Cyclic preference scheduling for nurses using branch and price

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch‐and‐price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

An efficient heuristic for the multi-item newsboy problem with a single constraint

This article treats the problem of determining optimal and approximately optimal order quantities for a multiple-item inventory system subject to a single constraint on space or budget. Although this problem can be solved by the usual method of Lagrange multipliers, we wish to consider a more efficient scheme that requires fewer computations. We provide calculations that compare and contrast four approximation techniques. In particular, we have discovered a method that yields a direct algebraic expression of the problem parameters for allocation and achieves an expected profit within 90% of the optimal in about 90% of the cases tested.     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

A single server queue with arrival rate dependent on server breakdowns

This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as an M/E_k/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. The durations of the operating and failed periods are exponential with mean 1/cβ and Erlang with mean 1/cβ, respectively. Generating functions are used to derive the steady-state quantities L and W, both of which, when viewed as functions of c, decrease at a rate inversely proportional to c². The paper includes an analysis of several special and extreme cases and an application to a production-storage system.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Northwest corner and banded matrix approximations to a Markov chain

In this paper, we consider approximations to discrete time Markov chains with countably infinite state spaces. We provide a simple, direct proof for the convergence of certain probabilistic quantities when one uses a northwest corner or a banded matrix approximation to the original probability transition matrix. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 187–197, 1999     

A Cryptographic Escrow for Treaty Declarations and Step-by-Step Verification

The verification of arms-control and disarmament agreements requires states to provide declarations, including information on sensitive military sites and assets. There are important cases, however, in which negotiations of these agreements are impeded because states are reluctant to provide any such data, because of concerns about prematurely handing over militarily significant information. To address this challenge, we present a cryptographic escrow that allows a state to make a complete declaration of sites and assets at the outset and commit to its content, but only reveal the sensitive information therein sequentially. Combined with an inspection regime, our escrow allows for step-by-step verification of the correctness and completeness of the initial declaration so that the information release and inspections keep pace with parallel diplomatic and political processes. We apply this approach to the possible denuclearization of North Korea. Such approach can be applied, however, to any agreement requiring the sharing of sensitive information.     

On the design of a tandem queue with blocking: Modeling,analysis, and gradient estimation

We demonstrate here how recent advances in the study of discrete-event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make-to-stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade-off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample-path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 1994 John Wiley & Sons, Inc.     

Replacing nonidentical vital components to extend system life

We consider a system that depends on a single vital component. If this component fails, the system life will terminate. If the component is replaced before its failure then the system life may be extended; however, there are only a finite number of spare components. In addition, the lifetimes of these spare components are not necessarily identically distributed. We propose a model for scheduling component replacements so as to maximize the expected system survival. We find the counterintuitive result that when comparing components' general lifetime distributions based on stochastic orderings, not even the strongest ordering provides an a priori guarantee of the optimal sequencing of components. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008