Dan Trietsch

This chapter introduces safe scheduling and discusses several problems that have a safe scheduling flavor – that is, problems in which safety time plays a key role. In doing so, it looks first at the problem of choosing due dates that are as tight as possible while maintaining stochastic feasibility. Next, the chapter considers the tightness/tardin...

This chapter first discusses the stochastic scheduling with an examination of stochastic counterpart problems. The objective in such problems is the expected value of a performance measure such as total flowtime, maximum tardiness, total cost, and the like. To help clarify the nature of stochastic counterpart models, the chapter explores a numerica...

Lot streaming is the process of splitting a job into sublots so that its operations can be overlapped. The basic lot streaming model is a one‐job flow shop model in which the lot size is known. Models may involve explicit consideration of several jobs, which gives rise to a sequencing problem as well as a lot streaming problem. This chapter focuses...

This chapter is about project analytics. It introduces recent results that make it possible to generate valid simulated samples for a new project, based on historical information regarding other projects. The methods of analytics constitute the main bridge from theory to practice. The chapter considers stochastic models that take into account the n...

In the development of scheduling models, the flow shop represents the most direct extension to jobs with multiple operations. This chapter deals with a model based on the design in which machines are arranged in series. In this design, jobs flow from an initial machine, through several intermediate machines, and ultimately to a final machine before...

In some settings, the grouping of jobs is a desirable or necessary tactic, usually because of some technological feature of the processing capability. The motivation for grouping often relates to the existence of changeover times, or setup times, on a machine. This chapter elaborates on the family scheduling model, relating the analysis to known re...

The job shop model has been a central paradigm for scheduling since the early days of scheduling theory. This chapter introduces the static version of the job shop problem and shows that, for regular measures of performance, the set of active schedules is the relevant dominant set. In particular, priority dispatching rules are very useful in practi...

This chapter introduces some generic heuristic procedures that have proven useful in solving scheduling problems. These procedures include dispatching and construction procedures, random sampling methods, neighborhood search approach, tabu search procedure, simulated annealing, genetic algorithm, and Evolutionary Solver. The chapter describes the a...

This chapter introduces the quintessential network methods for project scheduling, namely, critical path method (CPM) and program evaluation and review technique (PERT). It also shows how to implement safe scheduling hierarchically. Network models are widely used in the formulation of resource allocation problems and sequencing problems, so it is a...

This chapter introduces more advanced safe scheduling models. It outlines how the approach can be extended to hierarchical scheduling problems. These models utilize reliable samples that reflect historical experience for simulation‐based analysis. Stochastic balance, in turn, is associated with achieving optimal criticalities. Specifically, balance...

The earliness/tardiness (E/T) problem has received considerable attention as just‐in‐time (JIT) concepts have become more prominent in practice. JIT encompasses a much broader set of principles than those relating to due dates, but scheduling models with both E/T costs address a fundamental scheduling dimension of the JIT approach. This chapter exa...

The single‐machine model is fundamental in the study of sequencing and scheduling. It is considered a rather simple scheduling problem because it does not have distinct sequencing and resource allocation dimensions. This chapter highlights two ways in which decision‐making flexibility can be added to the basic model: allowing due dates to be treate...

In the stochastic flow shop model, the makespan typically exhibits a positive Jensen gap even with two machines, so the problem is inherently more complex than its deterministic counterpart. This chapter explores stochastic counterparts of models under the assumption of stochastic independence. It introduces safe scheduling models, subject to stoch...

In general, scheduling requires both sequencing and resource allocation decisions. Scheduling theory covers three basic types of multimachine models: parallel systems, serial systems, and hybrid systems. In parallel systems, jobs consist of one operation, as in the single machine model; but in flow shops and job shops, the structure of jobs is more...

One of the most thoroughly studied and widely applied areas of scheduling research involves the dynamic version of the job shop model. The dynamic job shop model usually connotes a different setting: Information about arriving jobs is not known in advance – even the timing of arrivals is unknown – and the arrivals are ongoing. This chapter focuses...

This chapter introduces two general purpose optimization methods for sequencing and scheduling problems and illustrates their application to the T‐problem. The methods include adjacent pairwise interchange, dynamic programming, and branch and bound. The adjacent pairwise interchange method is sufficient to prove optimality for only a limited class...

This chapter addresses the deterministic resource‐constrained project scheduling model. It briefly discusses stochastic counterpart models. The resource‐constrained project scheduling model contains both types of constraints: precedence constraints and resource constraints. A general resource structure contains multiple units of each of several dif...

The basic single‐machine model provides an opportunity to study a variety of scheduling criteria as well as a number of solution techniques. This chapter deals with additional models in which the assumptions of the basic model are relaxed. It introduces the basic model with seven assumptions. The assumptions include there are n single‐operation job...

An up-to-date and comprehensive treatment of the fundamentals of scheduling theory, including recent advances and state-of-the-art topics Principles of Sequencing and Scheduling strikes a unique balance between theory and practice, providing an accessible introduction to the concepts, methods, and results of scheduling theory and its core topics. W...

The Research Notes series (copyright © 2009, 2010 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced re...

The Research Notes series (copyright © 2009, 2010 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced re...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book’s coverage for advanced readers,...

The Research Notes series (copyright © 2009, 2010 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced re...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009, 2010 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced re...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

The Research Notes series (copyright © 2009 by Kenneth R. Baker and Dan Trietsch) accompanies our textbook Principles of Sequencing and Scheduling, Wiley (2009). The main purposes of the Research Notes series are to provide historical details about the development of sequencing and scheduling theory, expand the book's coverage for advanced readers,...

This paper was written at a time when I interpreted TOC as a method that helps focus on current bottlenecks but supports balance in the long run. Since typical TQM authorities did not stress the need for focusing, I proposed using TOC for that purpose, thus enhancing the benefit of TQM. Later, when I realized that my interpretation of TOC was not s...

In this paper we discuss improvement in a cybernetics context, including both OR and other methods, and show how they should be coordinated. That is, we highlight two important roles OR should assume in a continuously improving environment without usurping the other improvement methods: (i) maintaining economic equilibrium, and (ii) prioritizing im...

We study the interplay between correlation in stochastic project networks and project completion time. Suppose the activity durations have arbitrary marginal distributions and a Gaussian copula. The impact of an increase in correlation between parallel activities is a stochastic decrease in project duration regardless of network topology, whereas t...

An approximate formula for reducing the total cost of an (n, c) sampling plan when the cost of selecting an item at random is not negligible. The procedure selects a single sample to be drawn randomly. Based on the result of that sample, the remainder is either accepted or subjected to a 100% inspection. In the latter case, the cost of selecting it...

Most of this paper has been published in Journal of Scheduling under the title "Minimizing the Number of Tardy Jobs with Chance constraints and Stochastically ordered Processing Times," but in the publication we did not include linearly associated processing times because the reviewers asked for a shorter paper.

A modified version of Process Setup Adjustment with Quadratic Loss.

We address the stochastic traveling salesperson problem (TSP) with distances measured by travel time. We study how to select the best tour and due date for the minimization of fundamental safe scheduling objectives. Model 1 requires minimizing the due date subject to a service level constraint. Model 2 addresses a weighted trade-off between the due...

We consider a scheduling problem in which the criterion for assigning due dates is to make them as tight as possible, while the criterion for sequencing jobs is to minimize their tardiness. Because these two criteria conflict, we examine the trade-off between the tightness of the due dates and the tardiness of the jobs. We formulate a version of th...

More than half a century after the debut of CPM and PERT, we still lack a project scheduling system with calibrated and validated distributions and without requiring complex user input. Modern decision support systems (DSS) for project management are more sophisticated and comprehensive than PERT/CPM. Nonetheless, in terms of stochastic analysis, t...

Based on theoretical arguments and empirical evidence we advocate the use of the lognormal distribution as a model for activity times. However, raw data on activity times are often subject to rounding and to the Parkinson effect. We address those factors in our statistical tests by using a generalized version of the Parkinson distribution with rand...

Crashing stochastic activities implies changing their distributions to reduce the mean. This can involve changing the variance too. Therefore, crashing can change not only the expected duration of a project but also the necessary size of its safety buffer. We consider optimal crashing of serial projects where the objective is to minimize total cost...

Crashing stochastic activities implies changing their distributions to reduce the mean. This can involve changing the variance too. Therefore, crashing can change not only the expected duration of a project but also the necessary size of its safety buffer. We consider optimal crashing of serial projects where the objective is to minimize total cost...

Although the deterministic flow shop model is one of the most widely studied problems in scheduling theory, its stochastic analog has remained a challenge. No computationally efficient optimization procedure exists even for the general two-machine version. In this paper, we describe three heuristic procedures for the stochastic, two-machine flow sh...

We address a single-batch lot streaming problem for a two-stage assembly system. The first stage consists of m parallel subassembly machines, each devoted to a component type. A single assembly machine at the second stage assembles a unit of a product after all m components (one each from the subassembly machines) are ready. The batch consists of U...

Crashing stochastic activities implies changing their distributions to reduce the mean. This can involve changing the variance too. Therefore, crashing can change not only the expected duration of a project but also the necessary size of its safety buffer. We consider optimal crashing of serial projects where the objective is to minimize total cost...

We address the stochastic traveling salesperson problem (TSP) with distances measured by travel time. We study how to select the best tour and due date for the minimization of fundamental safe scheduling objectives. In Model 1 the objective is minimizing the due date subject to a service level constraint. In Model 2 the objective reflects a trade-o...

We consider single-machine stochastic scheduling models with due dates as decisions. In addition to showing how to satisfy given service-level requirements, we examine variations of a model in which the tightness of due-dates conflicts with the desire to minimize tardiness. We show that a general form of the trade-off includes the stochastic E/T mo...

Introduction to Sequencing and Scheduling Scheduling Theory Philosophy and Coverage of the Book References

______________________________________________________________________ Abstract: Traditionally, resource balance has been measured by utilization. Because 100% utilization of all resources all the time is impossible, some advocate intentional imbalance so all resources except one—the bottleneck (BN)—have enough excess capacity to enable 100% BN uti...

Introduction Adjacent Pairwise Interchange Methods A Dynamic Programming Approach Dominance Properties A Branch and Bound Approach Summary References Exercises

Introduction Minimizing Deviations from a Common Due Date The Restricted Version Asymmetric Earliness and Tardiness Costs Quadratic Costs Job-Dependent Costs Distinct Due Dates Summary References Exercises

Introduction Stochastic Balance Principles For Activity Networks Crashing Stochastic Activities Summary References Exercises

Introduction Extending the Job Shop Model Extending the Project Model Heuristic Construction and Search Algorithms Summary References Exercises

Introduction Logical Constraints and Network Construction Temporal Analysis of Networks The Time/Cost Trade-off Traditional Probabilistic Network Analysis Summary References Exercises

Introduction Model Elements Types of Dispatching Rules Reducing Mean Flowtime Meeting Due Dates Summary References

Introduction The Basic Two-Machine Model The Three-Machine Model with Consistent Sublots The Three-Machine Model with Variable Sublots The Fundamental Partition Summary References Exercises

Introduction Stochastic Counterpart Models Safe Scheduling Models with Stochastic Independence Flow Shops with Linear Association Empirical Observations Summary References Exercises

Introduction Permutation Schedules The Two-Machine Problem Special Cases of The Three-Machine Problem Minimizing the Makespan Variations of the m-Machine Model Summary References Exercises

Introduction Basic Stochastic Counterpart Models The Deterministic Counterpart Minimizing the Maximum Cost The Jensen Gap Stochastic Dominance and Association Using Risk Solver Summary References Exercises

Introduction Meeting Service-Level Targets Trading Off Tightness and Tardiness The Stochastic E/T Problem Setting Release Dates The Stochastic U-Problem: A Service-Level Approach The Stochastic U-Problem: An Economic Approach Summary References Exercises

Introduction Minimizing the Makespan Minimizing Total Flowtime Stochastic Models Summary References Exercises

Introduction Nonsimultaneous Arrivals Related Jobs Sequence-Dependent Setup Times Stochastic Models with Sequence-Dependent Setup Times Summary References Exercises

Important Processing Time Distributions Increasing and Decreasing Completion Rates Stochastic Dominance Linearly Associated Processing Times References

Introduction Scheduling Job Families Scheduling with Batch Availability Scheduling with a Batch Processor Summary References Exercises

Introduction The Single-Machine Model The Flow Shop Model References

Introduction Preliminaries Problems Without Due Dates: Elementary Results Problems with Due Dates: Elementary Results Summary References Exercises

Half Title Title Copyright Contents Preface Contributors

Introduction Types of Schedules Schedule Generation The Shifting Bottleneck Procedure Neighborhood Search Heuristics Summary References Exercises

We consider the single-machine sequencing model with stochastic processing times and the problem of minimizing the number of stochastically tardy jobs. In general, this problem is NP-hard. Recently, however, van den Akker and Hoogeveen found some special cases that could be solved in polynomial time. We generalize their findings by providing a poly...

Traditional approaches to stochastic scheduling have yet to make an impact on scheduling practice. We review a number of results in stochastic scheduling in a historical context in order to highlight its shortcomings. We explain the logic of safe scheduling and present some of its basic results. We discuss different approaches to the formulation of...

In a companion paper I argued that Management by Constraints (MBC) should be improved by replacing Step 4 (elevate the constraint) by a revised version that seeks to match the criticality of each constraint (defined as the probability it will be the binding constraint in any period) with its economic value. The result is Management by Criticalities...

Due to more frequent use of short production runs and the need for shorter setup times in order to make these runs cost-effective, there has lately been a great deal of interest in the statistical properties of X control charts with control limits that are based on unknown process parameters. Typically the true process distribution can be assumed t...

The in-control statistical properties of X̄ charts have usually been studied from the perspective of the average run length (ARL) until the first (false) signal, known as the in-control ARL. We argue that the ARL is a confusing concept when used with charts with estimated limits and that the rate of false signals (RFS), which focuses on the behavio...

Gilbert and Pollak conjectured that the length of the minimal Steiner tree (MST) is at least that of the minimal spanning tree. In a subsequent paper, Gilbert generalized the Steiner tree problem by adding flow dependent weights to the arcs. We refer to the generalized problem as the Minimal Gilbert Network Problem, and to its optimal solution as t...

A set of n jobs with statistically independent random processing times has to be processed on a single machine without idling between jobs and without preemption. It is required to set due dates and promise them to customers. During the production stage, earliness and tardiness against the promised due dates will be penalized. The goal is to minimi...

Theoretical results about Johnson’s problem with stochastic processing times are few. In general, just finding the expected makespan of a given sequence is already difficult, even for discrete processing time distributions. Furthermore, to obtain optimal service level we need to compute the entire distribution of the makespan. Therefore the use of...

In project scheduling or batch supply chain operations, a positive (negative) feeding buffer is created by starting an activity before (after) its expected latest start time. Positive feeding buffers provide protection against project tardiness. Assuming linear costs for starting activities earlier and a linear project tardiness penalty, early opti...

Existing mathematical models for setting buffers for time or cost in project management assume that project activities are sta-tistically independent. This leads to a highly counterintuitive and damaging conclusion that project buffers should become relatively negligible for projects with long chains of activities. We present a model that considers...

To maximize the potential of Critical Chain (CC) to enrich project management practice, I discuss Eliyahu Goldratt’s work in the context of his entrepreneurial career. I show that PERT/CPM had been an instance of Goldratt’s “Theory of Constraints” (TOC) before Goldratt had articulated it. I also highlight errors and questionable recommendations he...

The five-step ‘Theory of Constraints’ as articulated and explained in Goldratt’s books, is touted as “not only beneficial but mandatory.” However, although it is indeed a useful focusing heuristic methodology with an impressive track record, it is not really a theory and it is certainly not mandatory. Furthermore, it involves a serious internal inc...

A feeding buffer is created by starting a project activity before its latest start time to provide adequate protection against project delay. Assuming linear costs for starting activities earlier and a linear project delay penalty, early optimization models for project buffers addressed simple project network structures and invoked the newsvendor m...

Existing research in stochastic scheduling often ignores the need to achieve high service levels. Optimality is usually de®ned in terms of minimizing the expected makespan, with the intent to increase the expected utilization of the facility. We argue that this does not address the full rami®cations of stochastic variation. Instead, we should minim...

A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The...

A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The...