Location-allocation Problem Research Articles

A robust possibilistic programming approach to multi-period location–allocation of organ transplant centers under uncertainty

This paper presents a novel robust possibilistic programming model for a multi-period location–allocation problem in an organ transplant supply chain under inherent uncertainty of input data. The minimization of total costs is considered as objective function to elevate the efficiency of the studied supply chain network. The significance of applicability of the developed model is demonstrated via numerical experiments and some sensitivity analyses on the data inspired by a real Iranian organ transplant supply chain.

A two-level location–allocation problem in designing local access fiber optic networks

This paper deals with a two-level facility location–allocation problem on tree topology arising from the design of access networks. The access network design problem seeks to find an optimal location of switch and allocation of demands such that the total cost of switch and fiber cable is minimized, while satisfying switch port constraint, switch capacity constraint, and no-split routing constraint. The problem is formulated as a mixed-integer programming model and alternative formulations are developed by the reformulation-linearization technique (RLT) for improving computational effectiveness. By exploiting the tree structure of the problem, we develop some valid inequalities that have complementary strength and devise separation problems for finding effective valid inequalities that cut off fractional LP solutions. Also, we develop an effective MIP-based tree partitioning heuristic for finding good quality solutions for large size problems. Computational results demonstrate the efficacy of the valid inequalities and the proposed heuristic.

Distribution network design under demand uncertainty using genetic algorithm and Monte Carlo simulation approach: a case study in pharmaceutical industry

Distribution network design as a strategic decision has long-term effect on tactical and operational supply chain management. In this research, the location–allocation problem is studied under demand uncertainty. The purposes of this study were to specify the optimal number and location of distribution centers and to determine the allocation of customer demands to distribution centers. The main feature of this research is solving the model with unknown demand function which is suitable with the real-world problems. To consider the uncertainty, a set of possible scenarios for customer demands is created based on the Monte Carlo simulation. The coefficient of variation of costs is mentioned as a measure of risk and the most stable structure for firm’s distribution network is defined based on the concept of robust optimization. The best structure is identified using genetic algorithms and 14 % reduction in total supply chain costs is the outcome. Moreover, it imposes the least cost variation created by fluctuation in customer demands (such as epidemic diseases outbreak in some areas of the country) to the logistical system. It is noteworthy that this research is done in one of the largest pharmaceutical distribution firms in Iran.

A multi-objective model for facility location–allocation problem with immobile servers within queuing framework

This research investigates a practical bi-objective model for the facility location–allocation (BOFLA) problem with immobile servers and stochastic demand within the M/M/1/K queue system. The first goal of the research is to develop a mathematical model in which customers and service providers are considered as perspectives. The objectives of the developed model are minimization of the total cost of server provider and minimization of the total time of customers. This model has different real world applications, including locating bank automated teller machines (ATMs), different types of vendor machines, etc. For solving the model, two popular multi-objective evolutionary algorithms (MOEA) of the literature are implemented. The first algorithm is non-dominated sorted genetic algorithm (NSGA-II) and the second one is non-dominated ranked genetic algorithm (NRGA). Moreover, to illustrate the effectiveness of the proposed algorithms, some numerical examples are presented and analyzed statistically. The results indicate that the proposed algorithms provide an effective means to solve the problems.

A multiobjective optimization approach for location‐allocation of clinics

AbstractIn order to establish new healthcare facilities, their optimal number and locations should be determined. Unsuitable locations for these facilities may result in substandard customer services and increased expenses. To solve this location‐allocation problem, this study applied a multiobjective model that combined geographical information system (GIS) analysis with a multiobjective genetic algorithm. Optimum sites for new clinics were determined by considering four objectives: minimizing total travel cost, minimizing inequity in access to clinics, minimizing the land‐use incompatibility in the study area, and minimizing the costs of land acquisition and facility establishment. Chromosomes of varying lengths were used in the multiobjective optimization process. An important advantage of this is that multiple optimal solutions with different numbers of healthcare facilities can be compared directly. An a posteriori preference method was used in this study. TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) was applied to assess and compare the Pareto‐optimal solutions and to select the best solution according to different weight vectors. Visualization of the best solution according to each weight vector and compromising among different objectives provided valuable possibilities for selection of the best alternative to decision makers.

Up- and downgrading the euclidean 1-median problem and knapsack Voronoi diagrams

We consider the 1-median problem with euclidean distances with uncertainty in the weights, expressed as possible changes within given bounds and a single budget constraint on the total cost of change. The upgrading (resp. downgrading) problem consists of minimizing (resp. maximizing) the optimal 1-median objective value over these weight changes. The upgrading problem is shown to belong to the family of continuous single facility location-allocation problems, whereas the downgrading problem reduces to a convex but highly non-differentiable optimization problem. Several structural properties of the optimal solution are proven for both problems, using novel planar partitions, the knapsack Voronoi diagrams, and lead to polynomial time solution algorithms.

A hybrid multi-objective approach to capacitated facility location with flexible store allocation for green logistics modeling

We propose an efficient evolutionary multi-objective optimization approach to the capacitated facility location–allocation problem (CFLP) for solving large instances that considers flexibility at the allocation level, where financial costs and CO2 emissions are considered simultaneously. Our approach utilizes suitably adapted Lagrangian Relaxation models for dealing with costs and CO2 emissions at the allocation level, within a multi-objective evolutionary framework at the location level. Thus our method assesses the robustness of each location solution with respect to our two objectives for customer allocation. We extend our exploration of selected solutions by considering a range of trade-offs for customer allocation.

A multi-objective harmony search algorithm to optimize multi-server location–allocation problem in congested systems

A novel bi-objective multi-server location–allocation (LA) model is developed in this paper, in which the facilities are modeled as an M/M/m queuing system. Further, capacity and budget limitations are provided to make the LA problem more realistic. The two objective functions include (1) minimizing aggregate waiting times and (2) minimizing the maximum idle time of all facilities. Since the proposed model is NP-hard, a meta-heuristic algorithm called multi-objective harmony search algorithm (MOHA) is developed to solve it. In this algorithm, a new presentation scheme that satisfies most of the model constraints is proposed. Since there is no benchmark available in the literature to validate the results obtained, the performance of MOHA is statistically compared with the ones of two other common meta-heuristics called multi-objective genetic algorithm (MOGA) and multi-objective simulated annealing (MOSA). The parameters of all algorithms are first calibrated by means of the Taguchi method using a novel metric. The comparison results based on different problem sizes are in favor of MOHA.

Efficient solution of a class of location–allocation problems with stochastic demand and congestion

We consider a class of location–allocation problems with immobile servers, stochastic demand and congestion that arises in several planning contexts: location of emergency medical clinics; preventive healthcare centers; refuse collection and disposal centers; stores and service centers; bank branches and automated banking machines; internet mirror sites; web service providers (servers); and distribution centers in supply chains. The problem seeks to simultaneously locate service facilities, equip them with appropriate capacities, and allocate user demand to these facilities such that the total cost, which consists of the fixed cost of opening facilities with sufficient capacities, the access cost of users׳ travel to facilities, and the queuing delay cost, is minimized. Under Poisson user demand arrivals and general service time distributions, the problem is set up as a network of independent M/G/1 queues, whose locations, capacities and service zones need to be determined. The resulting mathematical model is a non-linear integer program. Using simple transformation and piecewise linear approximation, the model is linearized and solved to ϵ-optimality using a constraint generation method. Computational results are presented for instances up to 400 users, 25 potential service facilities, and 5 capacity levels with different coefficients of variation of service times and average queueing delay costs per customer. The results indicate that the proposed solution method is efficient in solving a wide range of problem instances.

A hyperbolic smoothing approach to the Multisource Weber problem

The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-distances clustering problem, also known as the continuous $$p$$ p -median problem. The mathematical modelling of this problem leads to a $$min-sum-min$$ m i n - s u m - m i n formulation which, in addition to its intrinsic bi-level nature, is strongly nondifferentiable. Moreover, it has a large number of local minimizers, so it is a typical global optimization problem. In order to overcome the intrinsic difficulties of the problem, the so called Hyperbolic Smoothing methodology, which follows a smoothing strategy using a special $$ \, C^{\infty } \, $$ C � differentiable class function, is adopted. The final solution is obtained by solving a sequence of low dimension $$ \, C^{\infty } \, $$ C � differentiable unconstrained optimization sub-problems which gradually approaches the original problem. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments making use of traditional test problems described in the literature was performed. Apart from consistently presenting better results when compared to related approaches, the novel technique introduced here was able to deal with instances never tackled before in the context of the Multisource Weber problem.

An access network design problem with end-to-end QoS constraints

In this paper, we present an access network design problem with end-to-end quality of service (QoS) requirement. The problem can be conceptualized as a two-level hierarchical location-allocation problem on the tree topology with nonlinear side constraints. The objective function of the nonlinear mixed integer programming model minimizes the total cost of switch and fiber cable, while satisfying demand within the prescribed level of QoS. By exploiting the inherent structure of the nonlinear QoS constraints, we develop linearization techniques for finding an optimal solution. Also, we devise an effective exact optimal algorithm within the context of disjunctive constraint generation. We present promising computational results that demonstrate the effectiveness of the proposed solution procedure.

An integrated fuzzy QFD and fuzzy goal programming approach for global facility location-allocation problem

Companies pursuing extension of their activities and new companies in establishment phase are using various concepts and techniques to consider location decision, because location greatly affects both fixed and variable costs and on the overall profit of the company. This paper suggests a new use of quality function deployment (QFD) for facility location selection problem instead of applying it to traditional product quality promotion. Fuzzy sets concept is also incorporated to deal with imprecise nature of the linguistic judgments of decision makers. First, fuzzy QFD as a stand-alone approach is presented to address international facility location selection decision. To consider resource limitations and operational constraints, fuzzy goal programming is combined with fuzzy quality function deployment to present a developed approach to deal with global facility location-allocation decision. A demonstration of the applicability of proposed methodologies in a real-world problem is presented.

The $$\alpha $$ α -cost minimization model for capacitated facility location-allocation problem with uncertain demands

Facility location-allocation problem aims at determining the locations of some facilities to serve a set of spatially distributed customers and the allocation of each customer to the facilities such that the total transportation cost is minimized. In real life, the facility location-allocation problem often comes with uncertainty for lack of the information about the customers' demands. Within the framework of uncertainty theory, this paper proposes an uncertain facility location-allocation model by means of chance-constraints, in which the customers' demands are assumed to be uncertain variables. An equivalent crisp model is obtained via the $$\alpha $$ ? -optimistic criterion of the total transportation cost. Besides, a hybrid intelligent algorithm is designed to solve the uncertain facility location-allocation problem, and its viability and effectiveness are illustrated by a numerical example.

An efficient optimization procedure for designing a capacitated distribution network with price-sensitive demand

This paper considers a location-allocation problem in a supply-chain distribution network with capacitated distribution centers and customers with price-sensitive demands. The problem determines location, allocation and price decisions in order to maximize the total profit under two supply policies. Serving all of the customers is compulsory under the first policy, but is optional under the second. The problem is formulated as a mixed-integer linear program and solved by a Lagrangian relaxation algorithm under each policy. The numerical study indicates that the proposed algorithms are highly efficient and effective for solving large-sized instances of the problem.

Distribution network design under demand uncertainty using genetic algorithm and Monte Carlo simulation approach: a case study in pharmaceutical industry

Distribution network design as a strategic decision has long-term effect on tactical and operational supply chain management. In this research, the location-allocation problem is studied under demand uncertainty. The purposes of this study were to specify the optimal number and location of distribution centers and to determine the allocation of customer demands to distribution centers. The main feature of this research is solving the model with unknown demand function which is suitable with the real-world problems. To consider the uncertainty, a set of possible scenarios for customer demands is created based on the Monte Carlo simulation. The coefficient of variation of costs is mentioned as a measure of risk and the most stable structure for firm's distribution network is defined based on the concept of robust optimization. The best structure is identified using genetic algorithms and 14% reduction in total supply chain costs is the outcome. Moreover, it imposes the least cost variation created by fluctuation in customer demands (such as epidemic diseases outbreak in some areas of the country) to the logistical system. It is noteworthy that this research is done in one of the largest pharmaceutical distribution firms in Iran.

Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD® , a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil; the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers; and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Minimum risk facility location-allocation problem with type-2 fuzzy variables.

Facility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers' demands on the choice of optimal location decisions and allocation plans. This leads to the formulation of the facility location-allocation (FLA) problem as a fuzzy minimum risk programming, in which the uncertain parameters are assumed to be characterized by type-2 fuzzy variables with known type-2 possibility distributions. Since the inherent complexity of type-2 fuzzy FLA may be troublesome, existing methods are no longer effective in handling the proposed problems directly. We first derive the critical value formula for possibility value-at-risk reduced fuzzy variable of type-2 triangular fuzzy variable. On the basis of formula obtained, we can convert original fuzzy FLA model into its equivalent parametric mixed integer programming form, which can be solved by conventional numerical algorithms or general-purpose software. Taking use of structural characteristics of the equivalent optimization, we design a parameter decomposition method. Finally, a numerical example is presented to highlight the significance of the fuzzy FLA model. The computational results show the credibility and superiority of the proposed parametric optimization method.

Offshore oil network design with transportation alternatives

Petroleum industry plays a vital role in the modern global economy, owing to the fact that it is the largest source of energy in the world. Design and planning of the oilfield developments have become crucial concerns of the oil industry managers. In addition, crude oil transportation plays a critical role in the global supply chain of oil industry. In this work, we develop a model to design the oilfield development and plan crude oil transportation problems. A mixed integer model is proposed to extend the classical facility location-allocation problems by several features. Additionally, the model supports the selection of the transportation system and the planning of pipeline networks installations. This work ends with two sensitivity analyses. Two one-factor-at-a-time sensitivity analyses have been done with respect to the length of the planning horizon and the number of potential wells.

Experiment Design for the Location-Allocation Problem

The allocation of facilities and customers is a key problem in the design of supply chains of companies. In this paper, this issue is approached by partitioning the territory in areas where the distribution points are allocated. The demand is modelled through a set of continuous functions based on the population density of the geographic units of the territory. Because the partitioning problem is NP hard, it is necessary to use heuristic methods to obtain reliable solutions in terms of quality and response time. The Neighborhood Variable Search and Simulated Annealing heuristics have been selected for the study because of their proven efficiency in difficult combinatorial optimization problems. The execution time is the variable chosen for a factorial experimental design to determine the best-performing heuristics in the problem. In order to compare the quality of the solutions in the territorial partition, we have chosen the execution time as the common parameter to compare the two heuristics. At this point, we have developed a factorial statistical experimental design to select the best heuristic approaches to this problem. Thus, we generate a territorial partition with the best performing heuristics for this problem and proceed to the application of the location-allocation model, where the demand is modelled by a set of continuous functions based on the population density of the geographical units of the territory.

Solving a Capacitated <i>p</i><sub><i></i></sub>-Median Location Allocation Problem Using Genetic Algorithm: A Case Study

Facility location-allocation problems have various applications in private and public sectors. A capacitated p-median problem is considered in this work which is computationally NP-Hard. The primary goal of this paper was to determine a set of p-facilities location in which all demand points are allocated and its average distance traveled from the customers’ location to the selected p-facilities is minimized. In addition, the model also considered supplier’s allocation for p facilities. A real world case study has been addressed, and genetic algorithm which consists of crossover and mutation operators was proposed in order to solve the problem. Computational results for different values of p were generated, and finally the optimum solution based on minimum cost was reported.