A Discrete Competitive Facility Location Model with Minimal Market Share Constraints and Equity-Based Ties Breaking Rule

Abstract

We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): a new facility will be opened only if a minimal market share is captured in the short-term. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equitybased rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems.

The Location Selection of Logistics Center in City Based on Particle Swarm Optimization

“…The total population was selected as 50 in the immunogenetic algorithm, and the value of memory bank capacity was 10, the crossover factor was set to 0.5, and the diversity evaluation factor was 0.95. The same iterations were evaluated 1000 times, and the results of optimal site selection were calculated as A36 (12,12), A39 (3,19), A14(10,3), A06(5,10), A17(22,15), A08 (20,5), A07 (20,21). The optimal tness value is 137,307.1613 million yuan, and the run time is 185 seconds.…”

“…In the comparison of the optimal location distributions derived by the two algorithms, A06 (5, 10), A20 (3,19), and A36 (12,12) are chosen as logistics center points, and each point covers the same subset. Among them, A06 (5, 10) corresponds to ve demand points A19, A21, A24, A28, and A31; A20 (3,19) corresponds to eight demand points A01, A10, A11, A12, A18, A32, A35, and A38. and A36 (12,12) corresponds to two demand points A25 and A27.…”

“…Pakravan [2] presents a stochastic programming model to deal with the opposition typically encountered in constructing an undesirable facility. Fernández [3] points out a nonlinear constrained discrete competitive facility location problem with minimal market share constraints, which is solved by heuristic algorithms. Other optimization models include a hierarchical model for emergency shelter location selection [4], and an energy power plant location selection based on a multi-criteria decision [5], a location selection problem for a military airport [6].…”

Tabu Search Based Hybrid Meta-Heuristic Approaches for Schedule-Based Production Cost Minimization Problem for the Case of Cable Manufacturing Systems

“…The most frequently used algorithms in the literature are genetic algorithm, simulated annealing, variable neighbourhood search, tabu search, etc. (see Gomes et al, 2014;Reisi-Nafchi and Moslehi, 2015;Kurdi, 2015;Zhang and Wong, 2016;Martin et al, 2016;Akbari and Rashidi, 2016;Niroomand et al, 2016;Quintana et al, 2017;Hsieh, 2017;Hu et al, 2016;Ghadiri Nejad and Banar, 2018;Misevičius et al, 2018;Vizvári et al, 2018;Dugonik et al, 2019;Ullah et al, 2020;Hassanpour, 2020;Aliya et al, 2020;Fernández et al, 2020;Hussain and Khan, 2020).…”

Experimental Analysis of Algebraic Modelling Languages for Mathematical Optimization

“…Internally, these tools use the combination of a mathematical model with an appropriate solution algorithm (e.g. Cosma et al, 2020;Fernández et al, 2020;Gómez et al, 2019;Lee et al, 2019;Paulavičius and Adjiman, 2020;Stripinis et al, 2019Stripinis et al, , 2021 to solve the problem at hand. Thus, the way mathematical models are formulated is critical to the impact of optimization in real life.…”