Oded Berman

Facility Reliability Issues in Network p-Median Problems: Strategic Centralization and Co-Location Effects

In this paper we analyze a facility location model where facilities may be subject to disruptions, causing customers to seek service from the operating facilities. We generalize the classical p-Median problem on a network to explicitly include the failure probabilities, and analyze structural and algorithmic aspects of the resulting model. The optimal location patterns are seen to be strongly dependent on the probability of facility failure - with facilities becoming more centralized, or even co-located, as the failure probability grows. Several exact and heuristic solution approaches are developed. Extensive numerical computations are performed

Optimal Location of Discretionary Service Facilities

Automatic teller machines and gasoline service stations are two examples of a growing number of “discretionary service facilities.” In consuming service from these facilities, a significant fraction of customers do so on an otherwise preplanned trip (e.g., on the daily commute to and from work). A system planner, in determining the best locations of such facilities, is more concerned with placing the facilities along paths of customer flow rather than, say, near the center of a cluster of residences or work places. We formally model this problem and present a method for determining the optimal locations of m discretionary service facilities so as to intercept the maximum possible potential customer flow. We also show how to determine the minimal number of facilities required to intercept a prespecified fraction of total customer flow. Computational results are included.

Optimal Server Location on a Network Operating as an M/G/1 Queue

This paper extends Hakimis one-median problem by embedding it in a general queueing context. Demands for service arise solely on the nodes of a network G and occur in time as a Poisson process. A single mobile server resides at a facility located on G. The server, when available, is dispatched immediately to any demand that occurs. When a demand finds the server busy with a previous demand, it is either rejected Model 1 or entered into a queue that is depleted in a first-come, first-served manner Model 2. Service time for each demand comprises travel time to the scene, on-scene time, travel time back to the facility and possibly additional off-scene time. One desires to locate the facility on G so as to minimize average cost of response, which is either a weighted sum of mean travel time and cost of rejection Model 1, or the sum of mean queueing delay and mean travel time. For Model 1, one finds that the optimal location reduces to Hakimis familiar nodal result. For Model 2, nonlinearities in the objective function can yield an optimal solution that is either at a node or on a link. Properties of the objective function for Model 2 are utilized to develop efficient finite-step procedures for finding the optimal location. Certain interesting properties of the optimal location as a function of demand rate are also developed.

Analysis of Transfer Lines Consisting of Two Unreliable Machines with Random Processing Times and Finite Storage Buffers

Abstract A Markov process model of a transfer line is presented in which there are two machines and a single finite buffer. The machines have exponential service, failure, and repair processes. The movement of discrete parts is represented. The model is analyzed and a compact solution is obtained. Limiting behavior is investigated and numerical results are discussed.

The generalized maximal covering location problem

We consider a generalization of the maximal cover location problem which allows for partial coverage of customers, with the degree of coverage being a non-increasing step function of the distance to the nearest facility. Potential application areas for this generalized model to locating retail facilities are discussed.We show that, in general, our problem is equivalent to the uncapacitated facility location problem. We develop several integer programming formulations that capitalize on the special structure of our problem. Extensive computational analysis of the solvability of our model under a variety of conditions is presented.

Competitive facility location and design problem

Abstract We develop a spatial interaction model that seeks to simultaneously optimize location and design decisions for a set of new facilities. The facilities compete for customer demand with pre-existing competitive facilities and with each other. The customer demand is assumed to be elastic, expanding as the utility of the service offered by the facilities increases. Increases in the utility can be achieved by increasing the number of facilities, design improvements, or locating facilities closer to the customer. We show that our model is able to capture some of the principal trade-offs involved in facility location and design decisions, including demand cannibalization, market expansion, and design/location trade-offs. Managerial insights are obtained through sensitivity analysis of the model and through several illustrative examples. An efficient near-optimal solution approach, with adjustable error bound, is developed for the special case where only a finite number of design alternatives are available. Several heuristic approaches capable of handling large instances are also presented.

The gradual covering decay location problem on a network

Abstract In covering problems it is assumed that there is a critical distance within which the demand point is fully covered, while beyond this distance it is not covered at all. In this paper we define two distances. Within the lower distance a demand point is fully covered and beyond the larger distance it is not covered at all. For a distance between these two values we assume a gradual coverage decreasing from full coverage at the lower distance to no coverage at the larger distance.

FLOW INTERCEPTING SPATIAL INTERACTION MODEL: A NEW APPROACH TO OPTIMAL LOCATION OF COMPETITIVE FACILITIES.

Abstract In this paper we propose a flexible new model for the location of competitive facilities that may derive their demand for service from both special-purpose purchase trips by their customers and from “intercepting” customers passing by a facility while en route to another destination on the network. Our model combines the features of the spatial interaction and flow interception models. An efficient heuristic procedure is developed, with worst case analysis provided. We also develop a tight upper bound and a branch-and-bound scheme for our model. Results of a set of computational experiments are presented.

Minimax regret p-center location on a network with demand uncertainty

Abstract We consider the weighted p-center problem on a transportation network with uncertain weights of nodes. Specifically, for each node, an interval estimate of its weight is known. The objective is to find the ‘minimax regret’ solution i.e. to minimize the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. We discuss properties of the problem and show that the problem can be solved by means of solving (n + 1) regular weighted p-center problems. This leads to polynomial algorithms for the cases where the regular weighted p-center problem can be solved in polynomial time, e.g. for the case of a tree network, and for the case of a general network with p = 1.

Incorporating congestion in preventive healthcare facility network design

Preventive healthcare aims at reducing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The level of participation to preventive healthcare programs is a crucial factor in terms of their effectiveness and efficiency. This paper provides a methodology for designing a network of preventive healthcare facilities so as to maximize participation. The number of facilities to be established and the location of each facility are the main determinants of the configuration of a healthcare facility network. We use the total (travel, waiting and service) time required for receiving the preventive service as a proxy for accessibility of a healthcare facility, and assume that each client would seek the services of the facility with minimum expected total time. At each facility, which we model as an M/M/1 queue so as to capture the level of congestion, the expected number of participants from each population zone decreases with the expected total time. In order to ensure service quality, the facilities cannot be operated unless their level of activity exceeds a minimum workload requirement. The arising mathematical formulation is highly nonlinear, and hence we provide a heuristic solution framework for this problem. Four heuristics are compared in terms of accuracy and computational requirements. The most efficient heuristic is utilized in solving a real life problem that involves the breast cancer screening center network in Montreal. In the context of this case, we found out that centralizing the total system capacity at the locations preferred by clients is a more effective strategy than decentralization by the use of a larger number of smaller facilities. We also show that the proposed methodology can be used in making the investment trade-off between expanding the total system capacity and changing the behavior of potential clients toward preventive healthcare programs by advertisement and education.