A healthcare facility location problem for a multi-disease,multi-service environment under risk aversion

This paper presents a stochastic optimisation model for locating walk-in clinics for mobile populations in a network. The walk-in clinics ensure a continuum of care for the mobile population across the network by offering a perpetuation of services along the transportation lines, and also establishing referral systems to local healthcare facilities. The continuum of care requirements for different diseases is modelled using coverage definitions that are designed specifically to reflect the adherence protocols for services for different diseases. The risk of not providing the required care under different realisations of health service demand is considered. In this paper, for a multi-disease, multi-service environment, we propose a model to determine the location of roadside walk-in clinics and their assigned services. The objective is to maximise the total expected weighted coverage of the network subject to a Conditional-Value-at-Risk (CVaR) measure. This paper presents developed coverage definitions, the optimisation model and the computational study carried out on a real-life case in Africa.     

A continuous location problem with different norms

This paper considers a set of problems of fixing the number and location of facilities to cover a given set of demand points, such that each demand point is served within a range of known distance standards, where each facility can be located on the entire plane and the distance can be either measured in rectilinear, Euclidean or Tchebycheff units. It is shown that an optimum solution can always be found on a small finite set of points. Thus the optimum itself can be found by either complete enumeration of these points or by zero one integer linear programming techniques. Furthermore, it is shown that the least and the largest number of facilities are required for the rectilinear and the Tchebycheff cases respectively.     

Sequential facility location with distance dependent demand

Systems providing identical service to many population centers frequently face the issue of where to locate the next retail outlet, branch, store, etc. In such systems the demand for the facilities' service depends mainly on the distance between facilities and customers. It is assumed that there are already m facilities located on a network to respond to the demand at the nodes. The paper addresses the problems of finding a location on the network for the (m +1 )st facility corresponding to a given total expected demand and of determining which demand points will be served by which facility. Also the range of the total expected demand values that can be realized along each link in the m +1 facility system is determined. Examples and a discussion of the results are provided.     

A goal programming model for facility location planning

The paper presents a goal programming model for facility location planning. Often the location-decision is coupled with multiple objectives, at times conflicting among themselves. Specifically the model considers the four major objectives: (i) necessary locations, (ii) maximum number of locations, (iii) capacity restrictions and (iv) transportation cost/walking distance minimization, simultaneously and proposes optimal locations in conjunction with the existing facilities in the region. The model developed has been illustrated with an example considering the location of community storage facilities in a specified region.     

Two planar facility location problems with high-speed corridors and continuous demand

The planar minisam (‘median’) and minimax (‘center’) facility location problems are examined under the assumptions that: demand is continuously and uniformly distributed: the L₁ (right-angle) metric is in use; and the planar region is traversed by a high-speed corridor (highway) running parallel to one of the directions of travel. For the minisum problem in a rectangular region, it is shown that, for any combination of problem parameters, there are only two candidate points in the region for the optimum location of the facility. This is also shown to be true for any convex and symmetric planar region. For the minimax problem in a rectangular region, there are only three candidate points for the optimal location. Some extensions and conjectures for the minisum problem involving more than one highway are also discussed.     

A new family of dispersive orderings

In this paper we introduce a new family of univariate dispersion orderings which, under mild conditions, includes the weakly dispersive ordering as a particular case. Different properties of the new class of dispersion orderings are analyzed. Some connections with other univariate dispersion orderings are stated. Finally an application of the new family of dispersion orders to the field of genetics is developed.     

A column generation-based approach to solve the preference scheduling problem for nurses with downgrading

The demand for nurses in virtually all western countries has been outpacing the supply for more than a decade. The situation is now at the point where the rules for good practice are being stretched to the limit and patient care is in jeopardy. The purpose of this paper is to present several ideas for maximizing the use of the available staff and to quantify the resultant benefits. Two approaches are investigated for substituting nurses with higher level skills for those with lower level skills when there is sufficient idle time to do so. Idle time is usually due to scheduling constraints and contractual agreements that prevent a hospital from arbitrarily assigning nurses to shifts over the week.When the substitution is skill-related, as it is here, it is often called downgrading. The models that we develop are for preference scheduling, which means that individual preferences are taken into account when constructing monthly rosters. There are several reasons for doing this in today's environment, the most important is the need to boost staff morale and increase retention. The problem is modeled as an integer program and solved with a column generation technique that relies on intelligent heuristics for identifying good candidate schedules. The computations show that high quality solutions, as measured by the reduction in the need for non-unit nurses as well as the degree to which preferences are satisfied, can usually be obtained in a matter of minutes.     

Simple methods for uncapacitated facility location/allocation problems

Facility location/allocation problems are encountered in many different areas of management science. The methods presented in the literature are complex and are not easily understood by practitioners who are not trained in the techniques of optimization. Simple heuristic methods are presented in this article. The methods are developed for three different types of uncapacitated problems: (1) unlimited facility capacity with no fixed cost; (2) unlimited facility capacity with a fixed cost for assignment; (3) multiperiod problems. Examples are included to illustrate the basic methods.     

时变环境下选址问题的一个启发式算法

配送中心选址作为物流管理中的一个重要研究问题受到广泛重视。然而,文献中所涉及的选址模型大都是静态的,即沿一条路径行进时所需的成本(或时间)是与出发时间无关的函数。但在实际生活中,它往往是会随时间的变化而变化的,这类问题被称为时变环境下的选址问题。文中讨论了时变环境下的单配送中心到多个零售点带容量约束的选址问题。由于该问题是NP-完备的,我们给出了一个启发式算法。     

Commentary on facility location in the presence of congested regions with the rectilinear distance metric

This paper is a commentary on the work of Butt and Cavalier (Socio-Econ. Plann. Sci. 31(2) (1997) 103), a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to find the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proceed to prove its adequacy for the case of rectangular congested regions in which the edges of the rectangles are parallel to the travel directions. In wake of the difficulties of the general problem, we consider a specific example of a convex quadrilateral congestion region and a pair of external origin and destination points. Finally, we revisit the example shown in Butt and Cavalier's paper and present a mixed integer linear programming formulation that determines the optimal locations of the entry and exit points for this example.     

Including deprivation costs in facility location models for humanitarian relief logistics

Humanitarian assistance is meant to save lives and alleviate human suffering during and in the aftermath of man-made and natural disasters. To prevent and strengthen preparedness for the occurrence of such situations, having available relief supplies in the short-term becomes crucial. The lack of access to life-sustaining items implies a loss in people's welfare, treated as an externality called deprivation costs which must be incorporated into decision-making processes. Since typical humanitarian applications are extensions of commercial logistic models, they usually do not account for externalities, leading to high social costs and likely to unfeasible or suboptimal solutions.This paper develops a facility location model for prepositioning supplies in preparation for disasters; the key feature of this formulation being the fact that it explicitly considers deprivation costs in the objective function. The model attempts to minimize the global social costs, as the sum of both private costs (i.e. costs of transportation, inventory costs and fixed costs of facilities) and deprivation costs, determining the amount per type of product to be prepositioned for serving the areas affected by a disaster during the initial response. The model focuses on those assistance interventions that should be carried out immediately, i.e. within the first 24 h of a humanitarian crisis. We applied the model, using real information, to the Colombian Caribbean region, which was affected by floods in 2010 and 2011. Results demonstrate that deprivation costs represent more than 50% of the total social cost.     

The maximal covering location problem with accessibility indicators and mobile units

We study the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units that maximizes the facilities coverage, the accessibility of the zones to the open facilities, and the spatial disaggregation. The main characteristic of our problem is that mobile units can be deployed from open facilities to extend the coverage, accessibility, and opportunities for the inhabitants of the different demand zones. We formulate the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units as a mixed-integer linear programming model. To solve larger instances, we propose a matheuristic (combination of exact and heuristic methods) composed of an Estimation of Distribution Algorithm and a parameterized Maximal Covering Location Problem with Accessibility Indicators and Mobile Units integer model. To test our methodology, we consider the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units model to cover the low-income zones with Severe Acute Respiratory Syndrome Coronavirus 2 patients. Using official databases, we made a set of instances where we considered the poverty index, number of population, locations of hospitals, and Severe Acute Respiratory Syndrome Coronavirus 2 patients. The experimental results show the efficiency of our methodologies. Compared to the case without mobile units, we drastically improve the coverage and accessibility for the inhabitants of the demand zones.     

The flow-refueling location problem for alternative-fuel vehicles

Beginning with Hodgson (Geogr.Anal.22(1990) 270), several researchers have been developing a new kind of location-allocation model for “flow capturing.” Instead of locating central facilities to serve demand at fixed points in space, their models aim to serve demand consisting of origin-destination flows along their shortest paths. This paper extends flow-capturing models to optimal location of refueling facilities for alternative-fuel (alt-fuel) vehicles, such as hydrogen fuel cells or natural gas. Existing flow-capturing models assume that if a flow passes just one facility along its path, it is covered. This assumption does not carry over to vehicle refueling because of the limited range of vehicles. For refueling, it may be necessary to stop at more than one facility in order to successfully refuel the entire path, depending on the vehicle range, the path length, and the node spacing. The Flow Refueling Location Model (FRLM) optimally locates p refueling stations on a network so as to maximize the total flow volume refueled. This paper presents a mixed-integer programming formulation for the nodes-only version of the problem, as well as an algorithm for determining all combinations of nodes that can refuel a given path. A greedy-adding approach is demonstrated to be suboptimal, and the tradeoff curve between number of facilities and flow volume refueled is shown to be nonconvex.     

西方城市公共服务设施区位研究进展

通过梳理国外公共服务设施区位理论的发展以及近年来研究的新动向,提出了对我国城市公共服务设施区位研究的展望。     

Optimization of the facility location-allocation problem in a customer-driven supply chain

This paper develops and applies an integrated multiple criteria decision making approach to optimize the facility location-allocation problem in the contemporary customer-driven supply chain. Unlike the traditional optimization techniques, the proposed approach, combining the analytic hierarchy process (AHP) and the goal programming (GP) model, considers both quantitative and qualitative factors, and also aims at maximizing the benefits of deliverer and customers. In the integrated approach, the AHP is used first to determine the relative importance weightings or priorities of alternative locations with respect to both deliverer oriented and customer oriented criteria. Then, the GP model, incorporating the constraints of system, resource, and AHP priority is formulated to select the best locations for setting up the warehouses without exceeding the limited available resources. In this paper, a real case study is used to demonstrate how the integrated approach can be applied to deal with the facility location-allocation problem, and it is proved that the integrated approach outperforms the traditional cost-based approach.     

Planning horizon results for the dynamic warehouse location problem

In the last decade, a number of models for the dynamic facility location problem have been proposed. The various models contain differing assumptions regarding the revenues and costs realized in the opening, operation, and closure of a facility as well as considering which of the facility sites are candidates for acquisition or disposal at the beginning of a time period. Since the problem becomes extremely large for practical applications, much of the research has been directed toward developing efficient solution techniques. Most of the models and solutions assume that the facilities will be disposed of at the end of the time horizon since distant future conditions usually can't be forecasted with any reasonable degree of accuracy. The problem with this approach is that the “optimal” solution is optimal for only one hypothesized post horizon facility configuration and may become nonoptimal under a different configuration. Post-optimality analysis is needed to assure management that the “optimal” decision to open or close a facility at a given point in time won't prove to be “nonoptimal” when the planning horizon is extended or when design parameters in subsequent time periods change. If management has some guarantee that the decision to open or close a facility in a given time period won't change, it can safely direct attention to the accuracy of the design parameters within that time period.This paper proposes a mixed integer linear programming model to determine which of a finite set of warehouse sites will be operating in each time period of a finite planning horizon. The model is general in the sense that it can reflect a number of acquisition alternatives—purchase, lease or rent. The principal assumptions of the model are: a) Warehouses are assumed to have infinite capacity in meeting customer demand, b) In each time period, any non-operating warehouse is a candidate for becoming operational, and likewise any operating warehouse is a candidate for disposal, c) During a given time period, the fixed costs of becoming operational at a site are greater than the disposal value at that site to reflect the nonrecoverable costs involved in operating a warehouse. These costs are separate from the acquisition and liquidation values of the site. d) During a time period the operation of a warehouse incurs overhead and maintenance costs as well as a depreciation in the disposal value.To solve the model, it is first simplified and a partial optimal solution is obtained by the iterative examination by both lower and upper bounds on the savings realized if a site is opened in a given time period. An attempt is made to fix each warehouse open or closed in each time period. The bounds are based on the delta and omega tests proposed by Efroymson and Ray (1966) and Khumawala (1972) with adjustment for changes in the value of the warehouse between the beginning and end of a time period. A complete optimal solution is obtained by solving the reduced model with Benders' decomposition procedure. The optimal solution is then tested to determine which time periods contain “tentative” decisions that may be affected by post horizon data by analyzing the relationship between the lower (or upper) bounds used in the model simplification time period. If the warehouse decisions made in a time period satisfy these relationships and are thus unaffected by data changes in subsequent time periods, then the decisions made in earlier time periods will also be unaffected by future changes.     

Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem

This study considers a situation in which agents choose the location of a public facility from a street according to a given mechanism. Agents have single-dipped preferences over a set of feasible locations. We analyze coalitional behavior for any given mechanism for this situation. We identify a necessary and sufficient condition for a mechanism to possess a strong Nash equilibrium by applying the minimax theorem of von Neumann and Morgenstern (1944). We introduce a class of core solutions and show that these solutions are characterized by strong Nash implementability. As a byproduct of these results, we propose a simple mechanism that implements any core solution in strong Nash equilibria.     

A new approach to inter-rater agreement through stochastic orderings: the discrete case

We wish to study inter-rater agreement comparing groups of observers who express their ratings on a discrete or ordinal scale. The starting point is that of defining what we mean by “agreement”. Given d observers, let the scores they assign to a given statistical unit be expressed as a d-vector in the real space. We define a deterministic ordering among these vectors, which expresses the degree of the raters’ agreement. The overall scoring of the raters on the sample space will be a d-dimensional random vector. We then define an associated partial ordering among the random vectors of the ratings, illustrate a number of its properties, and look at order-preserving functions (agreement measures). In this paper we also show how to test the hypothesis of greater agreement against the unrestricted hypothesis, and the hypothesis of equal agreement against the hypothesis that an agreement ordering holds. The test is applied to real data on two medical observers rating clinical guidelines.     

A note on preference for flexibility

A result of Kreps (1979) on preference for flexibility is extended from two to three periods (formally from preferences over sets to preferences over sets of sets). An intuitively easier route to Kreps' original result is also presented, making the proof essentially ready for use in a decision theory class. Received: 23 April 2001 / Accepted: 1 September 2001 First version October 1997.     

A free-rider problem with a free-riding principal

In a moral hazard problem caused purely by joint production and not by uncertainty, we examine the problem faced by a principal who actively participates in production along with a group of agents. We show that, when designing the optimal output sharing rule, the principal need not look for anything more complicated than the frequently observed simple linear or piecewise linear rules. We also confirm the presence of a friction between the principal’s residual claimant role and her incentive to free-ride in the production process that prohibits her from completely mitigating the moral hazard problem. This paper is from the first chapter of my Ph.D. dissertation at The University of British Columbia, Canada, 1993. I would like to thank my thesis supervisor John Weymark for his many helpful comments and suggestions. I have also benefitted from the comments of Charles Blackorby, David Donaldson, Mukesh Eswaran, Kenneth Hendricks, Ashok Kotwal and Guofu Tan. An anonymous referee and an associate editor provided helpful suggestion. I am also grateful for the hospitality of the Indian Statistical Institute, Delhi Centre, and the Centre for Development Economics, Delhi School of Economics, where parts of the paper were revised while I was a visitor. I am solely responsible for any remaining errors and omissions.