Interim equipment shutdown planning for a wafer fab during economic downturns

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Interim equipment shutdown planning for a wafer fab during economic downturns

Shu-Hsing Chung

⇑

, Ming-Hsiu Hsieh

Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 12 January 2010

Received in revised form 12 July 2010 Accepted 23 August 2010

Available online 26 August 2010 Keywords: Tool portfolio Cost reduction Capacity planning Semiconductor

a b s t r a c t

Because of the low equipment utilization during periods of economic recession, managers of wafer fabs are forced to plan equipment shutdowns in order to reduce variable cost and reallocate resources. Unfor-tunately, few studies have proposed effective solutions for equipment shutdown planning in response to economic downturns. Taking into consideration the product mix, corresponding output target, excessive capacity, production performance impact and the variable cost savings, this paper presents a new mech-anism for equipment shutdown planning using a developed integer programming model. The proposed mechanism effectively provides valuable recommendations for the managements of wafer fabs regarding the type and quantity of equipment to shut down.

1. Introduction

Due to low equipment utilization during periods of economic downturn, the managers of semiconductor ﬁrms must plan equip-ment shutdowns to drive down variable costs and make the related resource arrangement more efﬁcient.

Equipment shutdown planning is one type of tool portfolio planning. Tool portfolio planning can generally be categorized as mid/long-term new tool planning for capacity expansion, mid/ long-term tool elimination planning due to relocation to other plants or disposal and interim equipment shutdown planning due to economic recession. All of these categories aim towards the common goal of determining the type and quantity of equip-ment to add (or remove). The ﬁrst and the second category will re-sult in an increase (or decrease) in capital expenditure (or depreciation) while the third category affects the variable cost. The interim equipment shutdown planning results serve as a guideline for dispatching, operator relief planning in the manufac-turing sector and ﬁnancial planning. In practice, the interim equip-ment shutdown plan is subject to review and revision on a monthly basis.

Shutting down different equipment types and quantities has different impacts on output, production performance and cost reduction. From the cost reduction aspect, more could be saved in manufacturing expenses if more units of equipment are shut down. However, there is a need to keep speciﬁc varieties and

quan-tities of equipment available to run operations smoothly, to meet the output target and to maintain high production performance. Therefore, semiconductor ﬁrm managers are compelled to develop a workable solution in an attempt to reconcile this conﬂict.

Equipment shutdown is an important topic for semiconductor ﬁrms requiring an efﬁcient planning mechanism. With this motive, this paper proposes a sound mechanism for interim equipment shutdown planning based on determining the type and quantity of equipment suitable for shutdown.

Few studies have focused on proposing effective mechanisms for interim equipment shutdown to cope with economic recession. Previous studies have concentrated on new tool planning for capacity expansion (Bard, Srinivasan, & Tirupati, 1999; Bretthauer, 1996; Chen & Chen, 1996; Chou, 1999; Chou & Wu, 2002; Chou & You, 2001; Chung & Hsieh, 2004; Connors, Feigin, & Yao, 1996; Donohue, Hopp, & Spearman, 2002; Eppen, Martin, & Schrage, 1989; Grewal, Bruska, Wulfm, & Robinson, 1998; Hood, Bermon, & Barahona, 2003; Hsieh & Lin, 2002; Hua & Banerjee, 2000; Iwata, Taji, & Tamura, 2003; Mollaghsemi & Evans, 1994; Neacy et al., 1993; Swaminathan, 2000, 2002; Wang & Lin, 2002; Wu, Hsiung, & Hsu, 2005; Yang, 2000; Yoneda, Wada, & Haruki, 1992). Chung and Hsieh (2008) proposed a mechanism for mid/long-term equip-ment elimination for equipequip-ment relocation to overseas facilities.

Tool portfolio planning is a relatively complex and difﬁcult problem. Common methodologies that are used to solve the tool portfolio planning problem in the literature include mathematics analytical method (for example, linear/integer programming and queuing network), simulation, heuristic algorithm, and combina-tions of the former ones. Linear/integer programming can deter-mine the optimum tool portfolio if the considered factors can be formulated in the static model. Queuing network can rapidly 0360-8352/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.cie.2010.08.009

⇑ Corresponding author. Address: 1001, Ta Hsueh Road, Hsinchu, Taiwan. Tel.: +886 3 5731 638; fax: +886 3 5722 392.

E-mail addresses:shchung@mail.nctu.edu.tw(S.-H. Chung),emilhsieh.iem92g@ nctu.edu.tw(M.-H. Hsieh).

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derive performance estimates such as cycle time, work-in-process (WIP) and throughput. However, these estimates may be less accurate than those obtained by simulation (Wu et al., 2005). Mollaghsemi and Evans (1994)pointed out that the popularity of simulation is due to its ﬂexibility and its ability to model systems when analytical methods have failed. In order to optimize a simu-lation model, it often must be used in conjunction with an opti-mum-seeking method. Heuristic algorithms can consider more important factors (for example, space and budget) under different manufacturing environments. Simulation and heuristic algorithms often require long calculation time because they must be repeated every time when a new tool is added (Neacy et al., 1993; Wu et al., 2005; Yoneda et al., 1992).

Bard et al. (1999)developed a heuristic algorithm to generate the candidate tools for new procurement and calculated the queu-ing time usqueu-ing the queuqueu-ing theory to determine the tool portfolio that minimizes cycle time within a limited budget. For the capacity expansion in a semiconductor testing facility,Wang and Lin (2002) developed a heuristic algorithm and used a genetic algorithm to determine the type and quantity of the testers to be invested under the limited budget.Wu et al. (2005)developed a genetic algorithm embedded with a queuing analysis to solve the tool portfolio prob-lem under cycle time constraints and demand uncertainty. It took about eight hours to complete the calculation.

Kishimoto, Ozawa, Watanabe, and Martin (2001) mentioned

that customer demands for fast delivery of prototypes or mass-produced components are increasing because the life cycles of products are becoming shorter. Semiconductor manufacturers have been required to aim for ‘‘low cost” and ‘‘short time to mar-ket” to satisfy customer requirements and remain competitive in the marketplace. Thus, in considering the factors affecting tool portfolio planning, cycle time and cost are two critical factors that determine competitiveness in the semiconductor industry (Bard et al., 1999; Chen & Chen, 1996; Chou & Wu, 2002; Chou & You, 2001; Connors et al., 1996; Grewal et al., 1998; Iwata et al., 2003; Wu et al., 2005).Table 1summarizes the tool portfolio planning litera-ture. These papers are classiﬁed by cycle time, cost and the prob-lem solving methodology.

Several studies have investigated cost reduction in the semicon-ductor industry (Carnes & Su, 1991; Dance, DiFloria, & Jimenez, 1996; Iwata & Wood, 2002; Nanez & Iturralde, 1995; Patel, Bos-well, & Nelson, 1995; Rahaim, 1994), but these studies focused only on developing a wafer cost model without linking it to tool portfolio planning. Atwater and Chakravorty (1994), Blackstone and Cox (2002), Blackstone (2004), Craighead, Patterson, and

Fredendall (2001), and Patterson, Fredendall, and Craighead

(2002)mentioned that in the past, the literature rarely took exces-sive capacity and cost into consideration when studying tool port-folio planning. By considering product mix, corresponding output target, excessive capacity, production performance impact and the variable cost savings, this paper proposes an equipment shutdown planning mechanism. This mechanism will produce an effective and explicit recommendation for which type and what quantity of equipment to be shut down.

The rest of this paper is structured as follows. The following section presents an equipment shutdown planning mechanism. Section3presents an application example based on the actual data collected from a wafer fabrication factory situated in the Science-Based Industrial Park in Taiwan. Section4 presents our conclusions.

2. Equipment shutdown planning mechanism

Before describing the mechanism, the notations used are listed and explained as follows.

2.1. Indexes I fi 2 N : 1 6 i 6 Ig Workstation type J fj 2 N : 1 6 j 6 Jig Machine number D fd 2 N : 1 6 d 6 Dg Product type K fk 2 N : 1 6 k 6 Kig Operator number Table 1

Literature review about tool portfolio planning.

Methodology Collocated methodology Recent literature Key factors considered

Cost Cycle time

Queuing network Simulated annealing Yoneda et al. (1992) O X

Marginal allocation procedure Connors, Feigin, and Yao (1996) O O Branch and bound algorithm Bretthauer (1996) O X

Qualitative reasoning Chou (1999) X O

Utility function Chou and Wu (2002) O

Mathematics analytical method Genetic algorithm Wu et al. (2005) O

Chou and You (2001) O O

Linear/integer programming Yang (2000) X X

Hsieh and Lin (2002) X O

Hua and Banerjee (2000) O X

Stochastic integer programming Eppen et al. (1989) O X

Hood et al. (2003) O X

Simulation STEP method Mollaghsemi and Evans (1994) X O

Response surface methodology Chen and Chen (1996) O O

Static capacity Grewal et al. (1998) O O

Heuristic Lagrangean relaxation, GB SB Swaminathan (2000) O X

Lagrangean relaxation, GB SB Swaminathan (2002) O X

Genetic algorithm Wang and Lin (2002) O X

BBCT Chung and Hsieh (2004) O O

Combinations Heuristic and queuing network Simulated annealing Bard et al. (1999) O O

Donohue et al. (2002) X O

Iwata et al. (2003) O O

Heuristic and simulation Neacy et al. (1993) X O

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2.2. Capacity related parameters

aphoto, ai Tool availability for each machine unit at photolithography workstation and non-photolithography workstation i respectively arphoto, ari Weighed average processing time for the

production of each piece of wafer fab at photolithography workstation and non-photolithography workstation i respectively. ari¼PDd¼1½ðodfd;iÞ=ðtd;iydÞ=

PD d¼1od

fd,i Re-entry times of product d for workstation i

FC Monthly wafer output target at

photolithography workstation operating on the full-scale capacity

h Working hours per month

Mphoto, Mi Upper-limit of equipment quantity at photolithography workstation and non-photolithography workstation i, respectively, for shutdown according to the given output plan mtphoto, mti Quantity of wafer product that one unit of

equipment at each photolithography workstation and non-photolithography workstation i can produce on a monthly basis respectively

od Output target for product d according to the given output plan. d = 1, . . . , D

oak Availability ratio denoting when any one operator k at a certain period is available for product processing operations

omk Mean time period that the operator k is not available for product processing operations oqi Total number of operators available for the

speciﬁc workstation i

qphoto, qi Original tool quantity for each photolithography workstation and non-photolithography workstation i respectively

QRi Minimum quantity of equipment at workstation i required for achieving the given output plan qbphoto Quantity of photolithography machines

reserved for allowing a lower workstation utilization rate to reduce the shutdown effect on cycle time increase. (0 6 qbphoto6Mphoto)

td,i Throughput rate of product d on workstation i ui,j Utilization rate of workstation i after the jth

piece of equipment at workstation i is shut down. ui;j¼PDd¼1½ðodfd;iÞ=ðtd;iydÞ=½ðqi jÞaih

wci,j Cycle time of workstation i before the jth piece of equipment at workstation i is shut down in the given output plan

wmi Mean time period in a day that machines in workstation i are unavailable for repair preventive maintenance, etc.

Dwcphoto,j, Dwci,j

Cycle time increases due to the shutdown of the jth piece of equipment at each photolithography workstation and non-photolithography workstation i, respectively

yd Yield rate of product d

x y

j k _{The largest integer that is equal to or less than x} divided by y

x y

l m _{The smallest integer that is equal to or larger} than x divided by y

2.3. Cost related parameters

Dcphoto,j, Dci,j

Variable cost savings for each photolithography workstation and non-photolithography workstation i respectively, if the jth piece of equipment is shut down

CBi,j Type II variable cost of workstation i when the jth piece of equipment at workstation i is shut down CFi,j Type III variable cost of workstation i when the jth piece of equipment at workstation i is shut down g Variable cost reduction target percentage TC Original total variable cost of a fab

vi,2

Average variable cost for rebooting each machine shut down at workstation i

vi,3

Average variable cost for the hourly consumption of each machine at workstation i

2.4. Decision variables

Ephoto,j, Ei,j

Indicate the jth piece of equipment shutdown at each photolithography workstation and non-photolithography workstation i. Ephoto,j(or Ei,j) = 1 if the jth piece of equipment at each photolithography workstation (or non-photolithography workstation i) is shut down, Ephoto,j(or Ei,j) = 0 otherwise.

2.4.1. Overall logic and framework

The equipment shutdown planning mechanism developed in this paper is designed to assist the semiconductor industry in effectively shutting down the appropriate type and quantity of equipment in an economic recession. When solving the equipment shutdown problem, the required product mix and output target must be satisﬁed, and the manufacturing cost savings, and the im-pact on production performance must be considered.

The proposed equipment shutdown planning mechanism in-cludes four modules: (I) capacity check module; (II) cost saving estimation module; (III) cycle time effect assessment module; and (IV) equipment shutdown planning module. The overall ﬂow of the mechanism is shown inFig. 1and explained as follows.

A typical semiconductor wafer fab includes several hundred pieces of equipment that are classiﬁed into many workstations. The products are loaded into the machines for processing by lots, with each production step conducted by a workstation. Each work-station usually consists of several identical equipments. The orga-nization of workstation and equipment is shown inFig. 2.

The photolithography tool is the most expensive piece of equip-ment in the foundry and has the highest number of repeated en-tries in the process and the longest procurement lead-time among all of the equipments. Previous studies (Yang, 2000,Shen and Leachman, 2003,Chung and Hsieh, 2008) on the equipment planning practice have identiﬁed the photolithography tool as the bottleneck equipment at the foundry. In this paper, photoli-thography tool is also views as the bottleneck.

The product mix and corresponding output target will inﬂuence the machine types and corresponding quantities required in the factory. Therefore, Module I calculates the maximum number of machines being shut down at each workstation based on the given output plan.

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Because the number of machine shutdowns will affect the oper-ating cost, Module II assesses the impact on manufacturing cost savings when one unit of speciﬁc equipment is shut down.

When one equipment unit at a speciﬁc workstation is shut down, the utilization rate of other machines at this workstation in-creases. The increase in utilization rate prolongs the production cy-cle time. As different equipment types and corresponding quantities are shut down in a fab, the cycle time will be different.

Module III identiﬁes the impact on the production cycle time when one unit of speciﬁc equipment is shut down.

The purpose of Module IV is to determine the optimum equip-ment shutdown portfolio through the integer programming model. The proposed integer programming model, Module IV, effectively and explicitly recommends which type of equipment and what quantity to shut down to achieve the output plan, cost reduction targets, and a minimum cycle time impact.

Capacity check module

-calculate the upper-limit of equipment quantity being shut down at each workstation

Module I

Cost saving estimation module

-assess the impacts on manufacturing cost savings when one unit of specific equipment is shut down.

Module II

Cycle time effect assessment module

-assess the impacts on production cycle time when one unit of specific equipment is shut down

Module III

Equipment shutdown planning module

-equipment shutdownportfolio planning through the developed integer programming model

Module IV Module IV i i d i d i d d

f

t

y

a

h

q

o

,

photo i

M

j photo j i

c

, ,

Δ

3 2 , ,

,

_i _i _i i

a

h

v

q

j photo j i

wc

, ,

Δ

j photo j i

E

, , j i k i k i i i i

u

om

oq

oa

ar

wm

q

a

, ,

,

photo i photo i photo i j photo j i j photo j i

mt

g

q

M

TC

c

wc

,

, , , ,

Δ

Input

Mechanism

Output

Fig. 1. Overall ﬂow of equipment shutdown planning mechanism.

Chemical Vapor Deposition (CVD) Physical Vapor Deposition(PVD) Output Wafer start Clean Workstation 2nd equipment 1st equipment Furnace Workstation 1st equipment 2nd equipment 3rd Etch Workstation Inspection Workstation 1st equipment 2nd equipment 3rd equipment

Photo Workstation 1st equipment 2nd 3rd 4th

Clean Workstation PR Stripper Workstation Implanter Workstation 1st equipment 2nd 3rd 4th 5th 1st 2nd 1st 2nd 1st 2nd

Sputter Workstation CVD Workstation PVD Workstation

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2.5. Equipment shutdown planning mechanism 2.5.1. Capacity check module

The Module I calculates the upper-limit for the quantity of equipment to be shut down at each workstation based on the given output plan. Steps (1) and (2) consider the essential factors includ-ing the output target (od), re-entry times for each product type at every workstation (fd,i), tool availability at each workstation (ai), yield rate for each product type (yd), and throughput rate at each workstation (td,i). This module adopts the same concept used by Chung and Hsieh (2008)but compresses the capacity formulas.

Step 1: Calculate QRi, the minimum quantity of equipment re-quired by workstation i according to the given output plan. QRi¼

XD d¼1

½ðodfd;iÞ=ðtd;iydÞ=ðaihÞ

& ’

i ¼ 1; . . . ; I ð1Þ

The numerator in Eq.(1)represents the required monthly pro-cessing time of workstation i to achieve the given output plan, and the denominator represents the monthly available capacity for each machine unit at workstation i.

Step 2: Calculate Mi, the upper-limit of equipment quantity pos-sible for shutdown according to the given output plan.

Mi¼ max ðqf i QRiÞ; 0g i ¼ 1; . . . ; I ð2Þ

Eq.(2)subtracts the minimum equipment quantity required to achieve the given output plan (QRi) from the quantity that the fab currently owns (qi) to determine the upper-limit of equipment quantity to be shut down at each workstation (Mi).

2.5.2. Cost saving estimation module

The fab manufacturing cost may be subdivided into ﬁxed cost and variable cost. Fixed cost includes the plant depreciation, machinery depreciation, direct and indirect labor, production sup-port and related costs. The variable cost includes the cost of direct materials (for example, silicon chips) and some indirect materials. Carnes and Su (1991)suggested that variable cost includes the cost of consumables that are typically unique to each process tool. Util-ity or power usage, chemicals, gases, expendable parts and waste disposal costs are included in the cost of consumables.

A cost item related to whether or not a machine is shut down can be reﬂected by its corresponding activity drivers. Activity driv-ers are those factors that drive the cost of operational activities. (Hansen & Mowen, 2000). A variable cost item can be classiﬁed into three types according to the activity drivers: (1) Type I: the variable cost item uses wafer pieces as the activity driver and in-creases with the number of wafers processed (for example, raw wafers, control wafers, chemicals, gases, and containers). (2) Type II: the variable cost item uses equipment units as the activity dri-ver and is used when any machine unit is shut down (for example, expendable parts for rebooting the machine). (3) Type III: the var-iable cost item uses time units as the activity driver and increases with the available time units for each operating machine (for example, utility, power supply, and waste disposal). The Types II and III variable costs are related to the amount of equipment shutdown.

When the machines that are shut down need to be turned on again, the Type II variable cost for rebooting j pieces of machines at workstation i, CBi,j, is:

CBi;j¼ jvi;2 ð3Þ

When the jth piece of equipment at workstation i is shut down, the Type III variable cost of workstation i, CFi,j, is:

CFi;j¼ ðqi jÞaih

v

i;3 ð4Þ

In Eq.(4): (qi j) is the remaining quantity at workstation i after the jth piece of equipment at workstation i is shut down. (qi j)aih

represents the available monthly hours of workstation i to perform work.

Therefore, when the jth piece of equipment at workstation i is shut down, the variable cost that could be saved at workstation i, Dci,jis

D

ci;j¼ ðCFi;j1þ CBi;j1Þ ðCFi;jþ CBi;jÞ ¼ aih

v

i;3

v

i;2;

8

j ð5Þ

Eq.(5)shows that the variable cost of shutting down any of the j pieces of equipment at the workstation is equal.

2.5.3. Cycle time effect assessment module

The shorter the cycle time, the quicker the fab can respond to customer needs. Therefore, cycle time is one vital indicator of pro-duction performance considered in equipment shutdown planning. However, the utilization rate of other machines at this workstation increases after the equipment at a speciﬁc workstation is shut down. Such an increase in utilization rate prolongs the production cycle time, particularly for workstations with a smaller quantity of equipment.

To assess the impact on production cycle time when each piece of equipment is shut down, this module, as inChung and Hsieh (2008), adopts the workstation cycle time estimation formula developed byKishimoto et al. (2001). Thus, given an output target (od), the re-entry times for each product type at each workstation (fd,i), the tool availability at each workstation (ai), the yield rate for each product type (yd), and the throughput of each workstation (td,i), the cycle time of workstation i, wci,j, when the jth piece of equipment at workstation i is shut down, is estimated as wci;j¼ f1 þ ½ð1 aiÞðqijÞ=ðqi j þ 1Þðwmi=ariÞ þ ð1 oakÞoqi=

ðoqiþ 1Þðomk=ariÞg½1 ðui;j=2Þ=ð1 ui;jÞar ð6Þ

When the jth piece of equipment at workstation i is shut down, the cycle time increase,Dwci,j, is:

D

wci;j¼ wci;j wci;j1 ð7Þ

2.5.4. Equipment shutdown planning module

Module IV targets equipment shutdown portfolio planning through the developed integer programming model. The model takes into considerations. (1) The upper-limit for the quantity being shutdown as derived in Module I for each workstation; (2) the shutdown effect of a speciﬁc equipment unit on the variable cost savings and on the cycle time according to the equipment type and total number of units already shut down; (3) the variable cost reduction target set by ﬁnancial management; and (4) the estab-lishment of protective capacity reserved at non-bottleneck work-stations. The model formulation is shown below:

C. IP Model: minimize X I i¼1 i–photo XMi j¼1 Ei;j

D

wci;jþ X Mphoto j¼1 Ephoto;j

D

wcphoto;j ð8Þ Subject to XI i¼1 iphoto XMi j¼1 Ei;j

D

ci;jþ X Mphoto j¼1 Ephoto;j

D

cphoto;j 0 B B @ 1 C C A=TC 2 6 6 4 3 7 7 5 P g ð9Þ qi XMi j¼1 Ei;j ! mtiPðqphoto X Mphoto j¼1

Ephoto;jÞmtphoto foralli – photo ð10Þ

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Ei;jPEi;jþ1

8

i; j 2 f1; . . . ; Mi 1g ð11Þ Ephoto;jPEphoto;jþ1 j 2 f1; . . . ; Mphoto 1g ð12Þ

Ei;j2 f0; 1g

8

i; j ð13Þ

Ephoto;j2 f0; 1g

8

j ð14Þ

Eq.(8)is the objective function used to measure the total cycle time impact on the entire fab after tool shutdown.

Eq.(9)requires that the variable cost reduction percentage after tool shutdown be greater than the variable cost cutting target ratio, g, to solve the corporate ﬁnancial dilemma during an economic downturn.

The design concept of Eq.(10)is based on the theory of con-straint (TOC) (Goldratt, 1990). That is, non-bottleneck workstations should reserve some capacity greater than the production needs to protect the system throughput and performance. The protective capacity of a non-bottleneck workstation is used to ensure that the production volume meets that of the photolithography workstation.

In Eq.(10), mtphotoand mtiare the wafer quantities that one unit of equipment at the photolithography workstation and non-photo-lithography workstation i can produce on a monthly basis, respec-tively. The production quantity is derived from the following equations: mtphoto¼ aphotoh arphoto ð15Þ mti¼ aih ari ð16Þ Eqs.(11) and (12)ensure that equipment shutdown at a non-photolithography workstation i and at a non-photolithography work-station are performed in sequential serial number order. The de-sign of Eqs.(11) and (12)ensures the correct result in calculating the shutdown effect of each additional unit, shown in Eq.(6). That is, the effect on the cycle time increase because the shutdown of the jth piece of equipment at workstation i can only be derived after shutting down (j 1) equipment units of workstation i.

Eqs. (13) and (14) restrict the decision variables to 0–1

variables.

If there are many output plans under consideration, we can repeatedly execute Modules I–IV for each output plan and to deter-mine the best type and quantity of equipment for shutdown according to each output plan. The number of shutdown equip-ment to be shut down at each workstation is determined as the

minimal shutdown number among all output plans to ensure that each possible output plan can be accomplished.

3. Application example

This section contains four parts: Section3.1presents the actual data from company X, a well-known semiconductor plant in the Hsinchu Science-Based Industrial Park of Taiwan that will be used as a case study to demonstrate how the proposed mechanism is used in practice. Section3.2presents an analysis of the shutdown effect under variable output plans and cost reduction targets. Sec-tion3.3presents two practical methods used in company X and in another well-known semiconductor company Y as a benchmark for comparison to highlight the contribution of this paper to industrial practice. Finally, we present an analysis of the shutdown effect un-der variable bottleneck capacities and cost down targets.

3.1. Fundamental application

There are 83 kinds of workstations at company X, 37 of which are batch workstations. Some of company X’s tool information is listed inTable 2, including tool quantity, availability at each work-station, throughput of each product type at each workwork-station, re-entry times of each product type at each workstation, and variable cost savings.

The actual output plan provided by company X is 13, 040 wafers per month with 1:1 product mix, including logic product A (o1= 6520 wafers per month) and memory product B (o2= 6520 wafers per month). This wafer output plan is equivalent to 80% of company X’s full-scale capacity. We implemented Eqs.(1) and (2) to identify 90 pieces of equipment available for shutdown. We then used Eqs.(3)–(7)to determine the shutdown effect of each piece of equipment at workstation i on variable cost savings and cycle time. Photolithography was identified as the bottleneck workstation. The goal was to reduce variable cost by 10%. This problem was solved by the branch and bound method using Lingo software to find the optimal solution of this problem. Experiments were carried out on a PC with a 2.66 Intel Core i5-750 CPU4. The required CPU time was around 5–10 s per run for 90 variables and 271 constraints. The final optimal solution showed that 19 units of equipment should be shut down, and the cycle time increased by 0.58% (42.3 min).

3.2. Shutdown effect under variable output plans

To illustrate the equipment shutdown decision problem accord-ing to different output plans, three scenarios are proposed, as

Table 2

Part of company X’s tool information.

Workstation qi ai t1,i(pcs/day) t2,i(pcs/day) f1,i f2,i wmi(min) Dci,j(USD K) Batch size

w01 2 0.97 12,000 12,500 17 21 0.133 700 1 w02 3 0.97 12,000 12,500 26 30 0.133 700 1 w03 1 1.00 35,928 72,000 1 1 0.000 529 1 w04 1 1.00 12,000 12,000 3 3 0.000 975 1 w05 1 1.00 1500 1500 1 1 0.000 400 1 w06 1 1.00 35,928 72,000 1 1 0.000 400 1 w07 7 0.97 2250 2250 12 20 0.150 660 2 w08 3 0.97 2667 2625 6 3 0.150 660 2 w09 3 0.98 562 563 1 3 0.067 400 1 w10 1 0.98 – 750 0 1 0.100 400 1 w11 2 0.98 621 625 1 1 0.100 300 1 wl2 5 0.96 400 400 2 2 0.200 900 1 w81 1 1.00 3429 3450 1 1 0.000 200 2 w82 4 1.00 500 500 1 1 0.000 390 1 w83 1 1.00 12,000 12,000 1 1 0.00 390 1

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shown inTable 3. Output plans I, II, and III are to operate at 80%, 60%, and 40% of full-scale capacity, respectively, each with the same product mix (1:1). Five cost reduction targets, namely 5%, 10%, 15%, 20%, 25%, were applied in the analysis of the shutdown impact on production performance.Fig. 3presents the following facts.

In each output plan, if the cost reduction percentage increases, the cycle time will increase. For example, in output plan I inFig. 3, when the cost reduction target increases from 10% to 25%, more equipment is removed and the cycle time increases from 0.58% to 6.80%. The results show that such an analysis could effectively indicate the trade-off relationship between cycle time increases and cost savings for equipment shutdown planning.

3.3. Comparison with current industrial practices

Comparing the performance of the proposed mechanism with that of the industry approach, two current practices at companies X and Y were investigated to analyze the equipment shutdown im-pacts on cycle time and cost savings in this section.

Company X uses the output drop-off percentage to determine the shutdown quantity for each workstation. The formula for cal-culating the shutdown quantity at each photolithography and non-photolithography workstation i is,

Mi¼ qi qi XD d¼1 od=FC ! & ’ i ¼ 1; . . . ; I ð17Þ where qi PDd¼1od=FC

is the minimum quantity of equipment re-quired for achieving the given output plan.

To maintain a high utilization rate for each workstation, company Y considers an 85% utilization rate as the threshold for making shut-down decisions. That is, no equipment will be shutshut-down if the work-station utilization rate is greater than 85%. The equations for calculating the shutdown quantity at each photolithography and non-photolithography workstation i is (Chung and Hsieh, 2008), Mi¼ maxfðqi dqiui=0:85eÞ; 0g; if ui<0:85 ð18Þ Mi¼ 0; if uiP0:85

where ui;j¼ XD

d¼1

½ðodfd;iÞ=ðtd;iydÞ=½ðqi jÞaih

To show the equipment shutdown effects on cycle time and on cost savings, we derived the results for output plans I–III by ﬁrst adopting the approaches used at companies X and Y. Based on the cost savings achieved by companies X and Y, we ran the pro-posed mechanism for each individual case. The corresponding re-sults, shown inTable 4, led us to the following conclusions.

1. With the same level of cost savings, the mechanism proposed in this paper will result in a lower cycle time impact than the cur-rent practice of company X. For example, for output plan II,

Table 3 shows that company X has a cost saving of 10.77%,

but the cycle time increase is as high as 13.65%. However, with the same cost saving target achieved by companies X (g% = 10.77%), the mechanism we propose has a cycle time impact of only 0.39%.

2. Compared to company Y’s approach, the results also show that the proposed mechanism has a lower cycle time impact using the same cost saving target. Company Y treats an 85% worksta-tion utilizaworksta-tion rate as the threshold for tool shutdown. This rate will result in an extreme increase in cycle time: 71.32%, 50%, and 57.68% for output plans I, II, and III with the cost sav-ing at 39.4%, 45.04%, and 53.72%, respectively. However, by using the same cost saving target achieved by companies Y, the mechanism we propose would result in lower cycle time impacts of 53.06%, 35.54%, and 39.88% for output plans I, II, and III, respectively.

Table 3

Monthly output plan and product mix under variable capacity scales (28 days/month, yield is assumed as 100%).

Output plan (1) Product 1, o1 (2) Product 2, o2 (3) Output = (1)+(2)

I 6520 6520 13,040 II 4890 4890 9780 III 3260 3260 6520 Unit: Wafers/month. 5% 10% 15% 20% 25% Cost down% 8000 7500 7000 6500 6000

Output plan III (original cycle time=6264.0) 7284.5 (0.17% ) 7314.7 (0.58% ) 7377.1 (1.44% ) 7495.7 (3.07% ) Output plan I

(original cycle time=7272.4) 7766.9 (6.8% ) 6699.6 (0.09% ) 6715.7 (0.33% ) 6747.1 (0.8% ) 6796.0 (1.53% ) 6896.6 (3.03% ) 6267.1 (0.05% ) 6275.3 (0.18% ) 6289.7 (0.41% ) 6312.2 (0.77% ) 6352.9 (1.42% ) Output plan II (original cycle time=6693.6)

8550

Cycle Time (min)

(8)

3. The study results demonstrate the superiority of the proposed mechanism and the value of this paper in industrial applications.

3.4. Shutdown effect under variable bottleneck capacities

In this section, to assess the cycle time increases based on dif-ferent shutdown photolithography machines quantities, we en-forced the number of shutdown to a speciﬁc value that is between the upper-limit of shutdown quantity (Mphoto) and 0. Thus, we designedly added a constraint, Eq.(19), into our integer programming model and treated qbphotoas a parameter:

X Mphoto

j¼1

Ephoto;j¼ Mphoto qbphoto ð19Þ

where qbphoto is the quantity of photolithography machines re-served to allow a lower workstation utilization rate to reduce the shutdown effect on cycle time increase.

From the results shown inFigs. 4–6andTable 5, we can see the following.

1. For each qbphotoin output plan I, II, and III, we can ﬁnd: the more the reduction target increases, the more the cycle time increases.

2. The shutdown quantity of photolithography machines is a crit-ical factor that inﬂuences the cycle time. For example, inFig. 4, when qbphotoincreases from 0 to 1, 2 units (i.e., PMphoto

j¼1 Ephoto;j decreases from 6 to 5, 4) with the cost reduction target set at 25% for output plan I, the cycle time increase rate will drop from 14.19% to 6.95%, and 6.8% respectively because the shutdown quantity of photolithography tools is decreased. The same situ-ation can be found inFig. 6, when qbphotoincreases from 0 to 1, 2, 3 units (i.e.,PMphoto

j¼1 Ephoto;jdecreases from 9 to 8, 7, 6) with the cost reduction target set at 25% for output plan III, the cycle time increase rate will drop from 2.34% to 1.56%, 1.44% and 1.42%.

3. Under the pre-established cost reduction target, if the shut-down quantity of photolithography tools is greatly decreased, many more additional units of non-photolithography tools must be shut down to compensate for the cost savings. Mean-while, the cycle time tends to move upwards. For example, in Fig. 4, when qbphotoincreases to 3 and 4 with the cost reduction Table 4

Equipment shutdown effect with industry’s approaches.

Output plan Company X Proposed mechanism Company Y Proposed mechanism

I Cycle time increase rate 4.16% 0.18% 71.32% 53.06%

(Cycle time after equipments shutdown) (7603.1) (7285.3) (12505.2) (11131.1)

Cost saving rate 5.38% 39.40%

(Saving amount) (205) (1503)

II Cycle time increase rate 13.65% 0.39% 50% 35.54%

III Cycle time increase rate 25.36% 0.48% 57.68% 39.88%

Remark: original total variable cost is USD 3814.7 K/month.

0.29% 0.21% 0.17% 8.99% 8.72% 0.97% 0.46% 1.27% 0.58% 0.69% 0.65% 0.78% 9.64% 1.96% 1.51% 1.44% 1.52% 1.91% 10.95% 3.43% 3.07% 3.40% 4.42% 7.70% 6.95% 14.19% 12.14% 7.69% 6.80% 0% 2% 4% 6% 8% 10% 12% 14% 6 5 4 3 2 1 25% 20% 15% Cycle Time Increase % 10% 5% Mphoto j photo

E

= j 1 ,

(9)

target set at 25% for output plan I, the cycle time increase rate moves up, which is 7.69% and 12.14%, respectively. InFig. 5, when qbphotoincreases to 3, 4, 5 and 6 (i.e.PEphoto,j= 4, 3, 2 and 1) with the cost reduction target set at 25% for output plan II, the cycle time increase rate moves up, which is 3.09%, 3.18%, 3.29% and 3.44%, respectively. This move-up results imply that to achieve the pre-established cost reduction target, more non-photolithography tools should be shut down to offset the cost effect of a lower shutdown quantity of photolithography tools. The additional units of non-photolithography tools being shut down are more inﬂuential on cycle time than the decreased number of photolithography tools being shut down. Finally, when qbphotoincreases to 5 or 6 in output plan I inFig. 4(or when qbphoto increases to 7 in output plan II in Fig. 5), the

non-bottleneck tools do not have enough capacity to satisfy Eq.(10) such that there is no feasible solution for the entire integer programming model.

4. The cycle time increase rate drops signiﬁcantly when qbphotois equal to 1. (i.e. PMphoto

j¼1 Ephoto;j decreases from 6 to 5 in Fig. 4, from 7 to 6 inFig. 5, and from 9 to 8 inFig. 6). Besides, com-paring withFigs. 5 and 6, the cycle time drop-off rate inFig. 4 is the most signiﬁcant when qbphoto is equal to 1. That is, reserving one unit of photolithography tool could lead to a good cycle time performance. The results are summarized in Table 5.

5. The above experiments show that an appropriate combination of machine quantities at bottleneck and non-bottleneck work-stations will help to substantially compress cycle time.

0.18% 0.14% 0.11% 0.10% 0.09% 1.26% 0.34% 0.86% 1.84% 3.44% 1.11% 0.46% 0.27% 0.34% 0.63% 0.34% 0.33% 0.38% 0.44% 0.83% 1.63% 1.01% 0.86% _0.81% 0.80% 0.81% 1.76% 2.27% 1.66% _1.56% 1.53% 1.57% 1.66% 3.29% 3.08% 3.60% 3.18% 3.09% 3.03% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 7 6 5 4 3 2 1 0 25% 20% 15% Cycle Time Increase % 10% 5% = photo M j j photo E 1 ,

Fig. 5. Shutdown effect on cycle time increase in output plan II.

0.05% 1.30% 0.18% 0.81% 0.85% 0.88% 0.92% 1.47% 1.52% 1.57% 1.67% 1.74% 0.05% 0.06% 0.07% 0.08% 0.11% 0.14% 1.23% 0.41% 0.23% 0.18% 0.18% 0.18% 0.48% 0.20% 0.18% 0.24% 0.31% 0.45% 0.44% 0.42% 0.41% 1.47% 0.66% 0.50% 0.44% 0.41% 0.41% 1.78% 0.98% 0.83% 0.77% 0.78% 0.78% 1.56% 2.34% 1.44% 1.42% 1.44% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 9 8 7 6 5 4 3 2 1 0 25% 20% 15% Cycle Time Increase % 10% 5%

∑

photo₌ M j j photo E 1 ,

(10)

4. Conclusion

To enhance operating performance during a period of economic downturn, managers of semiconductor ﬁrms engage in strategic equipment shutdown planning to drive cost reduction and adjust the allocation of resources. Building a sound mechanism to deter-mine the type and quantity of equipment suitable for shutdown is very important.

This paper proposed an equipment shutdown planning mecha-nism and developed an integer programming model to assist ﬁrms in effectively mapping out the optimum portfolio for equipment shutdown. Factors including product mix, corresponding output

targets, protective capacity and the variable cost reduction targets were taken into consideration. The objective of the proposed inte-ger programming model is to minimize the effect of shutdown on cycle time to maintain the time-to-market competitiveness during an economic recession. Compared with two current industry prac-tices, the portfolio derived by our proposed mechanism has a smal-ler cycle time impact while achieving the threshold cost savings.

The experimental results show that the equipment shutdown planning mechanism proposed in this paper is an excellent tool for analyzing the trade-off relationship between cycle time in-creases and cost savings. We also determined that appropriately decreasing bottleneck machine utilization and reserving some Table 5

Shutdown effect on cycle time under variable bottleneck capacity. Output Plan Original cycle time Mphoto qb photo PMphoto

i¼1 Ephoto Photo utilization Cost down target

5% 10% 15% 20% 25% I (7272.4) 6 0 6 97.9% 8.72% 8.99% 9.64% 10.95% 14.19% (7906.6) (7926.2) (7973.5) (8068.7) (8304.4) 1 5 85.7% 0.97% 1.27% 1.96% 3.43% 6.95% (7342.6) (7364.8) (7414.9) (7521.9) (7777.8) 2 4 76.2% 0.46% 0.78% 1.51% 3.07% 6.80% (7305.6) (7329.1) (7382.2) (7495.7) (7766.9) 3 3 68.6% 0.29% 0.65% 1.44% 3.40% 7.69% (7293.2) (7319.5) (7377.1) (7519.7) (7831.7) 4 2 62.3% 0.21% 0.58% 1.52% 4.42% 12.14% (7287.3) (7314.7) (7382.9) (7593.8) (8155.3) 5 1 57.1% 0.17% 0.69% 1.91% 7.70% – (7284.5) (7322.3) (7411.3) (7832.4) – 6 0 52.7% – – – – – – – – – – II (6693.6) 7 0 7 85.7% 1.11% 1.26% 1.63% 2.27% 3.60% (6768.2) (6777.9) (6802.7) (6845.5) (6934.9) 1 6 73.4% 0.46% 0.63% 1.01% 1.66% 3.08% (6724.6) (6735.9) (6761.4) (6804.7) (6899.7) 2 5 64.3% 0.27% 0.44% 0.86% 1.56% 3.03% (6711.5) (6723.0) (6751.5) (6798.0) (6896.6) 3 4 57.1% 0.18% 0.38% 0.81% 1.53% 3.09% (6705.6) (6719.0) (6747.8) (6796.0) (6900.4) 4 3 51.4% 0.14% 0.34% 0.80% 1.57% 3.18% (6702.9) (6716.3) (6747.1) (6798.7) (6906.4) 5 2 46.7% 0.11% 0.33% 0.81% 1.66% 3.29% (6700.9) (6715.7) (6747.8) (6804.7) (6913.8) 6 1 42.8% 0.10% 0.34% 0.83% 1.76% 3.44% (6700.3) (6716.3) (6749.1) (6811.4) (6923.8) 7 0 39.5% 0.09% 0.34% 0.86% 1.84% (6699.6) (6716.3) (6751.1) (6816.7) – III (6264.0) 9 0 9 85.8% 1.23% 1.30% 1.47% 1.78% 2.34% (6340.9) (6345.5) (6355.9) (6375.5) (6410.6) 1 8 68.6% 0.41% 0.48% 0.66% 0.98% 1.56% (6289.4) (6294.1) (6305.2) (6325.2) (6361.6) 2 7 57.2% 0.23% 0.31% 0.50% 0.83% 1.44% (6278.4) (6283.4) (6295.0) (6315.8) (6354.0) 3 6 49.0% 0.14% 0.24% 0.44% 0.77% 1.42% (6272.8) (6279.0) (6291.5) (6312.2) (6352.9) 4 5 42.9% 0.11% 0.20% 0.41% 0.78% 1.44% (6270.9) (6276.5) (6289.7) (6312.8) (6354.2) 5 4 38.1% 0.08% 0.18% 0.41% 0.78% 1.47% (6269.0) (6275.3) (6289.7) (6312.8) (6356.1) 6 3 34.3% 0.07% 0.18% 0.41% 0.81% 1.52% (6268.4) (6275.3) (6289.7) (6314.7) (6359.2) 7 2 31.2% 0.06% 0.18% 0.42% 0.85% 1.57% (6267.7) (6275.3) (6290.3) (6317.2) (6362.3) 8 1 28.6% 0.05% 0.18% 0.44% 0.88% 1.67% (6267.1) (6275.3) (6291.5) (6319.1) (6368.6) 9 0 26.4% 0.05% 0.18% 0.45% 0.92% 1.74% (6267.1) (6275.3) (6292.2) (6321.6) (6373.0)

(11)

protective capacity for non-bottleneck machines help to hold down the cycle time increase rate during the shutdown.

The managerial implications are concluded as follows. 1. The shutdown quantity of photolithography machines is a

crit-ical factor that inﬂuences the cycle time. An appropriate combi-nation of machine quantities at bottleneck and non-bottleneck workstations will help to substantially compress cycle time. 2. Reserving insufﬁcient or too many units of photolithography

tools could result in poor cycle time performance when plan-ning equipment shutdown. The proposed mechanism can effec-tively provide a valuable analysis tool and trade-off information for management decision-making.

3. For future research, the problems related to mid-term or short-term capacity adjustment, such as inter-fab backup of equip-ment for meeting monthly capacity requireequip-ments, the timing of equipment disposal, and application in other industry, can be studied.

Acknowledgements

The authors graciously acknowledge the great supports of Frank Kao (human resources director), Charles Hung (production plan-ning director), Chen-Fu Chien (IE deputy director), and Tom Wu (capacity planning manager) of the Taiwan Semiconductor Manu-facturing Company.

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Shu-Hsing Chung is Professor of the Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC. She received her PhD degree in Industrial Engineering from Texas A&M University, College Station, TX, USA. Her research interests include production planning, scheduling, cycle time estimation, and performance evaluation. She has published and presented research papers in the areas of production planning and scheduling for IC manufacturing. Ming-Hsiu Hsieh is a manager in the Department of Industrial Engineering, Taiwan Semiconductor Manufacturing Company, and a PhD candidate at the Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC. He received his MS degree in Industrial Engineering and Management from National Chiao Tung University. His research interests include capacity planning and production/operation management.