Multiple facility location on a network with linear reliability order of edges

We study the problem of locating facilities on the nodes of a network to maximize the expected demand serviced. The edges of the input graph are subject to random failure due to a disruptive event. We consider a special type of failure correlation. The edge dependency model assumes that the failure of a more reliable edge implies the failure of all less reliable ones. Under this dependency model called Linear Reliability Order (LRO) we give two polynomial time exact algorithms. When two distinct LRO’s exist, we prove the total unimodularity of a linear programming formulation. In addition, we show that minimizing the sum of facility opening costs and expected cost of unserviced demand under two orderings reduces to a matching problem. We prove NP-hardness of the three orderings case and show that the problem with an arbitrary number of orderings generalizes the deterministic maximum coverage problem. When a demand point can be covered only if a facility exists within a distance limit, we show that the problem is NP-hard even for a single ordering.     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.     

A nested-compliance table policy for emergency medical service systems under relocation

The goal of Emergency Medical Service (EMS) systems is to provide rapid response to emergency calls in order to save lives. This paper proposes a relocation strategy to improve the performance of EMS systems. In practice, EMS systems often use a compliance table to relocate ambulances. A compliance table specifies ambulance base stations as a function of the state of the system. We consider a nested-compliance table, which restricts the number of relocations that can occur simultaneously. We formulate the nested-compliance table model as an integer programming model in order to maximize expected coverage. We determine an optimal nested-compliance table policy using steady state probabilities of a Markov chain model with relocation as input parameters. These parameter approximations are independent of the exact compliance table used. We assume that there is a single type of medical unit, single call priority, and no patient queue. We validate the model by applying the nested-compliance table policies in a simulated system using real-world data. The numerical results show the benefit of our model over a static policy based on the adjusted maximum expected covering location problem (AMEXCLP).     

Robust,multi-objective optimization for the military medical evacuation location-allocation problem

Determining where to locate mobile aeromedical staging facilities (MASFs) as well as identifying how many aeromedical helicopters to allocate to each MASF, commonly referred to as the medical evacuation (MEDEVAC) location-allocation problem, is vital to the success of a deployed MEDEVAC system. Within this research, we develop an integer mathematical programming formulation to determine the location and allocation of MEDEVAC assets over the phases of a military deployment to support operations ranging from peacekeeping through combat to post-combat resolution. Our model seeks to address the multi-objective problem of maximizing the expected demand coverage as a measure of solution effectiveness, minimizing the maximum number of located MASFs in any deployment phase as a measure of solution efficiency, and minimizing the total number of MASF relocations throughout the deployment as a measure of solution robustness. This research makes two contributions. First, it formulates a representative mathematical programming formulation and identifies an accompanying solution methodology (i.e., the ε-constraint Method) to assess and recommend improvements to deployed military MEDEVAC systems designed to provide large-scale emergency medical response for contingency operations that range in casualty-inducing intensity (i.e., demand) over the phases of a deployment. Second, the research illustrates the application of the model for a realistic, synthetically generated medical planning scenario in southern Azerbaijan. Comparisons are made between the model’s (multi-phase) optimal solution and the phase-specific optimal solutions that disregard concerns of transitions between phases. The results highlight the conflicting nature between the objectives and illustrate the trade-offs between objectives as restrictions applied to the second and third objectives are respectively tightened or relaxed.     

Multiobjective Decision-Tree Analysis1

Single-objective-based decision-tree analysis has been extensively and successfully used in numerous decision-making problems since its formal introduction by Howard Raiffa more than two decades ago. This paper extends the traditional methodology to incorporate multiple noncommensurate objective functions and use of the conditional expected value of the risk of extreme and catastrophic events. The proposed methodology considers the cases where (a) a finite number of actions are available at each decision node and (b) discrete or continuous states of nature can be presented at each chance node. The proposed extension of decision-tree analysis is introduced through an example problem that leads the reader step-by-step into the methodological procedure. The example problem builds on flood warning systems. Two noncommensurate objectives—the loss of lives and the loss of property (including monetary costs of the flood warning system)–are incorporated into the decision tree. In addition, two risk measures—the common expected value and the conditional expected value of extreme and catastrophic events—are quantified and are also incorporated into the decision-making process. Theoretical difficulties associated with the stage-wise calculation of conditional expected values are identified and certain simplifying assumptions are made for computational tractibility. In particular, it is revealed that decisions concerning experimentation have a very interesting impact on the noninferior solution set of options—a phenomenon that has no equivalence in the single-objective case.     

The facility location problem with Bernoulli demands

This paper presents the facility location problem with Bernoulli demands. In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the expected value of the recourse function. The problem is formulated as a two-stage stochastic program and two different recourse actions are considered. For each of them, a closed form is presented for the recourse function and a deterministic equivalent formulation is obtained for the case in which the probability of demand is the same for all customers. Numerical results from computational experiments are presented and analyzed.     

A Case Study of De-randomization Methods for Combinatorial Approximation Algorithms

We study three different de-randomization methods that are often applied to approximate combinatorial optimization problems. We analyze the conditional probabilities method in connection with randomized rounding for routing, packing and covering integer linear programming problems. We show extensions of such methods for non-independent randomized rounding for the assignment problem. The second method, the so-called random walks is exemplified with algorithms for dense instances of some NP problems. Another often used method is the bounded independence technique; we explicit this method for the sparsest cut and maximum concurrent flow problems.     

Location optimization of strategic alert sites for homeland defense

This research uses a location analysis approach for selecting aircraft alert sites for the defense of important national areas of interest identified by the US Department of Defense. Solutions are generated in a two step approach where the minimum number of sites is first identified using the location set covering problem and then the result is improved by finding the minimum aggregate network distance or p-median solution from the alternate optimal solutions to the LSCP. This approach also identifies the p-center solution to the problem ensuring equitable response to all areas of interest. Sensitivity analysis is performed to determine the impact of altering aircraft launch and flying times on the number of required alert sites and the amount of coverage provided by selecting fewer locations. Results indicate a significant increase in the number of alert locations needed in comparison to original military estimates. The research points out significant implications about future military base closure decisions and the trade-offs between cost and required response times of aircraft in a defense emergency.     

Flows with unit path capacities and related packing and covering problems

Since the seminal work of Ford and Fulkerson in the 1950s, network flow theory is one of the most important and most active areas of research in combinatorial optimization. Coming from the classical maximum flow problem, we introduce and study an apparently basic but new flow problem that features a couple of interesting peculiarities. We derive several results on the complexity and approximability of the new problem. On the way we also discover two closely related basic covering and packing problems that are of independent interest. Starting from an LP formulation of the maximum s-t-flow problem in path variables, we introduce unit upper bounds on the amount of flow being sent along each path. The resulting (fractional) flow problem is NP-hard; its integral version is strongly NP-hard already on very simple classes of graphs. For the fractional problem we present an FPTAS that is based on solving the k shortest paths problem iteratively. We show that the integral problem is hard to approximate and give an interesting O(log?m)-approximation algorithm, where m is the number of arcs in the considered graph. For the multicommodity version of the problem there is an $O(\sqrt{m})Since the seminal work of Ford and Fulkerson in the 1950s, network flow theory is one of the most important and most active areas of research in combinatorial optimization. Coming from the classical maximum flow problem, we introduce and study an apparently basic but new flow problem that features a couple of interesting peculiarities. We derive several results on the complexity and approximability of the new problem. On the way we also discover two closely related basic covering and packing problems that are of independent interest. Starting from an LP formulation of the maximum s-t-flow problem in path variables, we introduce unit upper bounds on the amount of flow being sent along each path. The resulting (fractional) flow problem is NP-hard; its integral version is strongly NP-hard already on very simple classes of graphs. For the fractional problem we present an FPTAS that is based on solving the k shortest paths problem iteratively. We show that the integral problem is hard to approximate and give an interesting O(log m)-approximation algorithm, where m is the number of arcs in the considered graph. For the multicommodity version of the problem there is an O(?m)O(\sqrt{m}) -approximation algorithm. We argue that this performance guarantee is best possible, unless P=NP.     

Heterogeneity and Unemployment Duration

ABSTRACT: Various unemployment duration models are estimated on a large Norwegian dataset covering labour market history 1.1.1989-31.12.1992 for all persons who became unemployed during October 1990. As many unemployed leave the unemployment register without going directly to a job, two alternative definitions of unemployment are used — register unemployment and joblessness. The problem of heterogeneity is addressed both by partitioning the individuals into four categories by previous unemployment history, and by including a random term in the job hazard. Observed as well as unobserved heterogeneity affects the estimates of expected duration to a great extent. When gamma-distributed unobserved heterogeneity is accounted for, the estimates of duration dependence become more positive relative to models where unobserved heterogeneity is ignored. Among persons who are entitled to unemployment benefit, the duration dependence appears to be significantly positive. Alternative specifications of the baseline hazard hardly affect estimates of the effects of the covariates on duration.     

Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona

Reverse logistics problems arising in municipal waste management are both wide-ranging and varied. The usual collection system in UE countries is composed of two phases. First, citizens leave their refuse at special collection areas where different types of waste (glass, paper, plastic, organic material) are stored in special refuse bins. Subsequently, each type of waste is collected separately and moved to its final destination (a recycling plant or refuse dump). The present study focuses on the problem of locating these collection areas. We establish the relationship between the problem, the set covering problem and the MAX-SAT problem and then go on to develop a genetic algorithm and a GRASP heuristic to, respectively, solve each formulation. Finally, the quality of the algorithms is tested in a computational experience with real instances from the metropolitan area of Barcelona, as well as a reduced set of set covering instances from the literature.     

基于双层规划的反恐应急设施选址模型及算法

恐怖袭击常以人流密集地区的平民作为袭击目标，并存在突发性和随机性等特点，极易造成严重的袭击后果。通过反恐应急设施的合理布局可以缩短救援人员和物资的到达时间，从而减轻袭击后果。首先，对反恐应急设施选址问题进行描述，并将其构造为一类离散双层规划模型。其中，上层规划是关于政府选址的0-1规划问题，下层规划则是关于恐怖分子袭击目标选择的0-1规划问题。其次，结合模型和问题的特征设计算法，利用分支定界算法实现上层选址变量的隐枚举，同时通过下层问题的求解来确定上下界并判断是否满足分枝或剪枝的条件。最后，结合南疆地区的交通拓扑网络进行算例分析，结果证明有效的选址方案可以大大降低袭击损失。     

The effect of MRP lot sizing on actual cumulative lead times in multi-level systems

This study investigates how different lot sizing techniques influence the cumulative lead time for multi-level production-inventory systems controlled by material requirements planning (MRP). Theoretical approaches, a numerical example, as well as simulation are used to analyse and illustrate the combined effect of lot sizing at different product structure levels. It is shown that lot-sizing requirements for more than a single period, such as fixed period requirements, period under quantity, Silver Meal algorithm, as well as economic order quantity will lead to longer actual cumulative lead times than would be expected, when taking the item lead times along the critical path through the product structure into account. Consequently, MRP will underestimate the cumulative lead time and will require a longer planning horizon. We show that the extension of the cumulative lead techniques covering the time is a lot-sizing related phenomenon and cannot be accounted for by, e.g. using safety lead time. Lot-sizing techniques with multi-period coverage will only occasionally provide the 'expected' cumulative lead time. We also show that average and maximum throughput times, as well as throughput time variability increases with increasing time-period coverage of lots.     

A set covering approach to bus stop location

This paper considers the problem of locating bus stops in the context of a set covering problem. Zero-one integer programming models are suggested for use in the location of bus stops on new routes and for use in the location of express bus stops on current routes. The models may be used to locate the minimum number of (express) bus stops required to ensure that no passenger need walk more than a specified distance to reach an (express) bus stop. A modified version of the model is presented which enables the router to locate a specified number of (express) bus stops in such a manner that the total distance walked by all boarders is minimized.     

Locating Emergency Warning Sirens

In this paper, we report on the application of set covering and maximal covering location models to the problem of locating emergency warning sirens in a midwestern city. Two siren types are available, each having different costs and covering radii. Using a modified version of the set covering location model, we analyze the cost implications of several policy options being considered by the city's planners. Results of the study indicate that location covering models can be powerful and efficient tools in the design of such systems, and their use can lead to significant cost savings. In addition, such models provide decision makers the flexibility to examine the inherent costs associated with various policy options.     

The P-Hub maximal covering problem and extensions for gradual decay functions

The p-hub maximal covering problem aims to find the best locations for hubs so as to maximize demands within a coverage distance with a predetermined number of hubs. Classically, the problem is defined in the framework of binary coverage only; an origin–destination pair is covered if the cost (time, etc.) is lower than the critical value, and not covered at all if the cost is greater than the critical value. In this paper, we extend the definition of coverage, introducing “partial coverage”, which changes with distance. We present new and efficient mixed-integer programming models that are also valid for partial coverage for single and multiple allocations. We present and discuss the computational results with different data sets.     

EDUCATION

The power of an integer programming approach—and more particularly a 0,1 programming approach—to resource allocation problems is not widely appreciated. Recent developments in mathematical programming and in problem formulation enable decision makers to deal explicitly with the special conditions which characterize real world problems in capital budgeting, scheduling, and facilities planning. In this paper, somewhat tutorial in nature, we seek to demonstrate formulation and solution of an equipment selection resource allocation problem with several special conditions. The problem can be solved on any reasonably equipped computer system. Sensitivity studies are also performed and discussed.     

Coverage by directional sensors in randomly deployed wireless sensor networks

We study a novel “coverage by directional sensors” problem with tunable orientations on a set of discrete targets. We propose a Maximum Coverage with Minimum Sensors (MCMS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the number of sensors to be activated is minimized. We present its exact Integer Linear Programming (ILP) formulation and an approximate (but computationally efficient) centralized greedy algorithm (CGA) solution. These centralized solutions are used as baselines for comparison. Then we provide a distributed greedy algorithm (DGA) solution. By incorporating a measure of the sensors residual energy into DGA, we further develop a Sensing Neighborhood Cooperative Sleeping (SNCS) protocol which performs adaptive scheduling on a larger time scale. Finally, we evaluate the properties of the proposed solutions and protocols in terms of providing coverage and maximizing network lifetime through extensive simulations. Moreover, for the case of circular coverage, we compare against the best known existing coverage algorithm.     

SCHEDULING JOBS ON PARALLEL PROCESSORS WITH DYNAMIC PROGRAMMING

The problem of scheduling jobs on M-parallel processors is one of selecting a set of jobs to be processed from a set of available jobs in order to maximize profit. This problem is examined and a dynamic programming solution is presented which decomposes it into a sequencing problem within an allocation problem. The computation required for solution is found to depend on the sequencing problem as it is affected by the waiting cost function. Various forms of the waiting cost function are considered. The solution procedure is illustrated by an example, and possible extensions of the formulation are discussed.     

Discrete parallel machine makespan ScheLoc problem

Scheduling–Location (ScheLoc) problems integrate the separate fields of scheduling and location problems. In ScheLoc problems the objective is to find locations for the machines and a schedule for each machine subject to some production and location constraints such that some scheduling objective is minimized. In this paper we consider the discrete parallel machine makespan ScheLoc problem where the set of possible machine locations is discrete and a set of n jobs has to be taken to the machines and processed such that the makespan is minimized. Since the separate location and scheduling problem are both \(\mathcal {NP}\)-hard, so is the corresponding ScheLoc problem. Therefore, we propose an integer programming formulation and different versions of clustering heuristics, where jobs are split into clusters and each cluster is assigned to one of the possible machine locations. Since the IP formulation can only be solved for small scale instances we propose several lower bounds to measure the quality of the clustering heuristics. Extensive computational tests show the efficiency of the heuristics.