Capacitated Plant Location Problem Research Articles

The capacitated location problem of precast concrete component factory

The location and capacity of precast concrete component factories (PC component factories) are not only the key factors for manufacturers to gain competitive advantage, but also the important factors affecting the operational efficiency of the prefabricated construction supply chain. This paper takes the capacitated location problem of PC component factories as the research object. Drawing on the model of traditional capacitated plant location problem, the model of capacitated location problem of PC component factories is constructed by setting the optional production scale by stages. According to the characteristics of this model, the optimal strategy of location is determined by using the Tabu search algorithm. Taking the location problem of PC component factory in the Beijing-Tianjin-Hebei region as the object, the calculation example is designed, in which the influence of the distance parameters on the results of location problem is analyzed. The results can make the configuration of regional PC component factories more reasonable and balanced.

Learning management system‐integrated spreadsheet exercises for facility location modeling

AbstractSupply chain management students are introduced to a variety of modeling concepts. Yet learning facility location and capacity allocation modeling to the level of application and mastery proves difficult for the typical undergraduate business student. Spreadsheets facilitate the teaching of optimization modeling; however, providing feedback to students on spreadsheet assignments is an onerous and time‐consuming task for instructors. In this teaching brief, a set of learning management system (LMS)‐integrated spreadsheet exercises is presented which helps students learn spreadsheet modeling for the capacitated plant location problem. These exercises are also designed to reduce the instructor's grading burden while providing timely feedback and assessment of student performance. The effectiveness of the exercises is demonstrated by assessment data gathered from the LMS as well as postmodule student survey results.

A capacitated plant location model for Reverse Logistics Activities

Product remanufacturing is one of the most profitable activities in reverse logistics. Running a business plan, in which companies take responsibility for the waste generated at their end-of-life products, involves making important strategic decisions. One of the challenges in planning the reverse flow of products is decide where installing the reprocessing facilities. This decision influences directly the transport variables costs and the facilities installation fixed costs. This paper proposes a model for the Capacitated Plant Location Problem in Reverse Logistics (CPL-RL), in which we assume that offered material in each collection center is aimed at a single facility for reprocessing. This restriction includes specific cases where there is no logistic availability in the network to send the collected material to different locations. The Mixed Integer Problem (MILP) is solved using an algorithm in two steps. In the first step, reduction tests are performed, which ones determine a priori which facilities are opened/closed. If all facilities are fixed opened or closed then the solution is optimal. Although not all facilities can have their status defined that way, the resultant problem has a less number of variables and it is solved using Benders method. The dataset was randomly generated and the results showed that the applied techniques are appropriate, achieving the optimal solution for all test problems.

Multi-Source Capacitated Plant Location Problem with Customer and Supplier Matching

In this paper, we study the multi-source capacitated plant location problem with customer and supplier matching. A distribution and a supply trip are merged into one triangular trip for saving transportation and allocation costs. Vehicles from plants visit a customer and a supplier for each trip, but each customer can be related to more than one plant and supplier. It is formulated as a mixed integer linear programming problem, and the Lagrangian relaxation is used to solve it. Our computational experiments on several randomly generated test problems confirm the effectiveness of the Lagrangian relaxation approach.

Approaches to Solve MID_CPLP Problem: Theoretical Framework and Empirical Investigation

In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses); and finally to the markets. We aim to minimize the sum of location costs of the warehouses at stage-1 and stage-2; plus the total distribution cost of goods to the markets. In this paper two-stage capacitated warehouse location problem (TSCWLP) is vertically decomposed into the smaller problems, which is attained by relaxing the associated flow balance constraints. This leads to three different versions of Capacitated Plant Location Problem (CPLP) referred as RHS_CPLP, MID_CPLP and LHS_CPLP (Verma and Sharma REF _Ref387068711 \r \h [1]). In this paper MID_CPLP is reduced to RHS_CPLP and a single constraint 0-1 Knapsack problem by relaxing a difficult constraint. Interesting results and conjectures are given. Later two more valid constraints are added to MID_CPLP which are relaxed further to get additional results.

The capacitated plant location problem with customer and supplier matching and interval demands uncertainty

The capacitated plant location problem with customer and supplier matching can be modeled as a mixed integer linear program, where the product distribution from plants to customers and the material supply from suppliers to plants are considered together. In order to save allocation cost, distribution trip and a supply trip is merged into one triangular trip. Moreover, vehicles from plants visit a customer and a supplier for each trip. In this paper, we assume interval uncertainties in the demands of costumers. We show that the robust counterpart of the original model with interval uncertainty is equivalent to a larger mixed integer linear program. Finally, the original and robust models are compared on several randomly generated examples showing the impact of uncertainty.

A risk management model for the plant location problem

This paper proposes a risk management model for the facility location problems in a fuzzy environment. We investigate the capacitated plant location problem in continuous space as a risk model. Three risk types are considered in the proposed model: customer risk, financial risk and supply risk. The risks are caused because of unsatisfied demands, budget constraint and capacity constraint, respectively. The introduced model is an extension of the continuous plant location model by adding capacity constraint. A facility belongs to a zone when it is located in a predetermined radius from the centre of the zone. Because of uncertain budget and demand, the model is considered in a fuzzy environment. Finally, a risk management model is proposed with the presentation of a degree of satisfaction concept for each risk as an objective function. Also, a numerical example with sensitivity analysis is presented to illustrate the proposed model.

Vertical Decomposition Approach to Solve Single Stage Capacitated Warehouse Location Problem (SSCWLP)

Single Stage Capacitated Warehouse Location Problem (SSCWLP) has been attempted by few researchers in the past. These are Geoffrion and Graves [1], Sharma [2], Sharma [3] and Sharma and Berry [4]. In this paper we give a “vertical decomposition” approach to solve SSCWLP that uses Lagrangian relaxation. This way SSCWLP is broken into two versions of capacitated plant location problem (the CPLP_L and CPLP_R) by relaxing the flow balance constraints. For CPLP_R, we use well known Lagrangian relaxations given in literature (Christofides and Beasley [5] and Nauss [6]); and adopt them suitably for solving CPLP_L. We show theoretically in this paper that SSCWLP can be more efficiently solved by techniques of vertical decomposition developed in this paper than the method available in literature (Sharma and Berry [4]). Encouraging computational study is reported in this paper.

A computational comparison of several models for the exact solution of the capacity and distance constrained plant location problem

The Capacity and Distance Constrained Plant Location Problem is an extension of the discrete capacitated plant location problem, where the customers assigned to each plant have to be assigned to vehicles. In addition to the capacity constraints on the plants, there is a limit on the total distance traveled by each vehicle to serve its assigned customers by means of round trips. This paper presents several formulations for the problem and proposes different families of valid inequalities. The results of extensive computational experiments are presented and analyzed.

A hybrid algorithm for capacitated plant location problem

This paper presents a new hybrid algorithm for a classical capacitated plant location problem. Benders’ decomposition algorithm has been successfully applied in many areas. A major difficulty with this decomposition lies in the solution of master problem, which is a “hard” problem, costly to compute. Our proposed algorithm, instead of using a costly branch-and-bound method, incorporates a genetic algorithm to obtain “good” suboptimal solutions to the master problem at a tremendous saving in the computational effort. The performance of the proposed algorithm is tested on randomly generated data and also well-known existing data. The computational results indicate that the proposed algorithm is effective and efficient for the capacitated plant location problem and competitive with the Benders’ decomposition algorithm.

Multiobjective capacitated plant location problem

Multicriteria decision-making is a field which is expanding rapidly. There has been increasing recognition that there is a practical need to explicitly consider several criteria simultaneously. It has been observed that most of the problems on facility location are in reality multicriteria problems. Fernandez, E. and Presto, J. (2003) have discussed the multiobjective uncapacitated plant location problem. In practice, facilities may have constraining capacities on the amount of demand they can serve. To bridge this gap between theory and practice, we have considered the multiobjective capacitated plant location problem. The multiobjective plant location problem is decomposed into two sub-problems. The allocation of plants to the clients when the capacities are restricted has been discussed in detail. Two algorithms are presented to solve the allocation problem. The method used by Fernandez and Puerto (2003) has been modified to solve this problem. It is illustrated with the help of examples.

The capacitated plant location problem with customers and suppliers matching

This paper introduces a new problem called the capacitated plant location problem with customer and supplier matching (CLCSM). The product distribution from plants to customers and the material supply from suppliers to plants are considered together. We merge a distribution trip and a supply trip into one triangular trip for saving allocation cost. Vehicles from plants visit a customer and a supplier for each trip. We provide a heuristic solution procedure based on Lagrangian relaxation. Computational results indicate that the proposed heuristic solution procedure is shown to be efficient yielding optimal or near-optimal solutions for randomly generated instances.

Study on capacitated plant location problem based on immune clone algorithm

The Capacitated Plant Location Problem (CPLP) is a NP problem and hard to get an optimal and satisfactory solution. Regarding the shortage of the existing solutions, an Immune Clone (IC)-based algorithm was presented in this paper. The algorithm adopted different coding, antibody generation, clonal selection, somatic hypermutation, clonal restraint, and antibody supplement strategies from the general IC algorithm. Experimental results show that the IC-based algorithm could converge to global optimal solution rapidly and solve the Capacitated Plant Location Problem effectively. It can avoid the convergence to the local optimal solution and overcome the slow convergence of the Genetic Algorithm (GA).

Lower and upper bounds for a capacitated plant location problem with multicommodity flow

In this paper, we introduce a capacitated plant location problem with multicommodity flow. Given a set of potential plant sites and a set of capacitated arcs linking plants, transshipment points and customers, the aim is to determine where to locate plants and how to move flows from open plants to customers through a set of transshipment points. This model extends the classical capacitated plant location problem by introducing a multicommodity flow problem in the distribution issue. The combination of the location problem and the flow distribution problem is reasonable and realistic since both of them belong to strategic planning horizons. We propose a Lagrangean-based method, including a Lagrangean relaxation, a Lagrangean heuristic and a subgradient optimization, to provide lower and upper bounds of the model. Then, we employ a Tabu search to further improve upper bounds provided by the Lagrangean procedure. The computational results demonstrate that our solution method is effective since gaps between the upper and lower bound are on average around 2%.

A branch and bound algorithm for the partial coverage capacitated plant location problem

In this paper, a branch and bound algorithm for the partial coverage capacitated facility locations problem is developed. We have to fix open a set of warehouses which are economically feasible. It is an extension of the algorithm given by B. M. Khumawala [10] and Sudha Arora and S.R. Arora [2]. The case when the demand of the customer may not be satisfied completely, giving rise to “opportunity demand” is also discussed. This is illustrated with the help of examples and their computational results.

The capacity and distance constrained plant location problem

This article introduces a new problem called the Capacity and Distance Constrained Plant Location Problem. It is an extension of the discrete capacitated plant location problem, where the customers assigned to each plant have to be packed in groups that will be served by one vehicle each. The constraints include two types of capacity. On the one hand plants are capacitated, and the demands of the customers are indivisible. On the other hand, the total distance traveled by each vehicle to serve its assigned customers in round trips plant–customer–plant is also limited. The paper addresses different modeling aspects of the problem. It describes a tabu search algorithm for its solution. Extensive computational tests indicate that the proposed heuristic consistently yields optimal or near-optimal solutions.

ANT COLONY OPTIMIZATION ALGORITHM FOR THE CAPACITATED PLANT LOCATION PROBLEM

There is considered the capacitated plant location problem in this paper. This problem is a generalization of the simple plant location problem, which is a well-known NP-hard combinatorial optimization problem. In the paper there is proposed an ant colony optimization algorithm for the capacitated plant location problem. Computational experiments on benchmark instances show that the method obtains solutions for the majority of test instances better than the best-known results obtained by other heuristics tested.

Bounds for the single source modular capacitated plant location problem

In this paper, we propose a discrete location problem, which we call the Single Source Modular Capacitated Location Problem (SS-MCLP). The problem consists of finding the location and capacity of the facilities, to serve a set of customers at a minimum total cost. The demand of each customer must be satisfied by one facility only and the capacities of the open facilities must be chosen from a finite and discrete set of allowable capacities. Because the SS-MCLP is a difficult problem, a lagrangean heuristic, enhanced by tabu search or local search was developed in order to obtain good feasible solutions. When needed, the lower bounds are used in order to evaluate the quality of the feasible solutions. Our method was tested computationally on randomly generated test problems some of which are with large dimensions considering the literature related to this type of problem. The computational results obtained were compared with those provided by the commercial software Cplex.

On Identifying Maximal Covers

In this paper we present an efficient procedure for identifying all maximal covers from the set of covers implied by a 0-1 knapsack constraint. It requires tight bounds for the cardinality of certain minimal covers and an ordering of the covers implied by the knapsack constraint. This type of maximal cover can be very useful for tightening 0-1 models. We also present a modification of the procedure to identify only maximal covers whose induced inequalities are violated by a given fractional solution. Some computational experiments are reported for randomly generated 0-1 knapsack constraints and for single source capacitated plant location problem instances drawn from the literature.

An ADD/DROP procedure for the capacitated plant location problem

The capacitated plant location problem with linear transportation costs is considered. Exact rules and heuristics are presented for opening or closing of facilities. A heuristic algorithm based on ADD/DROP strategies is proposed. Procedures are implemented with the help of lower and upper bounds using Lagrangean relaxation. Computational results are presented and comparisons with other algorithms are made.