A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones

Quantity and Location Decision of Fresh Food Distribution Centers for a Supermarket Chain under Carbon Policies

Supermarket chains handle frequent deliveries of fresh food to the stores, which have led to the non-ignorable high transportation cost. Then a question arises that is it possible to reduce cost by establishing more refrigerated distribution centers (DC)? To answer this question, on basis of data from a large supermarket chain in China, we analyze the decision making process to construct new sub DCs. A balance of the DC cost and the transportation cost is achieved to gain the optimal number and location of sub DCs. We also extend the model to situations with carbon policies (carbon tax policy and carbon cap-and-trade policy). The locations of sub DCs remain the same under carbon policies. Furthermore, a carbon tax policy does not change the number of sub DCs and only causes an increase in the total cost. Under a carbon cap-and-trade policy the optimal decision of the DC number is dependent on the carbon selling rule

Enhanced cell-based algorithm with dynamic radius in solving capacitated multi-source weber problem

Capacitated Multi-source Weber Problem (CMSWP) is a type of Location Allocation Problem (LAP) which have been extensively researched because they can be applied in a variety of contexts. Random selection of facility location in a Cell-based approach may cause infeasible or worse solutions. This is due to the unprofitable cells are not excluded and maybe selected for locating facilities. As a result, the total transportation cost increases, and solution quality is not much improved. This research finds the location of facilities in a continuous space to meet the demand of customers which minimize the total cost using Enhanced Cell-based Algorithm (ECBA). This method was derived from previous study that divides the distribution of customers into smaller cells of promising locations. The methodology consists of three phases. First, the profitable cells were constructed by applying ECBA. Second, initial facility configuration was determined using fixed and dynamic radius. Third, Alternating Transportation Problem (ATL) was applied to find a new location. The algorithm was tested on a dataset of three sizes which are 50, 654 and 1060 customers. The computational results of the algorithm prove that the results are superior in terms of total distance compared to the result of previous studies. This study provides useful knowledge to other researchers to find strategic facilities locations by considering their capacities

Hybrid Cell Selection-based Heuristic for capacitated multi-facility Weber problem with continuous fixed costs

This is the final version. Available on open access from EDP Sciences via the DOI in this recordLocation-allocation problem (LAP) has attracted much attention in facility location field. The LAP in continuous plane is well-known as Weber problem. This paper assessed this problem by considering capacity constraints and fixed costs as each facility has different setup cost and capacity limit to serve customers. Previous studies considered profitable areas by dividing continuous space into a discrete number of equal cells to identify optimal locations from a smaller set of promising locations. Unfortunately, it may lead to avoid choosing good locations because unprofitable areas are still considered while locating the facilities. Hence, this allows a significant increment in the transportation costs. Thus, this paper intelligently selected profitable area through a hybridization of enhanced Cell Selection-based Heuristic (CSBH) and Furthest Distance Rule (FDR) to minimize total transportation and fixed costs. The CSBH divides customer distribution into smaller set of promising locations and intelligently selected profitable area to increase possibility of finding better locations, while FDR aims to forbid the new locations of the facilities to be close to the previously selected locations. Numerical experiments tested on well-known benchmark datasets showed that the results of hybrid heuristic outperformed single CSBH and FDR, while producing competitive results when compared with previously published results, apart from significantly improving total transportation cost. The new hybrid heuristic is simple yet effective in solving LAP

A new local search for . . .

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulatio

An allocation based modeling and solution framework for location problems with dense demand /

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm