https://ira.lib.polyu.edu.hk/bitstream/10397/1269/1/SetupSurvey-2006%28June-19%29.pdf

A survey of scheduling problems with setup times or costs

Preventive maintenance planning, and production scheduling are two activities that are inter-dependent but most often performed independently. Considering that preventive maintenance, and repair affect both available production time, and the probability of machine failure, we are surprised that this inter-dependency seems to be overlooked in the literature. We propose an integrated model that coordinates preventive maintenance planning decisions with single-machine scheduling decisions so that the total expected weighted completion time of jobs is minimized. Note that the machine of interest is subject to minimal repair upon failure, and can be renewed by preventive maintenance. We investigate the value of integrating production scheduling with preventive maintenance planning by conducting an extensive experimental study using small scheduling problems. We compare the performance of the integrated solution with the solutions obtained from solving the preventive maintenance planning, and job scheduling problems independently. For the problems studied, integrating the two decision-making processes resulted in an average improvement of approximately 2% and occasional improvements of as much as 20%. Depending on the nature of the manufacturing system, an average savings of 2% may be significant. Certainly, savings in this range indicate that integrated preventive maintenance planning, and production scheduling should be focused on critical (bottleneck) machines. Because we use total enumeration to solve the integrated model for small problems, we propose a heuristic approach for solving larger problems. Our analysis is based on minimizing total weighted completion time; thus, both the scheduling, and maintenance problems favor processing shorter jobs in the beginning of the schedule. Given that due-date-based objectives, such as minimizing total weighted job tardiness, present more apparent trade-offs & conflicts between preventive maintenance planning, and job scheduling, we believe that integrated preventive maintenance planning & production scheduling is a worthwhile area of study.

Integrating preventive maintenance planning and production scheduling for a single machine

Most machine scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines need to be maintained and hence may become unavailable during certain periods. In this paper, we study the problem of processing a set of n jobs on m parallel machines where each machine must be maintained once during the planning horizon. Our objective is to schedule jobs and maintenance activities so that the total weighted completion time of jobs is minimized. Two cases are studied in this paper. In the first case, there are sufficient resources so that different machines can be maintained simultaneously if necessary. In the second case, only one machine can be maintained at any given time. In this paper, we first show that, even when all jobs have the same weight, both cases of the problem are NP-hard. We then propose branch and bound algorithms based on the column generation approach for solving both cases of the problem. Our algorithms are capable of optimally solving medium sized problems within a reasonable computational time. We note that the general problem where at most j machines, 1 ≤ j ≤ m, can be maintained simultaneously, can be solved similarly by the column generation approach proposed in this paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 145–165, 2000

Scheduling jobs and maintenance activities on parallel machines

An integrated production and preventive maintenance planning model

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology.

Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

The majority of scheduling literature assumes that the machines are available at all times. In this paper, we study single machine scheduling problems where the machine maintenance must be performed within certain intervals and hence the machine is not available during the maintenance periods. We also assume that if a job is not processed to completion before the machine is stopped for maintenance, an additional setup is necessary when the processing is resumed. Our purpose is to schedule the maintenance and jobs to minimize some performance measures. The objective functions that we consider are minimizing the total weighted job completion times and minimizing the maximum lateness. In both cases, maintenance must be performed within a fixed period T, and the time for the maintenance is a decision variable. In this paper, we study two scenarios concerning the planning horizon. First, we show that, when the planning horizon is long in relation to T, the problem with either objective function is NP-complete, and we present pseudopolynomial time dynamic programming algorithms for both objective functions. In the second scenario, the planning horizon is short in relation to T. However, part of the period T may have elapsed before we schedule any jobs in this planning horizon, and the remaining time before the maintenance is shorter than the current planning horizon. Hence we must schedule one maintenance in this planning horizon. We show that the problem of minimizing the total weighted completion times in this scenario is NP-complete, while the shortest processing time (SPT) rule and the earliest due date (EDD) rule are optimal for the total completion time problem and the maximum lateness problem respectively. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 845–863, 1999

Scheduling maintenance and semiresumable jobs on a single machine

Analytical foundations of physical security system assessment

External performance assessments for teachers of mathematics have traditionally been accomplished through reviews of student comments as well as through formal evaluations by superiors. Additionally, evaluating lecture-based teaching (as opposed to more active learning environments) focuses primarily on classroom performance, curriculum planning, materials development, and assessment of student performance. In this article we identify four additional qualities that are desirable when one is teaching mathematics in a problem-solving curriculum. We then offer various modes of feedback that teachers can use to help achieve a comprehensive assessment of their own teaching effectiveness.

How Are You Doing? Assessing Effectiveness in Teaching Mathematics

As the Army undergoes a transformation from the logistics intensive organizations that currently comprise the force to a more agile and sustainable force, changes in logistics concepts and organizations are inevitable. Because much of the Army's future equipment and most future organizations are still in the conceptual stages, these elements must be modeled. Simulation provides a valuable tool for not only modeling the structure or attributes of a future system, but also for comparing alternative concepts for how systems should be employed and equipped. In this paper, we present three applications of how simulation was used within the U.S. Army Combined Arms Support Command in the design and analysis of current and emerging logistical systems in the Army.

Applications of simulation in logistics combat developments

This project was developed as an interdisciplinary application of the optimization of a single-variable function. It was used in a freshman-level single-variable calculus course. After the first month of the course, students had been exposed to the concepts of the derivative as a rate of change, average and instantaneous velocities, derivatives of exponential functions, the chain rule, and single-variable optimization problems. They had also begun to use a computer algebra system to explore functions graphically, estimate local extrema, and differentiate functions. Prior to taking this course, all students had completed a course in mathematical modeling with an introduction to differential calculus.

Gregory H. Graves

Papers

Scheduling maintenance and semiresumable jobs on a single machine

Analytical foundations of physical security system assessment

How Are You Doing? Assessing Effectiveness in Teaching Mathematics

Applications of simulation in logistics combat developments

Predicting the Health of a Natural Water System