Scheduling of stochastic tasks on two parallel processors

We consider the problem of scheduling n tasks on two identical parallel processors. We show both in the case when the processing times for the n tasks are independent exponential random variables, and when they are independent hyperexponentials which are mixtures of two fixed exponentials, that the policy of performing tasks with longest expected processing time (LEPT) first minimizes the expected makespan, and that in the hyperexponential case the policy of performing tasks with shortest expected processing time (SEPT) first minimizes the expected flow time. The approach is simpler than the dynamic programming approach recently employed by Bruno and Downey.     

On a single-server queue with state-dependent service

This paper discusses a class of queueing models in which the service time of a customer al a single server facility is dependent on the queue size at the onset of its service. The Laplace transform for the wait in queue distribution is derived and the utilization of the server is given when the arrival is a homogeneous Poisson process.     

Adaptive disposal models

This paper reconsiders the classical model for selling an asset in which offers come in daily and a decision must then be made as to whether or not to sell. For each day the item remains unsold a continuation (or maintenance cost) c is incurred. The successive offers are assumed to be independent and identically distributed random variables having an unknown distribution F. The model is considered both in the case where once an offer is rejected it may not be recalled at a later time and in the case where such recall of previous offers is allowed.     

Redundant spares allocation to reduce reliability costs

The problem considered here is the optimal selection of the inventory of spares for a system built from two kinds of modules, the larger of which can be connected so it performs the role of the smaller one. The optimal inventory is the least costly one which achieves a specified probability that the spares will not be exhausted over the design lifetime. For some costs and failure rates it is most economical to use the larger module for both roles, due to the resulting increase in flexibility in the deployment of a single type of spare module. Both analytical and simulation methods have been used to study this problem.     

Engineering costs and customer costs in designing product support

Product support encompasses activities undertaken by durable goods producers to ensure their customers the continued use of the product. Examples of product support elements include after the sale activities such as providing repair services and warranty programs, as well as all the activities undertaken at the design and production stage to improve the reliability of products before they reach the market. The implications of incorporating customer costs while designing product support packages are the concern of this study. We study how the parameters of support package impact the costs incurred by customers and provide insights about selecting appropriate levels of product support. We show that the engineering orientation of maximizing the product's availability ignores market characteristics, and results in a mismatch between the corporation's support package and the customer's needs. The research is intended to be a step in understanding the interaction between design engineering parameters and customer's costs. © 1993 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.     

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.     

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.     

A proof for the longest-job-first policy in one-machine scheduling

We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.