Mixture selection for maximal stochastic performance

Methodology for the optimal selection of a mixture of components for the attainment of a required performance level is developed. This accommodates both cost and stochastic variation and is applied to gasoline blending. © 1994 John Wiley & Sons, Inc.     

Properties of a three-dimensional estimator

A large-scale simulation was conducted to investigate the statistical properties and the suitability of an estimator that estimates the coordinates of a three-dimensional source, according to the angles at which several observers view the source. The estimator uses a heuristical averaging method of estimates obtained from the solution of six two-dimensional problems that utilize line-to-point transformations. The estimator was found to be approximately unbiased with low standard deviations for normal error distributions. An effective and easy-to-use forecasting formula was developed to forecast the parameters of the distributions of the estimates. © 1994 John Wiley & Sons, Inc.     

A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand

A stochastic optimization model for capacity expansion for a service industry that incorporates uncertainty in future demand is developed. Based on a weighted set of possible demand scenarios, the model generates a recommended schedule of capacity expressions, and calculates the resulting sales under each scenario. The capacity schedule specifies the size, location, and timing of these expansions that will maximize the company's expected profit. The model includes a budget constraint on available resources. By using Lagrangian relaxation and exploiting the special nested knapsack structure in the sub-problems, an algorithm was developed for its solution. Based on the initial computational results, this algorithm appears to be more efficient than linear programming for this special problem. © 1994 John Wiley & Sons, Inc.     

Scheduling with earliness and tardiness penalties

We show that the deterministic nonpreemptive scheduling problem with earliness and tardiness penalties can be solved in polynomial time for certain forms of an objective function provided that a certain optimization problem can be solved. We give instances where this problem has a solution and show that this generalizes several results from the literature. These results do not require symmetric penalization and the penalty functions need only be lower semicontinuous.     

What you should know about simulation and derivatives

Derivatives (or gradients) are important for both sensitivity analysis and optimization, and in simulation models, these can often be estimated efficiently using various methods other than brute‐force finite differences. This article briefly summarizes the main approaches and discusses areas in which the approaches can most fruitfully be applied: queueing, inventory, and finance. In finance, the focus is on derivatives of another sort. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A bounded dual (all-integer) integer programming algorithm with an objective cut

In this article, we describe a new algorithm for solving all-integer, integer programming problems. We generate upper bounds on the decision variables, and use these bounds to create an advanced starting point for a dual all-integer cutting plane algorithm. In addition, we use a constraint derived from the objective function to speed progress toward the optimal solution. Our basic vehicle is the dual all-integer algorithm of Gomory, but we incorporate certain row- and column-selection criteria which partially avoid the problem of dual-degenerate iterations. We present the results of computational testing.     

A note on allocating jobs to two machines

A recent article in this journal by Mehta, Chandrasekaran, and Emmons [1] described a dynamic programming algorithm for assigning jobs to two identical parallel processors in a way that minimizes the average delay of these jobs. Their problem has a constraint on the sequence of the jobs such that any group of jobs assigned to a processor must be processed in the order of the sequence. This note has two purposes. First, we wish to point out a relationship between this work and some prior work [2]. Second, we wish to point out that Mehta, Chandrasekaran, and Emmons formulation, slightly generalized, can be used to find the optimum assignment of jobs to two machines in a more general class of problems than they considered including a subclass in which the jobs are not constrained to be processed in a given sequence.     

The lower bounded and partial upper bounded distribution model

This paper pruvides a smaller equivalelnt bounded variable transportation problem than that in Charnes, Glover, and Klingman [1] for the lower bounded and partial upper bounded distribution model.