Simulating nonhomogeneous poisson processes with proportional intensities

The purpose of this research is to investigate simulation algorithms for nonhomogeneous Poisson processes with proportional intensities. Two algorithmic approaches are studied: inversion and thinning. Motivated by industrial practices, the covariate vector involved in the simulation is permitted to change after every event (or observation). The algorithms are extended to permit the simulation of general nonhomogeneous Poisson processes with possible discontinuities both in baseline intensity and covariate vector. This latter extension can be used to facilitate a wide range of failure situations that can arise with repairable systems. © 1994 John Wiley & Sons, Inc.     

Single machine scheduling with a restricted rate‐modifying activity

In this paper we consider the problem of scheduling a set of jobs on a single machine on which a rate‐modifying activity may be performed. The rate‐modifying activity is an activity that changes the production rate of the machine. So the processing time of a job is a variable, which depends on whether it is scheduled before or after the rate‐modifying activity. We assume that the rate‐modifying activity can take place only at certain predetermined time points, which is a constrained case of a similar problem discussed in the literature. The decisions under consideration are whether and when to schedule the rate‐modifying activity, and how to sequence the jobs in order to minimize some objectives. We study the problems of minimizing makespan and total completion time. We first analyze the computational complexity of both problems for most of the possible versions. The analysis shows that the problems are NP‐hard even for some special cases. Furthermore, for the NP‐hard cases of the makespan problem, we present a pseudo‐polynomial time optimal algorithm and a fully polynomial time approximation scheme. For the total completion time problem, we provide a pseudo‐polynomial time optimal algorithm for the case with agreeable modifying rates. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

An algorithm (GIPC2) for solving integer programming problems with separable nonlinear objective functions

This paper presents an algorithm for solving the integer programming problem possessing a separable nonlinear objective function subject to linear constraints. The method is based on a generalization of the Balas implicit enumeration scheme. Computational experience is given for a set of seventeen linear and seventeen nonlinear test problems. The results indicate that the algorithm can solve the nonlinear integer programming problem in roughly the equivalent time required to solve the linear integer programming problem of similar size with existing algorithms. Although the algorithm is specifically designed to solve the nonlinear problem, the results indicate that the algorithm compares favorably with the Branch and Bound algorithm in the solution of linear integer programming problems.     

Server scheduling on parallel dedicated machines with fixed job sequences

We consider server scheduling on parallel dedicated machines to minimize the makespan. Each job has a loading operation and a processing operation. The loading operation requires a server that serves all the jobs. Each machine has a given set of jobs to process, and the processing sequence is known and fixed. We design a polynomial‐time algorithm to solve the two‐machine case of the problem. When the number of machines is arbitrary, the problem becomes strongly NP‐hard even if all the jobs have the same processing length or all the loading operations require a unit time. We design two heuristic algorithms to treat the case where all the loading times are unit and analyze their performance.     

Optimal renewal policies for complex systems

Most maintenance and replacement models for industrial equipment have been developed for independent single-component machines. Most equipment, however, consists of multiple components. Also, when the maintenance crew services several machines, the maintenance policy for each machine is not independent of the states of the other machines. In this paper, two dynamic programming replacement models are presented. The first is used to determine the optimal replacement policy for multi-component equipment. The second is used to determine the optimal replacement policy for a multi-machine system which uses one replacement crew to service several machines. In addition, an approach is suggested for developing an efficient replacement policy for a multi-component, multi-machine system.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

An FPTAS for scheduling a two‐machine flowshop with one unavailability interval

We study a deterministic two‐machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP‐hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n⁵/ε⁴) time complexity. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Exploiting symmetry in the reliability analysis of coherent systems

Components in a complex system are usually not structurally identical. However, in many cases we may find components that are structurally symmetric, and one should make use of this additional information to simplify reliability analysis. The main purpose of this article is to define and study one such class of systems, namely, those having symmetric components, and to derive some reliability-related properties. © 1996 John Wiley & Sons, Inc.