Hierarchical hub location problems locate hub facilities on the first and second of three levels under the best economic conditions. The present study introduced a novel hierarchical hub set **covering** **problem** with capacity constraints. This study showed the significance of fixed charge costs for locating facilities, assigning hub links and designing a productivity network. Set **covering** was imposed to use the minimum number of variables and coverage constraints. The proposed model employs mixed integer programming to locate facilities and establish links between nodes according to the travel time between an origin-destination pair within a given time bound. The demand nodes are fairly covered at each service level and no demand node remains unanswered. The formulation was linearized by replacing the non-linear constraints with less intuitive linear structures. The resulting linear model was solved using GAMS and tested on the Australian Post dataset and the Iranian Airport dataset. Keywords : Small Hub location; Hub set **covering**; Hierarchical; Capacity constraint.

Show more
17 Read more

We consider in this paper the **problem** of finding optimal CAS’s for incomplete AS’s. The paper introduces some notions including the connected-super-forbidden-family and the lower-forbidden-family for general AS’s. We show that an optimal CAS can be derived from some smaller sized BIP whose variables (constraints, resp.) are based on the connected-super-forbidden-family (lower-forbidden-family, resp.) of the given AS. The paper further builds the close relationship between the **problem** of finding optimal CAS’s and the set **covering** **problem** (SCP) [11]. We prove that the **problem** of finding a CAS with minimum cardinality of the primitive share set (or minimum average information rate) is equivalent to the SCP, and thus is NP-hard [15]. Other contributions of the paper include: 1) two types of AS’s are recognized so that we can construct the corresponding optimal CAS’s directly; and 2) a greedy algorithm is proposed to find CAS’s with smaller worst information rate.

Show more
12 Read more

The weighted set **covering** **problem** is to choose a number of subsets to cover all the elements in a universal set at the lowest cost. It is a well-studied classical **problem** with applications in various fields like machine learning, planning, information retrieval, facility allocation, etc. Deep web crawling refers to the process of gathering documents that have been structured into a data source and can be retrieved through a search interface. Its query selection process calls for an efficient solution to the set **covering** **problem**.

70 Read more

Abstract— In this paper, we propose a CLONALG-based simple heuristic, which is one of the most popular artifi- cial immune system (AIS) models, for the non-unicost set **covering** **problem** (SCP). In addition, we have modified our heuristic to solve the unicost SCP. It is well known that SCP is an NP-hard **problem** that can model several real world situations such as crew scheduling in airlines, facility location **problem**, production planning in industry etc. In real cases, the **problem** instances can reach huge sizes, making the use of exact algorithms impractical. So, for finding practically efficient approaches for solving SCP, different kind of heuristic approaches have been applied in the literature. To the best of our knowledge, our work here is the first attempt to solve SCP using Artificial Immune System. We have evaluated the performance of our algorithm on a number of benchmark non-unicost instances. Computational results have shown that it is capable of producing high-quality solutions for non-unicost SCP. We have also performed some experiments on unicost instances that suggest that our heuristic also performs well on unicost SCP.

Show more
Moreover, there are two supply models for generalized and variable-sized bin **covering** **problem**: unit supply model and infinite supply model. In the unit model there is exactly one bin of each type, i. e., there are individual bins. By contrast, in the infinite supply model, there are arbitrarily many bins of each type. In this paper, we consider the offline Generalized Bin **Covering** **problem** in unit supply mode.

10 Read more

The goals of hub location problems are finding the location of hub facilities and determining the allocation of non-hub nodes to these located hubs. In this work, we discuss the multi-modal single allocation capacitated p-hub **covering** **problem** over fully interconnected hub networks. Therefore, we provide a formulation to this end. The purpose of our model is to find the location of hubs and the hub links between them at a selected combination of modes for each origin-destination. Furthermore, it determines the allocation of non-hub nodes to the located hubs at the best mode for each allocation such that the travel time between any origin–destination pair is not greater than a given time bound. In addition, the capacity of hub nodes is considered. Six valid inequalities are presented to tight the linear programming lower bound. We present a heuristic based on tabu search algorithm and test the performance of it on the Australian Post (AP) data set.

Show more
12 Read more

A practical application of SCC could be in the wireless communication services. In this application, a number of signal towers need be constructed to send signals to customer regions. Each signal tower can send signals to all customer regions within a certain distance, and each customer region must receive signals from (be covered by) at least one signal tower. Furthermore, in order to avoid electromagnetic interference, the distance between each pair of signal towers must be no less than a given distance. Such a situation can be represented by means of a set **covering** **problem** with conflict constraints, considering each customer region as a row and each signal tower location as a column of the zero-one matrix. The corresponding model, i.e., set **covering** **problem** with conflict constraints, seeks to identify conflict-free collection of signal tower locations to cover all customer regions at minimum cost.

Show more
139 Read more

In this study, to deal with the periodic variations of parameters, a mathematical formulation for the bi- objective multi-period maximal hub **covering** **problem** (BOMMHCP) is developed. Another contribution in the model is the simultaneous consideration of the goals of maximizing the covered demand of all O/D Pairs and minimizing the cost of hub establishment. The purpose of most MHCPs is maximizing the flow due to the coverage limits and the number of hubs, while most network owners seek to reduce the cost of the network construction. Therefore, by designing a bi-objective model and presenting non-dominated solutions, managers can choose one of them according to their preferences. The ε-constraint method has been developed for obtaining non-dominated solutions. Given that the single-objective **problem** found in the ε- constraint method is computationally intractable, Benders decomposition algorithm is developed to accelerate the solution process by adding valid inequalities.

Show more
12 Read more

The total **covering** **problem** under facility location prob- lem is an important **problem** to determine the minimum number of sites to locate the facilities to cover all the customers. Since, this **problem** comes under combinato- rial category, in this paper, an attempt has been made to develop heuristics and compare them in terms of their performance. In the first phase, the design of GA based heuristic is given and it is followed by the design of GRASP based heuristic. Later, a complete factorial ex- periment has been conducted to compare the perform- ance of the two heuristics by assuming three factors, Factor A (Percentage Sparsity), Factor B (**Problem** Size) and Factor C (Algorithms). The Factor A is assumed with 5 levels, which are viz. 16%, 18%, 20%, 22% and 24%. The Factor B is assumed with 6 levels, which are, viz. 30 × 30, 40 × 40, 50 × 50, 60 × 60, 70 × 70 and 80 × 80. The Factor C is assumed with 2 levels, which are viz. Alg 1 and Alg 2 . For each experimental combination, 5

Show more
12 Read more

SAT problems: local search algorithms that start with a certain set of values (though, it does not satisfy all the formula), and then modify it trying to consistently get closer to performed set, and so-called DPLL-algorithms (by names of inventors: Davis, Putnam, Logemann, Loveland; description of basic principles of this method dates back to 1968), which traverse a tree of all possible sets and perform depth-first search. The purpose of this paper is to develop efficient exact algorithm for solving 3-SAT-**problem** and an arbitrary k-SAT- **problem** of polynomial complexity.

Show more
15 Read more

In this study, we define a new **covering** **problem** called the CSP with Nodes and Segments (CSPNS). To illustrate the CSPNS, we consider advertising, which is one of inevitable activities in modern business. It requires a medium for sending promotional messages to targeted people, for example, an advertising truck (AD-truck) that drives on town streets while displaying and broadcasting information about a new product or a local event. The aim of the AD-truck is to promote new products or local events to people on the street. Even though the truck is moving, announcements from the truck can be heard by people on the street. Therefore, the AD-truck does not have to stop for people to see and hear the advertising. This is the most important difference between the CSP and the CSPNS. In the CSP, the nodes on the tour can only cover the nodes not on the tour. However, in the CSPNS, not only the nodes but also the segments on the

Show more
14 Read more

An interesting logistic **problem** arises when there is a set of agents who wish to (or must) be provided with a service which has to be located at several different points in order to serve all those agents. This is a very well-known **problem** in operations research, called the “set **covering** **problem**” (Berge, 1957; Toregas et al., 1971). In particular, there are a set of potential locations, such that each of them covers a subset of agents to be served. Each potential location has a fixed construction and start-up cost associated with it. Therefore, the goal is to choose a subset of potential locations such that all agents are covered and the cost is minimized. Set **covering** problems are important and interesting

Show more
26 Read more

Marianov and ReVelle (1994) relaxed the assumption in the PLSCP of independence between the probabilities of different servers being busy. They modelled the behaviour in each region as an M/M/S-loss queueing system. The use of an acceptable probabilistic structure inside an optimisation model for facility siting is the distinctive contribution of this model. This model is called the queueing probabilistic location set **covering** **problem** (Q-PLSCP). In addition, to find the maximum availability level α, which gives the desired number of servers when applied to Q- PLSCP, a procedure, MASH, is devised, which maximises the minimum system-wide reliability level obtainable with the desired number of servers. Marianov and ReVelle (1996) further developed the MALP. Their new model is called Queueing Maximal Availability Location **Problem** (Q-MALP). The main difference between MALP and Q-MALP resides in the methodology for the calculation of the smallest integer that satisfies the required reliability. In addition, in this model they treated the distances/times as random. The smallest integer satisfying the required reliability is calculated using the M/G/S-loss queueing system. Therefore, the independence assumption for servers' busy fractions in the original MALP model is avoided in Q- MALP.

Show more
18 Read more

This model is a kind of **covering** **problem**; it decides the number of vehicles in each location in order to maximize the expected number of demands that can be covered, given that vehicles may be unavailable (in use). The model assumes that there is an equal probability that a vehicle is busy at any location. As the objec- tive function is the expected number of demands, the decision variables that choose the number of vehicles in each location appear in an exponential term. This makes the objective function non-linear, just like the LMRP **problem**. Das- kin introduces a set of parameters to represent the increase in the expected cov- erage for each additional vehicle, as well as a set of binary decision variables to indicate whether the customer is covered a specific numbers of times. By using the sum of all th0e benefits of adding a new vehicle to represent the expected coverage, he changes the **problem** into one that is linear and easy to solve. So we apply the same idea to convert the LMRP into a linear mixed-integer program- ming **problem** and compare it with the Lagrangian method of Mark S. Daskin, Collette R. Coullard, and Zuo-Jun Max Shen to see if it will give us a more effi- cient method [5] [6]. Daskin and Teo [7] presented a stochastic version of the LMRP **problem**, and they developed a Lagrangian method for this **problem**. They also discussed the influence of changing the key parameters.

Show more
13 Read more

Hub location **problem** is one of the most important issues in location problems because it is widely used in many telecommunication and transportation networks. Hubs are facilities that serve as transshipment and switching point to consolidate flows at certain locations for transportation and telecommunication systems [1-2]. Hub **covering** **problem** can be used to model different telecommunication networks and mobile communications: such as wireless network, internet networks, computer networks. The coverage radius controls the number of hubs and the assignment of nodes to hubs. Determining the coverage radius in hub **covering** **problem** depends on many factors like demand growth over planning horizon, moreover environmental and meteorological condition affect the cover radius and travel time. The association of different uncertainty with these parameters makes determination of coverage radius complicated. These uncertainties affect the coverage radius and the coverage radius has in turn the great impact on the structure of the network. Designing a network with desirable reliability level which guaranty the performance and survivability of network from any disruption and malfunction, is the most importand issue in network design problems [8-9]. Hub location **problem** is a strategic decision making activity which should be considered for a long time and it should take into account the long term goals of the system. These kind of decisions can not be changed easily because any changes incure heavy costs and expenses to the system.

Show more
In this paper a Vertex **Covering** Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist- ing facility points; 2) Maximize the minimum distance from the facility to be located to the existing facility points; 3) Maximize the number of existing facility points covered. Area restriction concept has been incor- porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal **covering** **problem**, that is **covering** maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region. Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective **problem**. A transformed non-linear pro- gramming algorithm has been designed for the proposed non-linear model. Rectilinear distance norm has been considered as the distance measure as it is more appropriate to various realistic situations. A numerical example has been presented to illustrate the solution algorithm.

Show more
The proposed algorithm is based on the solution of the set **covering** **problem** where each row of the set **covering** matrix corresponds to a sample point, and is determined by the constraint satisfaction at that sampled point, therefore the sampling method- ology is very important to this algorithm. Hence, we want to generate as many observations as we can for the matrix E. One way to do this is to sample along the line segment L ′ (x k , s k ). This is done by taking advantage of the constraint intersec-

58 Read more

Considering quality aspects during winner determination in a combinatorial reverse auction for transport contracts is of practical importance. In this paper, we studied a bi-objective winner determination **problem** that is based on the set **covering** **problem** and minimizes the total transport costs and the total transport quality simultaneously. To solve this **problem**, the heuristic PNS was developed. PNS is inspired by the metaheuristics GRASP and LNS. To construct an initial set of non dominated solutions, PNS applies a dominance-based randomized greedy heuristic which uses a two-stage candidate bid selection procedure. The initial solutions are improved by means of a search in large neighborhoods which switches the applied parameters (removal probability of bids and greedy rating function) in a self-adaptive manner. Self-adaptive configurations depend on individual solutions and not on the entire approximation set. PNS was tested by means of 37 benchmark instances. In terms of approximation set quality, PNS outperforms all known heuristics on each of the 37 benchmark instances. Furthermore, PNS is the second fastest method tested. Subject of our future research will be the development of solution approaches for bi-objective winner determination problems which take into account additional business constraints proposed e.g. by Caplice and Sheffi [6].

Show more
27 Read more

problem as a set covering problem, they used greedy method [7] [9] to select a proper.. set of queries based on a sample database.[r]

70 Read more

In the facility location **problem** usually reducing total transferring cost and time are common objectives. In the p -hub **covering** **problem** it is attempted to locate hubs and allocate customers to established hubs while allocated nodes to hubs are inside of related hubs **covering** radius. In this paper, we attempt to consider capability of established hubs to achieve a more reliable network. Also, the proposed model try to construct a network with more **covering** reliability by determining operating **covering** radius inside of nominal radius. Then, a sensitivity analysis is performed to analyze effect of parameters in the model. The proposed multi objective model is solved by ε-constraint algorithm for small size instances. For large scale instances a non-dominated sorting genetic algorithm (NSGA-II) is presented to obtain Pareto solutions and its performance is compared with results of ε-constraint algorithm. The model and solution algorithm were analyzed by more numerical examples such as Turkish network dataset. The sensitivity analysis confirms that the network extracted by the proposed model is more efficient than classic networks.

Show more
13 Read more