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Setup time and batch size reduction

Factory Automation Laboratory

Seoul National University

July 23, 1999

Byun, MyungHee

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A workload balancing model for determining set-up time and batch size reductions in GT flow line work cells

R.R.GUNG and H.J.STEUDELSupply Chain Optimization, IBM Manufacturing Industry

Solutions Lab, USA

IE, University of Wisconsin-Madison, USA

INT. J. PROD. RES., 1999, VOL 37, No 4, 769-791

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Contents

• Introductions

• Capacity constraints

• A workload balancing model

• Heuristic model to determine the MWL

• Performance improvement

• Illustrated example

• Conclusions

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Introduction

• The need for reduced inventory costs and shortened manufacturing lead times is prompting companies to reduce their production batch sizes.

• But, the batch size’s reduction means that the number of set-up operations are increased.

• So, Set-up time reduction has become a prerequisite for batch size reduction.

• However, reduction plan is not always beneficial and cost effective.

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Introduction-Objective of the study

• To present a general approach to guide the selection of set-up time and batch size reductions in order to improve the performance of a flow line work cell.

• Measure

- average job-throughput time

- WIP inventory level

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Capacity constraints(1/3)

• The total capacity constraints(the theory of constraints : Goldratt)

for any production unit,

Tik expected set-up + cycle time for a job of part i at workstation k

Ni expected number of job arrivals of part i for the year

Qk total number of production hours available for the year at workstation k

npt total number of unique part types

nws total number of workstations in the cell

nwskfor

ornwskfor

TNQ

QTN

ik

npt

iik

k

npt

iiki

,,,2,10

,,,,2,1

1

1

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Capacity constraints(2/3)

• The total capacity constraints in the queuing theory

- the job arrival rate must be less than the service rate.

- the reason for this phenomena

the stochastic arrival process

can occasionally cause the

system to become idle, and

the loss of service capacity

is never gained back.

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Capacity constraints(3/3)

• For the flow line work cell, the reserved capacity constraint is expressed as follows.

Uk capacity cushion at workstation k

npt

ikikik

npt

ikkiki

nwskfor

ornwskfor

UTNQ

UQTN

1

1

,,,2,1

,,,,2,1

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A Workload Balancing Model

• The minimum level of set-up time reduction(SR) required at each workstation for a given level of batch size reduction.

MWL maximum allowed machine workload

nk number of machines at the workstation k

zk number of shifts that the workstation k operates

SM set-up time multiplier which is dependent on the degree of

batch size reduction(BR) : SM = (1-BR)-1

)1(setupSMn

cycleznMWLSR

kk

kkkk

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Example of the concept of workload balancing model

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Rationale explanation(1/2)

• When original utilization is less than MWL

- utilization increases to MWL average number of jobs(L) increases : average WIP increases

• batch size = 1/SM × original sizes

• So, If L is less than SM × original number of jobs,

average WIP inventory level will decreases.

• Little’s law w=L/ (w : average job-throughput time)

• job arrival rate = SM × original arrival rate

• if the increased L is less than SM × original average number of

jobs , the average job-throughput time will decrease.

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Rationale explanation(2/2)

• When original utilization is higher than MWL - utilization will be reduced to MWL average number of jobs(L) decreases : average WIP will decrease, average job-throughput time will decrease.

Based on the above rationale,

only workstations with low utilization tend to deteriorate performance.

So, in such case, a lower level of MWL has to applied to each workstation.

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Heuristic model to determine the MWL(1/3)-Based on GI/G/1 queuing model

• STEP 1 : Determine base model’s dynamic parameters • external job arrival process

• job arrival rate

• mean, square coefficient of variation(s.c.v) for the service time

service time

• s.c.v for the inter-arrival time

jobstheinavailablehoursproductionofnumberTotalN ik

ik

nCST

k

ikikik

cccc asad kkkk kk

222222

1

)1(

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Heuristic model to determine the MWL(2/3)

• STEP 2 : Evaluate base model’s performance

• average number of jobs

• average batch size of jobs

• average WIP inventory level

• average job-throughput time

k

k

kk

ccL sa kk

)

1)(

2(

222

npt

i k

ikik BABS

1

ABSLWIP kkk

k

kk

LTT

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Heuristic model to determine the MWL(3/3)

• STEP 3 : Determine new model’s dynamic parameters • Calculate SR with a selected MWL alternative

• Follow STEP 1 to calculate the parameters

• STEP 4 : Evaluate new model’s performance • Follow STEP 2 to calculate the parameters

• STEP 5 : Adjust MWL

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Performance improvement(1/2)

• Percentage improvement of cell performance

• Percentage improvement of average job-throughput time

%100

11

1

'

nws

SM

nws

k k

k

LL

%1001

1%100''

'

SML

LL

LL

k

k

k

k

k

k

k

k

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Performance improvement(2/2)-M/M/1 model is used

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Illustrated Example-simulation study

• Using actual data from a U-shaped flow line work cell for gear manufacturing

• Six workstations, production capacity = 20000 hours

• Maximum feasible reduction in batch sizes = 90%(1 < SM 10)

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Illustrated example-design setting

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Illustrated example-results

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Conclusions

• A model is proposed in this paper which determines the amount of set-up time reduction at each workstation for a given level of batch size reduction, in order to improve the performance of a flow line work cell.

• To ensure the cell performance improvement, a heuristic model is presented to determine the maximum allowed machine workload(MWL).

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Investment policy for multiple product setup reduction under budgetary and

capacity constraints

Avijit Banerjee, Vijay R.Pyreddy, Seung Lae KimDepartment of Management & Organizational Sciences, Col

lege of Business & Administration,

Drexel University, Philadelphia, USA

Int. J. Production Economics 45 (1996)

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Contents

• Introduction

• Assumptions

• Notations and Model

• Heuristic procedures

• Numerical Illustrations

• Conclusions

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Introduction

• This paper examines the impact of setup reduction on the lot sizes, inventory levels and total relevant cost in a batch manufacturing process, that produces several items with similar setup reduction functions, under budget and capacity constraints.

• More specifically, the amount to be invested in setup reduction for each product and the resultant decreases in its batch size and relevant cost.

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Assumptions for this paper

• Simple and inexpensive methods have already been taken.

• A convex setup reduction function

• Adopting the common cycle approach to obtain schedule feasibility.

• Setup cost is directly proportional to the setup time

• Setup sequence is independent.

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Notations and Model(1/2)

• Ki amortized annual investment in setup reduction for product i

• Qi production batch size of product i

• N number of common cycles for all products per year

• Li/Ui lower/upper limit of setup cost of product i

• Si(Ki) setup cost of product i as function of investment

• Sit(Ki) setup time of product i expressed in hours

• b proportionality constant i.e. Si(Ki) = b Sit(Ki)

• m total number of products

• k vector of investment Ki

• T total time available for setup and production all the products over a year

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Notations and Model(2/2)

• TRC : annual total relevant cost per year

subject to

m

i

m

i

m

ii

i

iiiii KP

DDHKS NkNTRCMinimizeP

1 1 1

12

1)(),()1(

)3(0)(1

)2(,0

11

1

m

iii

m

i i

i

m

ii

KSPD

K

b

NT

K

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Heuristic Procedures(1/2)

• STEP 1 : Solve the unconstrained problem about (P1)

• STEP 2 : Check for violation of the constraints (2)&(3) Case a : If both the constraints are satisfied, solutions are optimal.

Case b : If (2) is satisfied , and (3) is violated, calculate N from (3)

This value of N and Ki*represent a feasible solution.

NKS

KS

PDHD

N

ii

i

m

ii

i

ii

m

ii

1)(

)(2

)1(

*'

1

1*

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Heuristic Procedures(2/2)

Case c : If (3) is satisfied and (2) is violated,

determine the ratio Ki*/iKi

*

feasible solution Ki = ratio × K and recalculate N

Case d : If both (2) and (3) are violated, recalculate Ki and N as case c

If current N satisfies (3), it is feasible.

else, recalculate N as case b.

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A numerical illustration(1/2)

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Example-Results and Discussion(2/2)

• Without any investment in setup reduction,

: cycle = 31, total relevant cost = $247471 per year

• Because this problem exceeded the solvers capabilities, it is applied in the heuristic procedures.

: cycle = 101, total relevant cost = $118908 per year

K1=$3869, K2 = $3955, K3 = $4062, K4 = $4015, K5 = $4100

• But, setup reduction programs may not always result in improvements.

• If setup reduction don’t yield any benefits, Ki will be zero.

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Concluding remarks

• This paper extends the current literature, not only by addressing the case of multiple products, but also by taking into account limitations on the total budget available for investing in setup reduction.

• Similar constraints on other resources can be readily incorporated in our suggested model.

• Our results of example are better than other report based on the basic period approach.

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References

• M.KUULA, A.STAM, S.LEINO, J.RANTA and J.WALLENIUS, 1999, Workload balancing in the manufacturing environment: a multi-criteria trade-off analysis, IJPR VOL. 37, No. 7

• 박순달 , 1994, Operations Research( 경영과학 ), 민영사