Humanitarian response to hurricane disasters: Coordinating flood‐risk mitigation with fundraising and relief operations

To alleviate flooding, caused by hurricanes, governments build structural barriers called levees. In addition, relief providers such as the nongovernmental organizations and charities raise funds, and procure and deliver supplies (food, water, and medicines) for humanitarian relief. The strategy for managing disasters must, therefore, weigh the costs and benefits of building levees as well as procuring and delivering supplies. We use a three‐stage decision making framework to study how the investment in levee capacity can be integrated with supply procurements, fundraising, and rapid response. One of our major findings is that a large fundraising cost discourages postdisaster funding, implying relatively large investments in levee and prepositioned supplies. That notwithstanding, a large social value (of saving life) can tilt the balance in favor of postdisaster funding. If the levee capacity increases, funding for predisaster procurement is reduced without affecting postdisaster funding. For a sufficiently large increase in capacity, however, postdisaster response becomes superfluous. We also find that hurricane uncertainty motivates levees with large capacity. In contrast, levee‐failures motivate levees with small capacity.     

Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue

We use the matrix‐geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady‐state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981), 945–958] can be extended to an upper triangular block structure. Moreover, the subblock matrices of matrix R also have such a structure. With this special structure, we develop a procedure to compute the matrix R. After obtaining the stationary distribution of the system, we study two primary performance indices, namely, the distributions of the number of jobs of each type in the system and their waiting times. Although most of our analysis is carried out for the case of K = 3, the developed approach is general enough to study the other cases (K ≥ 4). © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 662–682, 2003.     

Scheduling patients in an ambulatory surgical center

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no‐wait, two‐stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search‐based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003     

An optimal ordering policy for situations with uncertainty in supply

A one-period inventory model where supply is a random variable with mean proportional to the quantity ordered has been considered. Under new better than used in expectation assumption on the supply variable, a strategy which maximizes a minimum profit has been suggested. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been proposed and almost sure convergence of this estimate to its true value with increasing sample size has been established.     

Asymptotic normality of the estimated optimal order quantity for one-period inventories with supply uncertainty

A one-period inventory situation where the supply is an NBUE random variable with mean proportional to the quantity ordered has been considered. The optimal exponential order quantity, which maximizes the minimum profit obtainable in the NBUE class of supply distributions, is a function of the demand distribution function. Here we show that an estimator of the maximin order quantity, which is already known to converge almost surely to its true value, converges also in distribution to an appropriate normal law with increasing sample size.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

An approach to postoptimality and sensitivity analysis of zero-one goal programs

In this article we present a methodology for postoptimality and sensitivity analysis of zero-one goal programs based on the set of k-best solutions. A method for generating the set of k-best solutions using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problem are discussed. Rules for determining the range of parameter changes that still allows a member of the k-best set to be optimal are developed. An investigation of a sufficient condition for postoptimality analysis is also presented.