Competitive Facility Location Research Articles

Extensions to Competitive Facility Location with Multi-purpose Trips

Extensions to Competitive Facility Location with Multi-purpose Trips

Wireless sensor networks-based adaptive differential evolution for multimodal optimization problems

In wireless sensor networks (WSN), we often detect the monitoring areas among different sensors so that the sensors can be switched on and off adaptively to save energy and extend their lifetime. Inspired by the principle of WSN, a WSN-based adaptive differential evolution (WSNADE) algorithm is proposed in this paper, together with a WSN-based adaptive niching technique (WANT) and two novel strategies called protection-based dual-scale mutation (PDM) strategy and multi-level reset (MLR) strategy, for solving multimodal optimization problems (MMOPs). In WANT, each individual is considered as a sensor with its monitoring area. If the monitoring areas of two individuals intersect, which means these two individuals monitor the similar area and should be partitioned into the same niche. In this way, WANT can adaptively form a niche for each individual, avoiding the sensitivity of niching parameters. Based on WANT, the PDM strategy is designed to select the appropriate mutation strategy for each individual. Besides, to save fitness evaluations (FEs) for exploring more promising areas, the MLR strategy is developed to store the promising individuals and reset the stagnant individuals. The experimental results on 20 multimodal benchmark test functions in CEC2015 multimodal competition show that the proposed WSNADE algorithm generally performs better than or at least comparable with other state-of-the-art multimodal algorithms, including the winner of the CEC2015 competition. Finally, WSNADE is applied to a real-world multimodal application in multiple competitive facilities location design (MCFLD) problem to illustrate its practical applicability.

Data-Guided Gravity Model for Competitive Facility Location

Data-Guided Gravity Model for Competitive Facility Location

Customer selection rules in competitive facility location

Customer selection rules in competitive facility location

Upper Bound for the Competitive Facility Location Problem with Demand Uncertainty

Upper Bound for the Competitive Facility Location Problem with Demand Uncertainty

A refinement of the gravity model for competitive facility location

A refinement of the gravity model for competitive facility location

UPPER BOUND FOR THE COMPETITIVE FACILITY LOCATION PROBLEM WITH DEMAND UNCERTAINTY

We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenario. The problem to find the best solutions for the parties is formulated as a discrete bi-level mathematical programming problem. In the paper, we suggest a procedure to compute an upper bound for the objective function on subsets. The procedure could be employed in implicit enumeration schemes capable to compute an optimal solution for the problem under study. Within the procedure, additional constraints iteratively augment the high-point relaxation of the initial bi-level problem, what strengthens the relaxation and improves the upper bound’s quality. New procedure to generate such cuts allows to construct the strongest cuts without enumerating the parameters encoding them.

Sequential customers’ decisions in facility location with comparison-shopping

In the competitive facility location problem, a newcomer firm optimally locates its facilities and offers a product that is a substitute for those of the already located competitors, aiming at maximizing its market. Usual facility location models assume single-stop or single-facility trips. However, when products are non-homogeneous substitutes, customers may want to compare the products before making a decision (comparison-shopping). Moreover, decisions are often made sequentially as facilities are visited. We model for the first time, sequential customers’ decisions in multi-stop trips, represented using a nested logit rule. Customers make decisions at the place of origin (which facility to visit first), at the first visited facility (whether to buy, or not, or to continue comparing), and at the second facility visited (whether to purchase or not and in which facility). To adequately represent the drive to compare, we include in the customers’ utility the value of the gathered information, and the disutility of visiting facilities without purchasing. We propose a linear formulation with an efficient branch-and-cut approach. We analyze the location patterns in randomly generated instances, as well as in a case study on municipalities in Spain. The three-level nested, two-level nested, and multinomial logit rules are compared.

The Obnoxious Competitive Facility Location Model

The Obnoxious Competitive Facility Location Model

Additional Constraints for Dynamic Competitive Facility Location Problem

Additional Constraints for Dynamic Competitive Facility Location Problem

Competitive facility location under attrition

Competitive facility location under attrition

Intermediate service facility planning in a stochastic and competitive market: Incorporating agent-infrastructure interactions over networks

This paper presents a network-based multi-agent optimization model for the strategic planning of service facilities in a stochastic and competitive market. We focus on the type of service facilities that are of intermediate nature, i.e., users may need to deviate from the shortest path to receive/provide services in between the users’ planned origins and destinations. This problem has many applications in emerging transportation mobility, including dynamic ride-sharing hub design and competitive facility location and allocation problems for alternative fuel vehicle refueling stations. The main contribution of this paper is establishing a new multi-agent optimization framework considering decentralized decision makings of facility investors and users over a transportation network and providing rigorous analyses of its mathematical properties, such as uniqueness and existence of system equilibrium. In addition, we develop an exact convex reformulation of the original multi-agent optimization problems to overcome computational challenges brought by non-convexity. Extensive analysis on case studies showed how the proposed model can capture the complex interaction between different stakeholders in an uncertain environment. Additionally, our model allowed quantifying the value of stochastic modeling and information availability by exploring stochastic metrics, including value of stochastic solution (VSS) and expected value of perfect information (EVPI), in a multi-agent framework.

Joint location and cost planning in maximum capture facility location under random utilities

We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new facilities, aiming to maximize an expected captured customer demand, assuming that customers choose a facility among all available facilities according to a RUM model. We examine two RUM frameworks in the discrete choice literature, namely, the additive and multiplicative RUM. While the former has been widely used in facility location problems, we are the first to explore the latter in the context. We numerically show that the two RUM frameworks can well approximate each other in the context of the cost optimization problem. In addition, we show that, under the additive RUM framework, the resultant cost optimization problem becomes highly non-convex and may have several local optima. In contrast, the use of the multiplicative RUM brings several advantages to the competitive facility location problem. For instance, the cost optimization problem under the multiplicative RUM can be solved efficiently by a general convex optimization solver, or can be reformulated as a conic quadratic program and handled by a conic solver available in some off-the-shelf solvers such as CPLEX or GUROBI. Furthermore, we consider a joint location and cost optimization problem under the multiplicative RUM and propose three approaches to solve the problem, namely, an equivalent conic reformulation, a multi-cut outer-approximation algorithm, and a local search heuristic. We provide numerical experiments based on synthetic instances of various sizes to evaluate the performances of the proposed algorithms in solving the cost optimization and the joint location and cost optimization problems.

The follower competitive facility location problem under the nested logit choice rule

Recently, more realistic customer choice rules based on the Multinomial Logit have been proposed for the follower competitive facility location problem, together with efficient exact solution methods based on cut generation approaches. We address this problem in the case in which a new chain, the entrant, decides to locate some stores in a market where there are already incumbent chains offering substitute products, which differ from the entrant's product in secondary features. The entrant's stores are very similar to each other, and this is also the case for the incumbent chains. In this case, for a given customer, purchases made at the stores of one of the chains are correlated, given the similitude between these stores. The Multinomial Logit rule does not capture this correlation. We propose using a Nested Logit rule which does capture this correlation and, in addition, represents a sequential decision process by the customer, who first chooses the chain and then the store. We prove the concavity of the objective function in the problem and find exact solutions using Branch and Cut over a generalized linear reformulation of the problem and four different types of cuts: submodular and an improvement of these, outer-approximation, and a set of new cuts. Our results show locations that fit better the intuition and practice. Furthermore, our computational times improve in many cases upon the known results for similar problems.

On the competitive facility location problem with a Bayesian spatial interaction model

AbstractThe competitive facility location problem arises when businesses plan to enter a new market or expand their presence. We introduce a Bayesian spatial interaction model which provides probabilistic estimates on location-specific revenues and then formulate a mathematical framework to simultaneously identify the location and design of new facilities that maximise revenue. To solve the allocation optimisation problem, we develop a hierarchical search algorithm and associated sampling techniques that explore geographic regions of varying spatial resolution. We demonstrate the approach by producing optimal facility locations and corresponding designs for two large-scale applications in the supermarket and pub sectors of Greater London.

A continuum perspective of customer choice rules for competitive facility location problems

Customer patronage behavior plays a critical role in estimating market share in the context of locating competitive facilities. Three common rules used to describe customer patronage behaviors are: the binary rule, the proportional rule, and the partially binary rule. Recently, we propose another customer choice rule, the partially proportional rule, to describe the behavior of customers when choosing a chain of facilities that offer exclusive services. Although these four rules describe very different customer patronage behaviors, this paper finds that they actually correspond to optimal solutions for four special cases of a class of optimization problems. For the general cases of this class of optimization problems, we also give the corresponding optimal solutions. This work provides a continuum perspective for understanding customer choice rules, while providing possible theoretical guidance for studying unexplored customer behavior patterns.

Developing a Mathematical Model for Competitive Facility Location with Multiple Commodities and Multiple Competitors

مکان‌یابی با درنظرگرفتن موضوع رقابت در بازار، یک تصمیم راهبردی و بلندمدت محسوب می­‌شود. چنانچه در انتخاب مکان، بررسی‌­های لازم صورت نگیرد، حیات سازمان در بلندمدت تحت تأثیر قرار می‌­گیرد. به‌­دلیل وجود پیچیدگی‌­های موجود در مسائل مکان‌یابی، ارائه مدل‌های مکان‌یابی با محدودیت­‌های متنوعی مواجه است. هدف این پژوهش، توسعه مدل مکان‌یابی رقابتی با درنظر­گرفتن دو محصول از سوی سه رقیب است؛ برای این منظور، مسئله به‌­صورت یک بازی مکان ـ قیمت تعریف و با استفاده از مدل ریاضی دوسطحی، مدل‌سازی شده است. در این مدل در سطح نخست، مکان بهینه تعیین و در سطح دوم با استفاده از نتایج تعادل نش، قیمت تعادلی به‌دست آمد. در این پژوهش، رفتار مشتری به‌­صورت احتمالی در نظر گرفته شده و با کمک تابع نمایی مدل‌­سازی شد. به­‌دلیل NP- hard­ بودن مسائل مکان‌یابی، برای حل مدل از الگوریتم فراابتکاری استفاده شده است. الگوریتم جست­وجوی ممنوع، روش انتخابی حل مدل پژوهش حاضر است. نتایج نشان داد بازی قیمت در شرایطی که پیش از ورود به بازار، بیش از یک رقیب حضور داشته باشد، در مقایسه با حالتی که بازار انحصاری است، شدت و اهمیت بیشتری دارد.

A comparative performance analysis of intelligence-based algorithms for optimizing competitive facility location problems

Most companies operate to maximize profits and increase their market shares in competitive environments. Since the proper location of the facilities conditions their market shares and profits, the competitive facility location problem (CFLP) has been extensively applied in the literature. This problem generally falls within the class of NP-hard problems, which are difficult to solve. Therefore, choosing a proper solution method to optimize the problem is a key factor. Even though CFLPs have been consistently solved and investigated, an important question that keeps being neglected is how to choose an appropriate solution technique. Since there are no specific criteria for choosing a solution method, the reasons behind the selection approach are mostly unclear. These models are generally solved using several optimization techniques. As harder-to-solve problems are usually solved using meta-heuristics, we apply different meta-heuristic techniques to optimize a new version of the CFLP that incorporates reliability and congestion. We divide the algorithms into four categories based on the nature of the meta-heuristics: evolution-based, swarm intelligence-based, physics-based, and human-based. GAMS software is also applied to solve smaller-size CFLPs. The genetic algorithm and differential evolution of the first category, particle swarm optimization and artificial bee colony optimization of the second, Tabu search and harmony search of the third, and simulated annealing and vibration damping optimization of the fourth are applied to solve our CFLP model. Statistical analyses are implemented to evaluate and compare their relative performances. The results show the algorithms of the first and third categories perform better than the others.

Can street markets be a sustainable strategy to mitigate food insecurity in emerging countries? Insights from a competitive facility location model

This research explores the sustainability of street markets to grant access to fruits and vegetables (F&Vs) to underserved communities in emerging economies. Specifically, this paper studies the impact of adding new street markets to satisfy the demand of end consumers in a real case. To do so, we developed a novel non-linear mathematical model to establish the location and number of street markets. This model, a variant of the competitive facility location problem, includes specific features of street markets, such as their itinerant nature and the dynamic shopping behavior of customers. To feed the model, we collected data from both primary and secondary sources: we surveyed the main competitors of the street markets (i.e., small, family-owned retailers or nanostores) to investigate their market share and purchasing habits. The problem was solved with an ad-hoc iterative method. The results suggest that street markets can provide better access to F&Vs to food-insecure households to some extent. Still, their management, operational complexity, and financial sustainability may limit their applicability in the long term.

A discrete competitive facility location model with proportional and binary rules sequentially applied

A discrete competitive facility location model with proportional and binary rules sequentially applied