Due DateQuotation Models

and Algorithms

Yiming Shan

Agenda

● Introduction● Overview● Notation used in the chapter● Sequencing and scheduling rules● Due Date Quotation Models● Jobshop and Flowshop Models

Introduction

When Firms operate in make-to-order environment, they must set due dates which are both relatively soon in the future and can be met reliably in order to compete effectively.

Overview

Two important elements: due date setting element and sequencing element.

Sequencing vs. due date quotation.

Notation used in the chapter

N jobs and M machines.

ri represents the release time of the job.

pi represents the processing time of the job.

Given a schedule,Ci represents the completion time of the job in that schedule.

Notation used in the chapter

Given a due date quotation approach, di is the due date of job i in that schedule.

Given Ci and di,Ei represents the earliness of job i,max{di −Ci,0}.

Given Ci and di,Ti represents the tardiness of job i,max{Ci −di,0}.

Notation used in the chapter

Quoted lead time, di − ri .

The flow time of a job, Ci − ri .

Given a sequence of jobs, job j[i] is the ith job in the sequence, with processing time p[i], release time r[i], etc.

Sequencing and scheduling rules

Three types of due date setting rules are commonly used:1. CON:Jobs are given constant lead times, so

that for job j,dj =rj+γ

2. SLK:Jobs are given lead times that reflect equal slacks, so that for job j, dj =rj + pj +β.

3. TWK: Jobs are assigned lead times proportional to their lengths, so, dj =rj +αpj.

Sequencing and scheduling rules

A variety of different sequencing and scheduling rules have been employed for these types of models.Some standard dispatch rules include:

1. Shortest Processing Time(SPT)2. Longest Processing Time(LPT)3. Weighted Shortest Processing Time(WSPT)4. Weighted Longest Processing Time(WLPT)

Sequencing and scheduling rules

5. Earliest Due Date (EDD)

6. Shortest Processing Time among Available jobs (SPTA)

7. Preemptive SPT (PSPT)

8. Preemptive EDD (PEDD)

Due date quotation models

1. Single Machine Static Common Due Date Models2. Single Machine Distinct Due Date Static Models3. Single Machine Dynamic Models4. Parallel Machine Models5. Jobshop and Flowshop Models6. Other Models

Jobshop and Flowshop Models

Assumptions

1. Jobs arrivals to the system form a Poisson process.

2. Each job consists of a series of operations, each performed by only one machine.

3. The processing times of all jobs at a specific machine are finite, iid, and can be determined before processing starts.

4. Jobs can wait between machines. 5. Jobs are processed without preemption.6. Machines are continuously available. 7. Jobs are processed on only one machine at a time.

Jobshop and Flowshop Models

Calculate a quantity called the service index of the job shop Is.

if Is = 1, the distribution of time spent in the shop is closely ∼approximated by an exponential distribution, ifIs 1, the distribution is best approximated by a generalized ≪Erlang distribution,ifIs 1, the distribution is best approximated by a ≫hyperexponential distribution. Then quote CON due dates to minimize the expected cost of the system.

Thank you