Solving time/cost trade-off problems with discounted cash flows using generalized benders decomposition

In this article we consider a project scheduling problem where there are cash flows throughout the life of the project and where shorter activity durations can be attained by incurring greater direct costs. In particular, the objective of this problem is to determine the activity durations and a schedule of activity start times so that the net present value of cash flows is maximized. We formulate this problem as a mixed-integer nonlinear program which is amenable to solution using the generalized Benders decomposition technique developed by Geoffrion. We test the algorithm on 140 project scheduling problems, the largest of which contains 30 nodes and 64 activities. Our computational results are quite encouraging inasmuch as 123 of the 140 problems require less than 1 CPU second of solution time. © 1993 John Wiley & Sons, Inc.     

A multi-run interactive method for bicriterion optimization problems

This article introduces a new conceptual and methodological framework for the use of decision makers and their interactions with the computer in bicriterion decision making. The new method, called the multirun interactive method, attempts to estimate the prior of the decision maker on his uncertain preference nature using the minimum cross-entropy principle. A computational study is performed with four hypothesized prior distributions under various interaction conditions. Other important aspects related to the method, such as implementation of the method, decision making under certainty, decision making with multiple decision makers, and bicriterion integer programming, are also discussed.     

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.     

Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs

This article considers the problem of equipment replacement in which the replacement decision at a particular time must take into account (i) the state of the existing machine in use, (ii) the available replacement alternatives at the time, (iii) the future advances in the relevant technologies with regard to the equipment under consideration, and (iv) costs of switching between different technologies. A methodology that attains minimal forecast horizons for the problem is developed. A numerical example illustrates the methodology.     

A single-machine problem with multiple criteria

The problem considered is that of finding the set of efficient sequences of jobs on a single machine with respect to the total flow time and the number of tardy jobs. We present some properties of an existing algorithm and the problem itself.     

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.     

An exact aggregation/disaggregation algorithm for large scale markov chains

Many Markov chain models have very large state spaces, making the computation of stationary probabilities very difficult. Often the structure and numerical properties of the Markov chain allows for more efficient computation through state aggregation and disaggregation. In this article we develop an efficient exact single pass aggregation/disaggregation algorithm which exploits structural properties of large finite irreducible mandatory set decomposable Markov chains. The required property of being of mandatory set decomposable structure is a generalization of several other Markov chain structures for which exact aggregation/disaggregation algorithms exist. © 1995 John Wiley & Sons, Inc.     

Algorithms for the design of finite-capacity service units

Finite-capacity queues arise naturally in many practical situations, notably in communications and manufacturing engineering. In this article, the matrix formalism of probability distributions of phase type is used to develop fast algorithms to compute various steady-state distributions for the finite-capacity PH/PH/1 queue. This algorithm is an important ingredient in solving nontraditional but significant design problems. Some of these are described as illustrative examples.     

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.