Survivable network design with shared-protection routing

In this paper we study the problem of designing a survivable telecommunication network with shared-protection routing. We develop a heuristic algorithm to solve this problem. Recent results in the area of global re-routing have been used to obtain very tight lower bounds for the problem. Our results indicate that in a majority of problem instances, the average gap between the heuristic solutions and the lower bounds is within 5%. Computational experience is reported on randomly generated problem instances with up to 35 nodes, 80 edges and 595 demand pairs and also on the instances available in SNDlib database.     

Covering continuous demand in the plane

Continuous demand is generated in a convex polygon. A facility located in the area covers demand within a given radius. The objective is to find the locations for p facilities that cover the maximum demand in the area. A procedure that calculates the total area covered by a set of facilities is developed. A multi start heuristic approach for solving this problem is proposed by applying a gradient search from a randomly generated set of p locations for the facilities. Computational experiments for covering a square area illustrate the effectiveness of the proposed algorithm.     

Worst-case analysis of demand point aggregation for the Euclidean p-median problem

Solving large-scale p-median problems is usually time consuming. People often aggregate the demand points in a large-scale p-median problem to reduce its problem size and make it easier to solve. Most traditional research on demand point aggregation is either experimental or assuming uniformly distributed demand points in analytical studies. In this paper, we study demand point aggregation for planar p-median problem when demand points are arbitrarily distributed. Efficient demand aggregation approaches are proposed with the corresponding attainable worst-case aggregation error bounds measured. We demonstrate that these demand aggregation approaches introduce smaller worst-case aggregation error bounds than that of the honeycomb heuristic [Papadimitriou, C.H., 1981. Worst-case and probabilistic analysis of a geometric location problem. SIAM Journal on Computing 10, 542–557] when demand points are arbitrarily distributed. We also conduct numerical experiments to show their effectiveness.     

Facility location for market capture when users rank facilities by shorter travel and waiting times

A firm wants to locate several multi-server facilities in a region where there is already a competitor operating. We propose a model for locating these facilities in such a way as to maximize market capture by the entering firm, when customers choose the facilities they patronize, by the travel time to the facility and the waiting time at the facility. Each customer can obtain the service or goods from several (rather than only one) facilities, according to a probabilistic distribution. We show that in these conditions, there is demand equilibrium, and we design an ad hoc heuristic to solve the problem, since finding the solution to the model involves finding the demand equilibrium given by a nonlinear equation. We show that by using our heuristic, the locations are better than those obtained by utilizing several other methods, including MAXCAP, p-median and location on the nodes with the largest demand.     

A note on the m-center problem with rectilinear distances

Given n demand points on a plane, the problem we consider is to locate a given number, m, of facilities on the plane so that the maximum of the set of rectilinear distances of each demand point to its nearest facility is minimized. This problem is known as the m-center problem on the plane. A related problem seeks to determine, for a given r, the minimum number of facilities and their locations so as to ensure that every point is within r units of rectilinear distance from its nearest facility. We formulate the latter problem as a problem of covering nodes by cliques of an intersection graph. Certain bounds are established on the size of the problem. An efficient algorithm is provided to generate this set-covering problem. Computational results with this approach are summarized.     

Incorporating the threat of terrorist attacks in the design of public service facility networks

In this paper, we consider the design problem of a public service facility network with existing facilities when there is a threat of possible terrorist attacks. The aim of the system planner, who is responsible for the operation of the network, is to open new facilities, relocate existing ones if necessary, and protect some of the facilities to ensure a maximum coverage of the demand that is assumed to be aggregated at customer zones. By doing so, the system planner anticipates that a number of unprotected facilities will be rendered out-of-service by terrorist attacks. It is assumed that the sum of the fixed cost of opening new facilities, the relocation costs, and the protection costs cannot exceed a predetermined budget level. Adopting the approach of gradual (or partial) coverage, we formulate a bilevel programming model where the system planner is the leader and the attacker is the follower. The objective of the former is the maximization of the total service coverage, whereas the latter wants to minimize it. We propose a heuristic solution procedure based on tabu search where the search space consists of the decisions of the system planner, and the corresponding objective value is computed by optimally solving the attacker??s problem using CPLEX. To assess the quality of the solutions produced by the tabu search (TS) heuristic, we also develop an exhaustive enumeration method, which explores all the possible combinations of opening new facilities, relocating existing ones, and protecting them. Since its time complexity is exponential, it can only be used for relatively small instances. Therefore, to be used as a benchmark method, we also implement a hill climbing procedure employed with the same type of moves as the TS heuristic. Besides, we carry out a sensitivity analysis on some of the problem parameters to investigate their effect on the solution characteristics.     

Multi-objective competitive location problem with distance-based attractiveness and its best non-dominated solution

The multi-objective competitive location problem (MOCLP) with distance-based attractiveness is introduced. There are m potential competitive facilities and n demand points on the same plane. All potential facilities can provide attractiveness to the demand point which the facility attractiveness is represented as distance-based coverage of a facility, which is “full coverage” within the maximum full coverage radius, “no coverage” outside the maximum partial coverage radius, and “partial coverage” between those two radii. Each demand point covered by one of m potential facilities is determined by the greatest accumulated attractiveness provided the selected facilities and least accumulated distances between each demand point and selected facility, simultaneously. The tradeoff of maximum accumulated attractiveness and minimum accumulated distances is represented as a multi-objective optimization model. A proposed solution procedure to find the best non-dominated solution set for MOCLP is introduced. Several numerical examples and instances comparing with introduced and exhaustive method demonstrates the good performance and efficiency for the proposed solution procedure.     

Local networks for computer communications: A. WEST and P. JANSON (Eds.) Proceedings of the IFIP Working Group 6.4, International Workshop on Local Networks,Zürich,Switzerland, August 27–29, 1980, North-Holland,Amsterdam, 1981, xiii + 470 pages,Dfl.125.00

In this paper we present two lower bounds for the p-median problem, the problem of locating p facilities (medians) on a network. These bounds are based on two separate lagrangean relaxations of a zero-one formulation of the problem with subgradient optimisation being used to maximise these bounds. Penalty tests based on these lower bounds and a heuristically determined upper bound to the problem are developed and shown to result in a large reduction in problem size. The incorporation of the lower bounds and the penalty tests into a tree search procedure is described and computational results are given for problems with an arbitrary number of medians and having up to 200 vertices. A comparison is also made between these algorithms and the dual-based algorithm of Erlenkotter.     

Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines

We consider the capacitated lot sizing problem with multiple items, setup time and unrelated parallel machines. The aim of the article is to develop a Lagrangian heuristic to obtain good solutions to this problem and good lower bounds to certify the quality of solutions. Based on a strong reformulation of the problem as a shortest path problem, the Lagrangian relaxation is applied to the demand constraints (flow constraint) and the relaxed problem is decomposed per period and per machine. The subgradient optimization method is used to update the Lagrangian multipliers. A primal heuristic, based on transfers of production, is designed to generate feasible solutions (upper bounds). Computational results using data from the literature are presented and show that our method is efficient, produces lower bounds of good quality and competitive upper bounds, when compared with the bounds produced by another method from the literature and by high-performance MIP software.     

The time constrained maximal covering salesman problem

We introduce the time constrained maximal covering salesman problem (TCMCSP) which is the generalization of the covering salesman and orienting problems. In this problem, we are given a set of vertices including a central depot, customer and facility vertices where each facility can supply the demand of some customers within its pre-determined coverage distance. Starting from the depot, the goal is to maximize the total number of covered customers by constructing a length constrained Hamiltonian cycle over a subset of facilities. We propose several mathematical programming models for the studied problem followed by a heuristic algorithm. The developed algorithm takes advantage of different procedures including swap, deletion, extraction-insertion and perturbation. Finally, an integer linear programming based improvement technique is designed to try to improve the quality of the solutions. Extensive computational experiments on a set of randomly generated instances indicate the effectiveness of the algorithm.     

Planar maximal covering location problem under block norm distance measure

This paper introduces a new model for the planar maximal covering location problem (PMCLP) under different block norms. The problem involves locating g facilities anywhere on the plane in order to cover the maximum number of n given demand points. The generalization, in this paper, is that the distance measures assigned to facilities are block norms of different types and different proximity measures. First, the PMCLP under different block norms is modelled as a maximum clique partition problem on an equivalent multi-interval graph. Then, the equivalent graph problem is modelled as an unconstrained binary quadratic problem (UQP). Both the maximum clique partition problem and the UQP are NP-hard problems; therefore, we solve the UQP format through a genetic algorithm heuristic. Computational examples are given.     

Scheduling on parallel identical machines to minimize total tardiness

This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time.     

A GRASP heuristic for the manufacturing cell formation problem

In this work, we address the Manufacturing Cell Formation Problem (MCFP). Cellular Manufacturing is a production strategy that has emerged to reduce materials handling and set up times in order to reduce lead times in production systems and to improve customer??s service levels while reducing costs. We propose a GRASP heuristic to obtain lower bounds for the optimal solution of the problem. To evaluate the performance of the proposed method, we test the heuristic with different instances from the literature and compare the results obtained with those provided by other heuristic methods from the literature. According to the obtained results, the proposed GRASP procedure provides good quality lower bounds with reasonable computational effort.     

Efficient heuristics for the rectilinear distance capacitated multi-facility Weber problem

In this paper, we consider the capacitated multi-facility Weber problem with rectilinear distance. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the rectilinear distance separating them. We first give a new mixed integer linear programming formulation of the problem by making use of a well-known necessary condition for the optimal facility locations. We then propose new heuristic solution methods based on this formulation. Computational results on benchmark instances indicate that the new methods can provide very good solutions within a reasonable amount of computation time.     

The two-machine total completion time flow shop problem

In this paper we study the NP-hard scheduling problem of minimizing total completion time in a two-machine flow shop. Five known lower bounds are discussed and two new ones are presented. A new dominance criterion is also proposed. Several versions of a branch and bound method are derived by applying, both individually and combined, these lower bounds. A heuristic procedure is also presented that uses a constructive O(n²) time method, which computes a good starting solution, together with a neighborhood search based on pairwise interchanges. Computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0.5% from the optimal value and less than 2.7% from the lower bound.     

Discrete cooperative covering problems

A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p facilities from a given set of potential sites. Two other problems that can be solved by the max-cover approach are the equivalents to set covering and p-centre problems. The problems are formulated, analysed and solved on networks. Optimal and heuristic algorithms are proposed and extensive computational experiments reported.     

A dynamic programming heuristic for the P-median problem

A new heuristic algorithm is proposed for the P-median problem. The heuristic restricts the size of the state space of a dynamic programming algorithm. The approach may be viewed as an extension of the myopic or greedy adding algorithm for the P-median model. The approach allows planners to identify a large number of solutions all of which perform well with respect to the P-median objective of minimizing the demand weighted average distance between customer locations and the nearest of the P selected facilities. In addition, the results indicate regions in which it is desirable to locate facilities. Computational results from three test problems are discussed.     

Single machine earliness and tardiness scheduling

We examine the problem of scheduling a given set of jobs on a single machine to minimize total early and tardy costs without considering machine idle time. We decompose the problem into two subproblems with a simpler structure. Then the lower bound of the problem is the sum of the lower bounds of two subproblems. A lower bound of each subproblem is obtained by Lagrangian relaxation. Rather than using the well-known subgradient optimization approach, we develop two efficient multiplier adjustment procedures with complexity O(nlog n) to solve two Lagrangian dual subproblems. A branch-and-bound algorithm based on the two efficient procedures is presented, and is used to solve problems with up to 50 jobs, hence doubling the size of problems that can be solved by existing branch-and-bound algorithms. We also propose a heuristic procedure based on the neighborhood search approach. The computational results for problems with up to 3 000 jobs show that the heuristic procedure performs much better than known heuristics for this problem in terms of both solution efficiency and quality. In addition, the results establish the effectiveness of the heuristic procedure in solving realistic problems to optimality or near optimality.     

An integrated approach to dynamic plant location and capacity planning

We consider a dynamic capacitated plant location problem in which capacities of opened plants are determined by acquisition and/or disposal of multiple types of facilities. We determine the opening schedule of plants, allocations of customers' demands and plans for acquisition and/or disposal of plant capacities that minimise the sum of discounted fixed costs for opening plants, delivery costs of products, and acquisition and operation costs of facilities. The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts. Several solution properties of the relaxed problem are found and used to develop efficient solution procedures for the relaxed problem. A subgradient optimisation method is employed to obtain better lower bounds. The heuristic algorithm is tested on randomly generated test problems and results show that the algorithm finds good solutions in a reasonable amount of computation time.     

Solving the Passive Optical Network with Fiber Duct Sharing Planning Problem Using Discrete Techniques

Similar to the constrained facility location problem, the passive optical network (PON) planning problem necessitates the search for a subset of deployed facilities (splitters) and their allocated demand points (optical network units) to minimize the overall deployment cost. In this paper we use a mixed integer linear programming formulation stemming from network flow optimization to construct a heuristic based on limiting the total number of interconnecting paths when implementing fiber duct sharing. Then, a disintegration heuristic involving the construction of valid clusters from the output of a k means algorithm, reduce the time complexity while ensuring close to optimal results. The proposed heuristics are then evaluated using a real-world dataset, showing favourable performance.