Maurice Queyranne

Dynamic Multipriority Patient Scheduling for a Diagnostic Resource

We present a method to dynamically schedule patients with different priorities to a diagnostic facility in a public health-care setting. Rather than maximizing revenue, the challenge facing the resource manager is to dynamically allocate available capacity to incoming demand to achieve wait-time targets in a cost-effective manner. We model the scheduling process as a Markov decision process. Because the state space is too large for a direct solution, we solve the equivalent linear program through approximate dynamic programming. For a broad range of cost parameter values, we present analytical results that give the form of the optimal linear value function approximation and the resulting policy. We investigate the practical implications and the quality of the policy through simulation.

The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling

The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jobs have to be processed at minimum cost on a single machine. The set-up cost associated with each job depends not only on the job that precedes it, but also on its position time in the sequence. The optimization method described here combines finding shortest paths in an associated multipartite network with subgradient optimization and some branch-and-bound enumeration. Minimizing the tardiness costs in one-machine scheduling in which the cost is a non-decreasing function of the completion time of each job is then attacked by this method. A branch-and-bound algorithm is designed for this problem. It uses a related time-dependent traveling salesman problem to compute the required lower bounds. We give computational results for the weighted tardiness problem.

An Exact Algorithm for Maximum Entropy Sampling

We study the experimental design problem of selecting a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations, and possibly, at different times. Information is measured by “entropy.” In the Gaussian case, the problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. We demonstrate that this problem is NP-hard. We establish an upper bound for the entropy, based on the eigenvalue interlacing property, and we incorporate this bound in a branch-and-bound algorithm for the exact solution of the problem. We present computational results for estimated covariance matrices that correspond to sets of environmental monitoring stations in the United States.

Approximation schemes for minimizing average weighted completion time with release dates

We consider the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. We present the first known polynomial time approximation schemes for several variants of this problem. Our results include PTASs for the case of identical parallel machines and a constant number of unrelated machines with and without preemption allowed. Our schemes are efficient: for all variants the running time for /spl alpha/(1+/spl epsiv/) approximation is of the form f(1//spl epsiv/, m)poly(n).

Structure of a simple scheduling polyhedron

In a one-machine nonpreemptive scheduling problem, the feasible schedules may be defined by the vector of the corresponding job completion times. For given positive processing times, the associated simple scheduling polyhedronP is the convex hull of these feasible completion time vectors. The main result of this paper is a complete description of the minimal linear system definingP. We also give a complete, combinatorial description of the face lattice ofP, and a simple, O(n logn) separation algorithm. This algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems.

Single Machine Scheduling with Release Dates

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent

On the structure of all minimum cuts in a network and applications

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Selected Applications of Minimum Cuts in Networks

-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least

On Dynamic Programming Methods for Assembly Line Balancing

e/(e-1) \approx 1.5819

Appointment Scheduling with Discrete Random Durations

. Both algorithms may be derandomized; their deterministic versions run in O(n2) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards.