Relevant Network Distances for Approximate Approach to Large p-Median Problems

Gábrišová

2019

Transport

The usual approach to emergency system design consists in deploying a given number of service centers to minimize the disutility perceived by an average user, what is called “min-sum” or “system approach”. As a user in emergency tries to obtain service from the nearest service center, the min-sum optimal deployment may cause such partitioning of the users’ set into clusters serviced by one center that population of users is unequally distributed among centers. Within this paper, we focus on user-fair design of emergency service systems, where the fair approach is not applied on the individual users, but on the clusters serviced by one center. The fairer deployment should prevent the users to some extent from frequent occurrence of the situation, when the nearest service center to a current demand location is occupied by servicing some previously raised demand. In such case, the current demand must be assigned to a more distant center. To achieve fairer design of emergency system, we present four approaches to the design problem together with their implementation and comparison using numerical experiments performed with several real-sized benchmarks.

Section: Literature Reviewmentioning

confidence: 99%

User-Fair Designing Emergency Service Systems

Gábrišová

2019

Transport

“…In the benchmarks, the generalized disutility perceived by a user sharing a given location was the sum of three distances from the user's location to the three nearest vehicle locations. The suffixes BG and BGh denote bisection approaches, where the IP-solver solves the optimization problem for a fixed value G t at each step t. The denotation BG corresponds to the models (18), (3)-(6), (8), (9), (19) or (23), (12), (13), (15), (16), (24), while the denotation BGh is used for the models (20), (3)- (6), (8), (9), (21), (22) or (25), (12), (13), (15), (16), (26), (22) depending on location-allocation or radial formulations. To solve the problems described by the mentioned models, optimization software FICO Xpress 7.3 (64-bit, release 2012) was used and the experiments were run on a PC equipped with the Intel® Core™ i7 3610 QM processor, at 2.3 GHz and with 8 GB RAM.…”

Section: Computational Studymentioning

confidence: 99%

“…In this paper, we focus on a problem-solving method for the initial phase, when the generalized disutility is considered. Based on our experiences in designing the min-sum optimal public service system, we found that the radial formulation of the problem can considerably accelerate the associated problem-solving process [1,4,6,8]. Furthermore, we can start from our previous research [7,10], where we developed and successfully tested radial formulation of the min-sum service system design problem with the generalized disutility.…”

Section: Introductionmentioning

confidence: 99%

Min-max optimization and the radial approach to the public service system design with generalized utility

Kvet

2016

Croat. Oper. Res. Rev.

Self Cite

Abstract. The paper deals with the min-max public service system design, where the generalized utility is considered. In contrast to the formulations presented in the literature, the generalized utility defined for a public service system assumes that the user's utility comes generally from more than one located service center and the individual contributions from relevant centers are weighted by reduction coefficients depending on a center order. Given that commercial IP-solvers often fail due to enormous computational times or extreme memory demands when resolving this issue, we suggested and compared several approaches based on a bisection process with the purpose of developing an effective max-min approach to the public service system design with a generalized utility.

“…Regardless of the type of distance, representing travelling time, cost or other form of social costs, this approach usually involves the weighted p-median problem [8,9]. Complexity of the pmedian problem and the necessity to solve large instances of the problem has led to the search for a suitable algorithm suitable to the task.…”

Section: Introductionmentioning

confidence: 99%

Min-max optimal public service system design

Kvet

2015

Croat. Oper. Res. Rev.

Self Cite

Abstract. This paper deals with designing a fair public service system. To achieve fairness, various schemes are be applied. The strongest criterion in the process is minimization of disutility of the worst situated users and then optimization of disutility of the better situated users under the condition that disutility of the worst situated users does not worsen, otherwise called lexicographical minimization. Focusing on the first step, this paper endeavours to find an effective solution to the weighted p-median problem based on radial formulation. Attempts at solving real instances when using a location-allocation model often fail due to enormous computational time or huge memory demands. Radial formulation can be implemented using commercial optimisation software. The main goal of this study is to show that the suitability solving of the minmax optimal public service system design can save computational time.