpected failures with site-dependent probabilities, as well as possible customer reassignment. This paper proposes a compact mixed integer program (MIP) formulation and a continuum approximation (CA) model to study the reliable uncapacitated fixed charge location problem (RUFL), which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios. The MIP determines the optimal facility locations as well as the optimal customer assignments and is solved using a custom-designed Lagrangian relaxation (LR) algorithm. The CA model predicts the total system cost without details about facility locations and customer assignments, and it provides a fast heuristic to find near-optimum solutions. Our computational results show that the LR algorithm is efficient for mid-sized RUFL problems and that the CA solutions are close to optimal in most of the test instances. For large-scale problems, the CA method is a good alternative to the LR algorithm that avoids prohibitively long running times.

A facility reliability problem: Formulation, properties, and algorithm

AbstractHaving a robustly designed supply chain network is one of the most effective ways to hedge against network disruptions because contingency plans in the event of a disruption are often significantly limited. In this article, we study the facility reliability problem: how to design a reliable supply chain network in the presence of random facility disruptions with the option of hardening selected facilities. We consider a facility location problem incorporating two types of facilities, one that is unreliable and another that is reliable (which is not subject to disruption, but is more expensive). We formulate this as a mixed integer programming model and develop a Lagrangian Relaxation‐based solution algorithm. We derive structural properties of the problem and show that for some values of the disruption probability, the problem reduces to the classical uncapacitated fixed charge location problem. In addition, we show that the proposed solution algorithm is not only capable of solving large‐scale problems, but is also computationally effective. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010

A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions

This paper studies the reliable uncapacitated fixed charge location problem (RUFL) where facilities are subject to spatially correlated disruptions that occur with location-dependent probabilities (due to reasons such as natural or man-made disasters). If a facility fails, its customers are diverted to other facilities and incur excessive transportation cost. We develop a continuum approximation (CA) model to minimize the sum of initial facility construction costs and expected customer transportation costs under normal and failure scenarios. The paper presents ways to formulate the correlation among adjacent facility disruptions, and incorporates such correlations into the CA model. Numerical experiments are conducted to illustrate how the proposed model can be used to optimize facility location design, and how the correlations influence the total system cost.

Reliability Models for Facility Location: The Expected Failure Cost Case

Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities “fail” from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.

Forecast horizons and dynamic facility location planning

We consider a dynamic facility location model in which the objective is to find a planning horizon, τ*, and a first period decision,X 1*, such thatX 1* is a first period decision for at least one optimal policy for all problems with planning horizons equal to or longer than τ*. In other words, we seek a planning horizon, τ*, such that conditions after τ* do not influence the choice of the optimal initial decision,X 1*. We call τ* aforecast horizon andX 1* anoptimal initial decision. For the dynamic uncapacitated fixed charge location problem, we show that simple conditions exist such that the initial decision depends on the length of the planning horizon. Thus, a strictly optimal forecast horizon and initial policy may not exist. We therefore introduce the concepts ofe-optimal forecast horizons and e-optimal initial solutions. Our computational experience inicates that such solutions can be found for practical problems. Although computing e-optimal forecast horizons and initial decisions can be cumbersome, this approach offers the potential for making significantly better decisions than those generated by other approaches. To illustrate this, we show that the use of the scenario planning approach can lead to the adoption of the worst possible initial decision under conditions of future uncertainty. On the basis of our results, it appears that the forecast horizon approach offers an attractive tool for making dynamic location decisions.