1

12

/ t

A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB

SHOP PODUCTION SYSTEMS

Henny P.G. van OoijenJ.Will M. Bertrand

2

12

/ t

Overview

• Introduction• Literature review• Research question• Policy for capacity adjustment• Evaluation• Future research

3

12

/ t

Introduction• Job shop (functionally organized work centers)

– Dynamic, stochastic arrival pattern– Stochastic behaviour on the shop floor

Highly fluctuating throughput times => Poor performance

• Fixed lead times– “Adjust” demand – Adjust available capacity

• Small change of capacity => big impact on the performance

• Setting cost optimal due dates– Prediction of throughput times

4

12

/ t

Literature (I)

• Palaka et al.– Customers sensitive to quoted lead times (fixed

capacity/ marginal expansion)• So and Song

– Demands are sensitive to both price and delivery time (optimal setting of price/delivery time/capacity expansion)

• Ray and Jewkes– Demand is function of delivery time and price, and

price is a function of delivery time

5

12

/ t

Literature (II)

• Barut and Shridharan– Allocation (dynamically) of capacity to multiple product

classes

• Van Mieghem– Review strategic capacity management literature

Setting capacity levels on medium or long term for “average” orders, based on average lead times and/or average delivery reliability

6

12

/ t

Research question

Given fixed, realistic short, lead times, and given dynamic,

stochastic demand, then how can we obtain an (economically

justified) as high as possible delivery reliability?

7

12

/ t

Research question

Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an

(economicallyjustified) as high as possible delivery reliability?

ADJUST THE CAPACITIES AROUND A GIVEN LEVEL

8

12

/ t

Research question

Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an

(economicallyjustified) as high as possible delivery reliability?

ADJUST THE CAPACITIES AROUND A GIVEN LEVEL

HOW MUCH?

9

12

/ t

Research question

Given fixed, realistic short, lead times, and given dynamic, stochastic demand, what can we do to obtain a

(economicallyjustified) high delivery reliability?

ADJUST THE CAPACITIES AROUND A GIVEN LEVEL

HOW MUCH? Estimate the lateness given certain capacity levels

10

12

/ t

Forecasting throughput times (I)

• Empirically constructed routing normalized waiting time distribution functions Fg(.) per order category g

• Upon arrival an order with g operations and a required reliability of gets due date:

wloadactual

loadnormwN

1

)(1

operations

gj Floadnorm

loadactualptDD

11

12

/ t

Forecasting throughput times (II)

In this research:

• Estimate of remaining waiting time of an order with g remaining operations, reliability :

gFloadnorm

loadactual 1

12

12

/ t

Policy for capacity adjustment (I)

• If ntj is the actual load at a certain work center j at time t, then the total expected lateness is:

)))(((

; ;

.;.

xg

xordersreleased

joperationsremaining

joperremsWorkcentertj

xjx Floadnorm

n

ptDD

13

12

/ t

Policy for capacity adjustment (II)

• Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity

• “Adjusting” the load can be done by adjusting the capacity.

14

12

/ t

Policy for capacity adjustment (II)

• Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity

• “Adjusting” the load can be done by adjusting the capacity.

)))(((

; ;

.;.

xg

xordersreleased

joperationsremaining

joperremsWorkcenter

tjj

xjx Floadnorm

n

ptDD

15

12

/ t

Policy for capacity adjustment (III)

• We assume : Capacity costs for adjusting the load with 1 unit is equal to c1; lateness costs is c2 per unit late.

))))((()1((min 2

; ;

.;.2

11

xg

xordersreleased

joperationsremaining

joperremsworkcenter

tjj

xjxti

m

ii F

loadnorm

n

ptDDcnc

16

12

/ t

Policy for capacity adjustment (IV)

• After some rewriting this leads to an equation of the form:

This is a Constrained Least Squares problem

)2

1(min

2

0aNcT

17

12

/ t

Evaluation

• Simulation study– Ideal job-shop; 5 work centers; 90%

utilization;First Come First Serve

– Capacities can be varied weekly or monthly– The same lead time for all orders/Different

lead times for orders of different categories

18

12

/ t

Future research

• Evaluation study• How to determine capacity adjustment costs• How to find the empirical distribution functions• Other priority rules