New valid inequalities and facets for the Simple Plant Location Problem

Abstract

The Simple Plant Location Problem is a well-known (and N P-hard) combinatorial optimisation problem, with applications in logistics. We present a new family of valid inequalities for the associated family of polyhedra, and show that it contains an exponentially large number of new facet-defining members. We also present a new procedure, called facility augmentation, which enables one to derive even more valid and facet-defining inequalities.

Conditional Markov Chain Search for the Simple Plant Location Problem Improves Upper Bounds on Twelve Körkel–Ghosh Instances

“…Most of the exact algorithms are based on a mathematical programming formulation of the SPLP (see for example, Cornuejols and Thizy [12], Morris [33], and Schrage [36]). Polyhedral results for the SPLP polytope have been reported in Trubin [38], Balas and Padberg [2], Cho et al [9], Cho et al [10], Farias [14], Cánovas et al [8], and Galli et al [17]. In theory, these results allow us to solve the SPLP by applying the simplex algorithm to the strong linear programming relaxation, with the additional stipulation that a pivot to a new extreme point is allowed only when this new extreme point is integral.…”

A separation algorithm for the simple plant location problem

“…For larger p, they must be strengthened ("lifted") to make them facet-defining [11,15]. Following [17], we will call the odd cycle inequalities with p = 3 3-cycle inequalities. Cho et al [10] showed that the 3-cycle inequalities, together with the assignment constraints, VUBs and trivial bounds, give a complete description of P (m, n) when m = 3.…”

“…We call (2) assignment constraints and (3) variable upper bounds (VUBs). Many families of valid and facet-defining inequalities have been derived for the above formulation [5,10,11,13,15,17,19]. On the other hand, very little work has been done on separation algorithms.…”

A simple multi-wave algorithm for the uncapacitated facility location problem

“…Employing a synthesis of several of the preceding ideas, De Armas et al 2017 have proposed a method for the stochastic instance of UFLP (SUFLP), using a simheuristic (simulation optimization) approach that first embeds a fast heuristic inside the metaheuristic framework of iterated local search (ILS) for the deterministic version of UFLP and then integrates this procedure with Monte Carlo simulation techniques. Additional recent investigations of UFLP have been carried out by Albareda-Sambola et al (2017), Atta et al (2018), Galli et al (2018), Sahman et al (2017), Tsuya et al (2017). There also exist several recent studies of variants and extensions of UFLP, including Akbaripour et al (2017), Chalupa and Nielsen (2018), Han et al (2018), Jiang et al (2018), Pearce and Forbes (2018), Todosijević et al (2017), An and Svensson (2017).…”