basic factory dynamics chapter 7

© Wallace J. Hopp, Mark L. Spearman, 1996, 2000 www.factoryphysics.com1

Basic Factory Dynamics

Chapter 7

Lecture 10


Topics

• Introduction (Chapter 0)• Inventory Control (Chapter 2)• Materials Requirements Planning (Chapter 3)• Just-in-Time and Lean manufacturing (Chapter 4)• Basic factory dynamics (Chapter 7)• Variability basics (Chapter 8)• Push and Pull Systems (Chapter 10)• Shop Floor Control (Chapter 14)• Production Scheduling (Chapter 15)• Aggregate Planning (Chapter 16)

Part I

Part II

Part III


Introduction

• Focus: Examine basic behavior of production lines (process flows)• Production line, instead of an entire factory or a single workstation

• A line is simple enough to analyze but complex enough to provide a link between the operational and financial performance

• Goal: Understand the factors that influence performance of production processes (Part II – Chapters 7-10)• Later in Part III (Chapters 14-16) we will address the problem of

how to improve or optimize performance


Introduction (Cont’d)

Definition: A manufacturing plant is a network of processesthrough which parts flow.

Structure: Plant is made up of routings (lines), which in turn are made up of processes.


DefinitionsWorkstations: a collection of one or more identical machines.

Ex: A turning station made up of several lathes.

Part: a raw material, component or sub-assembly that moves through workstations.

End Item: parts sold directly to customers; its relationship to constituent (lower-level) items is defined in bill of material.

Consumable: materials used in process but do not become part of the product that is sold Ex: bits, chemicals, gasses

Routing (Line): sequence of workstations that the part passes through during its production

Order: request from customer for a part; contains quantity and due date of the request.

Job: a part that traverses the production line along with associated info (e.g., BOM, drawings).


Definitions: Inventory

Raw Material Inventory (RMI): material stocked at beginning of routing.

Crib Inventory: intermediate inventory prior to further processing

Finished Goods Inventory (FGI): inventory for storing end items prior to shipping to customer.

Work in Process (WIP): inventory between the start and endpoints of a product routing.E.g., parts


Definitions: Performance Measures

Throughput (TH): Average production rate of a process (machine, workstation, line, plant) per unit time E.g., parts per hour

Capacity: Upper limit of the TH of a process.

Cycle Time (CT): time from release of the job at beginning of routing until it reaches an inventory point at end of routing (time part spends as WIP). E.g., hoursCT is defined for single routings only.

Utilization: the fraction of time a workstation is not idle for lack of parts

Utilization = (Arrival Rate )/ (Effective Production Rate)


Parameters

Descriptors of a Line:1) Bottleneck Rate (rb): Rate (parts per hour) of the workstation

with the highest utilization.

2) Raw Process Time (T0): Sum of the average process times of each station in the line.

3) Critical WIP (W0): WIP level for which a line can achieve maximum throughput (rb) with minimum cycle time (T0).

W0 = rb T0


Basic Factory Dynamics

Chapter 7

Lecture 11


7.3.1. Best Case Performance

Simulation of Penny Fab OneCharacteristics:

• Four machines in series.• Each machine takes 2 hours to process a penny• No variability in processing times• WIP kept constant over time – CONWIP (Chapter 10)

Parameters:rb =

T0 =

W0 =

0.5 pennies/hour

8 hours0.5 × 8 = 4 pennies


The Penny Fab


The Penny Fab (WIP=1)

Time = 0 hours



Time = 2 hours



Time = 4 hours



Time = 6 hours



Time = 8 hours



Time = 10 hours



Time = 12 hours



Time = 14 hours



Time = 16 hours


Penny Fab Performance

WIP TH CT TH×CT 1 0.125 8 1 2 3 4 5 6



Time = 0 hours



Time = 2 hours



Time = 4 hours



Time = 6 hours



Time = 8 hours



Time = 10 hours



Time = 12 hours



Time = 14 hours



Time = 16 hours



Time = 18 hours



WIP TH CT TH×CT 1 0.125 8 1 2 0.250 8 2 3 4 5 6



Time = 0 hours



Time = 2 hours



Time = 4 hours



Time = 6 hours



Time = 8 hours



Time = 10 hours



Time = 12 hours



Time = 14 hours



WIP TH CT TH×CT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 6



Time = 0 hours



Time = 2 hours



Time = 4 hours



Time = 6 hours



Time = 8 hours



Time = 10 hours



Time = 12 hours



WIP TH CT TH×CT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 0.500 10 5 6 0.500 12 6

Critical WIP


TH vs. WIP: Best Case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

rb

W0

1/T0


CT vs. WIP: Best Case

02468

101214161820222426

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

T0

W0

1/rb


A Manufacturing Law

Little's Law: (John D.C. Little) The fundamental relation between WIP, CT, and TH is:

Insights:• Fundamental relationship• Simple units transformation• Definition of cycle time (CT = WIP/TH)

CTTHWIP ×=

hrhr

partsparts ×=


Best Case Performance

Best Case Law: The minimum cycle time (CTbest) for a given WIP level, w, is given by

The maximum throughput (THbest) for a given WIP level, w is given by,

⎩⎨⎧ ≤

=otherwise.

if ,/

,CT 00

best

Wwrw

T

b

⎩⎨⎧ ≤

=otherwise.

if ,

,/TH 00

best

Wwr

Tw

b


Best Case Performance (cont.)

Example: For Penny Fab One, rb = 0.5 and T0 = 8, so W0 = 0.5 ×8 = 4,

which are exactly the curves we plotted.

⎩⎨⎧ ≤

=otherwise.

4 if ,2

,8CTbest

ww

⎩⎨⎧ ≤

=otherwise.

4 if ,5.0,8/

THbest

ww


Worst Case

Observation: The Best Case yields the minimum cycle time and maximum throughput for each WIP level.

Question: What conditions would cause the maximum cycle time and minimum throughput?

Experiment:• set average process times same as Best Case (so rb and T0

unchanged)• follow a marked job through system• imagine marked job experiences maximum queueing


Worst Case Penny Fab

Time = 0 hours



Time = 8 hours



Time = 16 hours



Time = 24 hours



Time = 32 hours Note:

CT = 32 hours= 4× 8 = wT0

TH = 4/32 = 1/8 = 1/T0


TH vs. WIP: Worst Case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

rb

W0

1/T0

Best Case

Worst Case


CT vs. WIP: Worst Case

048

121620242832

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

T0

W0

Best Case

Worst Case


Worst Case Performance

Worst Case Law: The worst case cycle time for a given WIP level, w, is given by,

CTworst = w T0

The worst case throughput for a given WIP level, w, is given by,

THworst = 1 / T0

basic factory dynamics chapter 7

Documents