Jeffrey L. Arthur

A Multiple Objective Nurse Scheduling Model

Abstract The authors present a model for the nurse scheduling problem which works in two phases. In the first phase, the nurses are assigned their day-on/day-off pattern for the two-week scheduling horizon by a goal programming model which allows for consideration of the multiple conflicting objectives inherent in scheduling a nursing staff. The second phase makes specific shift assignments through the use of a heuristic procedure. The two-phase approach results in considerable reductions in problem size, thus reducing the solution effort. Extensions to the basic model are also examined.

WEIGHING CONSERVATION OBJECTIVES: MAXIMUM EXPECTED COVERAGE VERSUS ENDANGERED SPECIES PROTECTION

Decision makers involved in land acquisition and protection often have mul- tiple conservation objectives and are uncertain about the occurrence of species or other features in candidate sites. Models informing decisions on selection of sites for reserves need to provide information about cost-efficient trade-offs between objectives and account for incidence uncertainty. We describe a site selection model with two important conser- vation objectives: maximize expected number of species represented, and maximize the likelihood that a subset of endangered species is represented. The model uses probabilistic species occurrence data in a linear-integer formulation solvable with commercial software. The model is illustrated using probabilistic occurrence data for 403 terrestrial vertebrates in 147 candidate sites in western Oregon, USA. The trade-offs between objectives are explicitly measured by incrementally varying the threshold probability for endangered species representation and recording the change in expected number of species represented. For instance, in the example presented here, we found that under most budget constraints, the probability of representing three endangered species can be increased from 0.00 (i.e., no guaranteed protection) to 0.90 while reducing expected species representation ;2%. However, further increasing the probability of endangered species representation from 0.90 to 0.99 results in a much larger reduction in species representation of ;14%. Although the numerical results from our analysis are specific to the species and area studied, the meth- odology is general and applicable elsewhere.

PAGP, A Partitioning Algorithm for (Linear) Goal Programming Problems

An algorithm Is presented for solving the hnear goal programming problem It is shown how the ordmal priomty factors m the goal programmmg objective function can be used to partmon the goal constraints of the problem, allowing a sequence of smaller subproblems to be solved in order to fred a solution to the original problem. Also discussed is the additional efficiency of the algorithm achieved by the use of variable elnninatmn and special terminatmn rules. Prehminary computatmnal results demonstrate the efficiency of the new algorithm.

Robust regression : analysis and applications

Robust Regression—Analysis and Applications. Edited by K. D. Lawrence and J. L. Arthur. ISBN 0 8247 8129 5. Dekker, New York, 1990. xiv + 288 pp.

Spatial-Endogenous Fire Risk and Efficient Fuel Management and Timber Harvest

107.50.

Finding all optimal solutions to the reserve site selection problem: formulation and computational analysis

This paper integrates a spatial fire-behavior model and a stochastic dynamic-optimization model to determine the optimal spatial pattern of fuel management and timber harvest. Each year’s fire season causes the loss of forest values and lives in the western United States. We use a multi-plot analysis and incorporate uncertainty about fire ignition locations and weather conditions to inform policy by examining the role of spatial endogenous risk—where management actions on one stand affect fire risk in that and adjacent stands. The results support two current strategies, but question two other strategies, for managing forests with fire risk. (JEL Q23)

Optimal spatial patterns of fuel management and timber harvest with fire risk.

The problem of selecting nature reserves has received increased attention in the literature during the past decade, and a variety of approaches have been promoted for selecting those sites to include in a reserve network. One set of techniques employs heuristic algorithms and thus provides possibly sub-optimal solutions. Another set of models and accompanying algorithms uses an integer programming formulation of the problem, resulting in an optimization problem known as the Maximal Covering Problem, or MCP. Solution of the MCP provides an optimal solution to the reserve site selection problem, and while various algorithms can be employed for solving the MCP they all suffer from the disadvantage of providing a single optimal solution dictating the selection of areas for conservation. In order to provide complete information to decision makers, the determination of all alternate optimal solutions is necessary. This paper explores two procedures for finding all such solutions. We describe the formulation and motivation of each method. A computational analysis on a data set describing native terrestrial vertebrates in the state of Oregon illustrates the effectiveness of each approach.

Economic and Spatial Impacts of an Existing Reserve Network on Future Augmentation

The stochastic and spatial nature of fire poses challenges for the cost-efficient allocation of fuel treatment over the landscape. A model that addresses complex but important components of fuel ma...

Analysis of the threshold and expected coverage approaches to the probabilistic reserve site selection problem

An optimization model for land reservation was developed that explicitly selects parcels in the most compact or contiguous manner possible while meeting habitat requirements and a budget limitation. The model was used to compare the effects of an existing reserve network on future parcel spatial locations and total cost. Using habitat and land value data from Josephine County, Oregon, it was found that a system of existing reserves created by various policies and overseen by different agencies can decrease future reserve compactness and contiguity, and increase total cost. This work suggests that coordinated planning can result in more efficient conservation efforts for less cost.

Multiple goal production and logistics planning in a chemical and pharmaceutical company

Two approaches to formulating the reserve site selection problem when species occurrence data is probabilistic were solved for terrestrial vertebrates in a small set of potential reserve sites in Oregon. The expected coverage approach, which maximizes the sum of the occurrence probabilities, yielded solutions that covered more species on average in Monte Carlo simulations than the threshold approach, which maximizes the number of species for which the occurrence probability exceeds some threshold.