China
Africa
Explore chapters and articles related to this topic
Facility Location
Published in Susmita Bandyopadhyay, Production and Operations Analysis, 2019
If the distance between the customer and the facility is less than or equal to a predefined number, then that distance is known as coverage distance and the problem is called covering problem. Examples of application areas of covering problem include finding warehouse locations, assembly line balancing, and so on. Covering problem is a type of binary programming problem. Therefore, the following subsection introduces the concept of binary programming problem. But before that the covering problem needs to be defined mathematically. The covering problem involves finding the minimum number of nodes such that each of the other nodes is connected to one of the selected nodes. Suppose a network contains a set of V nodes and A number of arcs. If the node i is connected to node j, then arc rij = 1. If the arc j is selected, then Xj=1. The formulation of the problem based on definition above is presented below: () MinimizeZ=∑j=1nXj
1
Published in Tugrul Daim, Marina Dabić, Yu-Shan Su, The Routledge Companion to Technology Management, 2023
Jonathan Bard, Boaz Golany, Fred Phillips
The first part of the design task, then, is to identify a subset of these entities (stakeholders) that (i) can provide, collectively, what the designer’s organization needs; and (ii) are motivated to do so, by reason of having their own needs satisfied in exchange. (The obvious additional requirement, that it be done in a way that leads to a financially viable consortium, is dealt with in the next section of the chapter.) This first part of the design task, expressed as a mathematical optimization, leads to a modified set-covering problem. This optimization identifies a possible exchange economy,2 without quantifying the amounts of the exchange items that will change hands.
Integer Programming
Published in Albert G. Holzman, Mathematical Programming, 2020
(The above model generalizes a problem in graph theory from which the name "covering problem" was acquired. The problem occurs in a graph with N nodes and E edges, with each edge joining certain pairs of nodes. The objective is to find a "cover" with the minimum number of edges, where a cover is defined as a subset of edges such that each of the N nodes is incident to some edge of the subset.)
Logistics of carpet recycling in the U.S.: designing the collection network
Published in The Journal of The Textile Institute, 2019
Iurii Sas, Jeffrey A. Joines, Kristin A. Thoney, Russell E. King
The set covering problem has been used in location science for more than 40 years (Farahani, Asgari, Heidari, Hosseininia, & Goh, 2012). Detailed reviews of set covering and related problems, as well as their application and solution techniques, can be found in Caprara, Toth, and Fischetti (2000), ReVelle, Eiselt, and Daskin (2008), Fallah, Naimisadigh, and Aslanzadeh (2009), and Farahani et al. (2012). The earliest heuristics for the covering problem are the deterministic greedy adding algorithm and greedy adding with substitution discussed in Church (1974), and Church and ReVelle (1974). While these algorithms are fast and simple to implement, they rarely produce good quality solutions. Therefore, the deterministic greedy approach was later improved by including randomized steps in the solution procedure (Bautista & Pereira, 2007; Feo & Resende, 1995; Haouari & Chaouachi, 2002; Lan, DePuy, & Whitehouse, 2007; Marchiori & Steenbeek, 1998; Resende, 1998). Most other approaches utilize differences in site opening costs and, as a result, they are not as effective for unicost problems (Kinney, Barnes, & Colletti, 2007; Lan et al., 2007).
Optimal junction localization minimizing maximum miners’ evacuation distance in underground mining network
Published in Mining Technology, 2023
Zhixuan Shao, Maximilien Meyrieux, Mustafa Kumral
The location problem focuses on the determination of one or more facilities serving a set of surrounding destinations as demand points in such a way as to optimize certain spatially dependent objectives (Brandeau and Chiu 1989). Such a problem could be classified in different ways based on specific criteria. As discussed in Farahani and Hekmatfar (2009), there could be (a) single or multi-facility problem based on the number of facilities, (b) continuous-space problem and discrete-space problem based on solution space settings, (c) deterministic and probabilistic problem based on demands, and (d) incapacitated and capacitated problems based on supply capacity. When the objectives and the applications are taken into consideration, the facility location problem could be categorized into the -median problem, covering problem, and -centre problem (Lotfian and Najafi 2019), where refers to the number of the facility to be located. The -median problem (a.k.a. MiniSum problem) is an NP-complete problem. It is to localize the desired facility (or facilities) in such a way as to minimize the total cost between the new facility (or facilities) and existing demand points. The covering problem focuses on finding a feasible location for the new facility (or facilities) such that all demand points are under coverage and the possible costs can be minimized. The -centre problem, also referred to as the MiniMax problem, attempts to localize the new facility (or facilities) surrounded by demand points under consideration such that the maximum distance between the demand points and the facility (or facilities) is minimized.