eg

, Y

alifo

s toll at prpro, w

making based on ABC systems while simultaneously improving the value of green manufacturingtechnology investments.

2013 Published by Elsevier Ltd.

n actie envit yearoncernalso b

their products and processes given regulatory requirements,

efuent.However, in practice, most companies continue to struggle to

invest their scarce resources to adopt newGMTs because of a lack ofproper justication tools that would both identify protable andnon-protable products and account for resource constraints.

resource constraints in the production process (Yahya-Zadeh, 1998;ns, the theory ofwhen making de-ing products fromand Taylor, 2007).se a mathematicalility of a product-h the adoption of

2. Background

Due to the growing awareness of environmental issues, newGMTs have been widely considered for maintaining a competitiveadvantage (Kong and White, 2010), enhancing production skills(Puurunen and Vasara, 2007) and copingwith pressure groups (Tsaiet al., 2011a). Nevertheless, facility managers still have difcultyanalyzing the impact of GMTs on prots because of a lack of

* Corresponding author. Tel.: 886 3 4267247; fax: 886 3 4222891.

Contents lists available at

Journal of Clean

els

Journal of Cleaner Production 57 (2013) 178e187E-mail address: whtsai@mgt.ncu.edu.tw (W.-H. Tsai).product stewardship, public image and potential competitive ad-vantages. In such circumstances, many organizations are ndingthat going beyond regulatory compliance can create value for theircustomers and respond to pressure groups. For example, many fa-cility operators are actively investigating the use of greenmanufacturing technologies (GMTs), such as aqueous degreasersand powder coatings, in an effort to reduce toxic air emissions andcontrol costs associated with the treatment of contaminated

Kee and Schmidt, 2000). Under such conditioconstraints (TOC) may provide a better solutioncisions about reducing environmentally-damagthe mix (Onwubolu and Mutingi, 2001; LockhartThe purpose of this research paper is to propoprogramming model that analyzes the protabmix decision based on the ABC and TOC, witnew GMTs.organizations to be more environmentally responsible for both value added activities, processes and products, ABC may ignoreGreen manufacturing technologies (GMTs)Theory of constraints (TOC)Product-mix decisionMathematical programming approach

1. Introduction

Since production and consumptioating negative impact effects on thproduction, use and disposal in recenhave increasingly become primary cment. Meanwhile, stakeholders have0959-6526/$ e see front matter 2013 Published byhttp://dx.doi.org/10.1016/j.jclepro.2013.04.011vities have been gener-ronment through theirs, environmental issuess of corporate manage-egun to put pressure on

Facility operators need accurate information from their manage-ment accounting systems in order to make protable choicesregarding environmental spending. The use of activity-basedcosting (ABC) on protability analysis is called upon to help breakdown and analyze the nature of environmental costs in productsthat generate those costs, in order to lead to the best decisions.Even though ABC provides a systematic approach to analyzing non-Keywords:Activity-based costing (ABC)component parts manufacturer in the automotive industry, the ndings of this study provide insight intothe value of mathematical programming approaches for GMTs investment and product-mix decisionA product-mix decision model using gretechnologies under activity-based costin

Wen-Hsien Tsai a,*, Hui-Chiao Chen a, Jun-Der Leu a

aNational Central University, Jhongli, Taoyuan 32001, Taiwanb Leventhal School of Accounting, Marshall School of Business, University of Southern C

a r t i c l e i n f o

Article history:Received 13 June 2012Received in revised form4 April 2013Accepted 9 April 2013Available online 15 June 2013

a b s t r a c t

The purpose of this study iof constraints (TOC), as wein making decisions abouproposes a mathematicalbased on the ABC and TOC

journal homepage: www.Elsevier Ltd.n manufacturing

ao-Chung Chang a, Thomas W. Lin b

rnia, Los Angeles, CA 90089-0808, USA

assess how the integration of activity-based costing (ABC) and the theorys the application of a mixed-integer programming (MIP) model, can assistoduct-mix using green manufacturing technologies (GMTs). This studygramming model to analyze the protability of a product-mix decisionith the adoption of new GMTs. Using a numerical example from a metal

SciVerse ScienceDirect

er Production

evier .com/locate/ jc lepro

anerappropriate performancemeasures (Azzone and Noci, 1998; Kuldip,2006), systematic analysis of overhead and xed operating costs(Kaplan and Cooper, 1998) and considerations of constrained re-sources in the production process (Wang et al., 2009; Tsai et al.,2011b, 2012b). Recently, researchers have suggested a number ofmethodologies and evaluation techniques that look promising in-sofar as the economic justication process for these advancedmanufacturing technologies is concerned. The solutions to theseshortages should be sought in the ABC and TOC.

2.1. Activity-based costing (ABC)

Currently, ABC has become a popular cost accounting system toovercome the shortcomings of traditional cost accounting systems.There are four key benets to the ABC system: (1) accurate iden-tication of product cost, especially overhead; (2) more preciseinformation about value-added and non-value-added costs by theidentication of cost drivers; (3) direct allotment of costs to prod-ucts or processes that consume resources; and (4) identication ofnon-value-adding costs (Kaplan, 1989; Canada et al., 1996; Hilton,2005). Various surveys have also indicated that the ABC approachhas been used to analyze different kinds of management decisions,including: pricing, quoting, product-mix and joint products de-cisions (Tsai and Lai, 2007; Kee, 2007, 2008), outsourcing decisions(Kee, 1998; Tsai and Lai, 2007; Tsai et al., 2007), quality improve-ment (Tsai, 1998), design and development (Qian and Ben-Arieh,2008), nancial and physical ows analysis (Comelli et al., 2008)and environmental management, among others (Tsai et al., 2007;Tsai and Hung, 2009a, 2009b; Silva and Amaral, 2009).

The ABC uses a two-stage procedure to assign resource costs tocost objects (Turney, 1991; Tsai, 2010). In the rst stage, resourcecosts are assigned by resource drivers to activity cost pools that canbe classied by activity levels such as unit, batch, product and fa-cility (Cooper, 1990). Each activity level can have several activitycost pools. In the second stage, activity cost pools are assigned tocost objects by activity drivers, which are activities that incur costs(Hilton, 2005). Because the problem of assessing the benets andcost drivers of the new GMTs are less well studied and understood,in this study, we follow Kims (2009) approach and attempt toidentify the resource and activity drivers of production processesusing new GMTs. First, we estimate overall costs and possible re-sources of various production processes using new GMTs. Second,we construct resource cost pools and develop resource cost drivers.Third, we dene the main activities that consume resources ofproduction and calculate a total cost of each activity. Finally, weidentify the second stage activity drivers and allocate activity coststo various products using the cost driver.

2.2. The theory of constraints (TOC)

In early ABC research, numerous studies demonstrated the dif-ferences between production costs using ABC and traditionalcosting systems. Nevertheless, a method to reach the optimalproduct-mix under ABC was seldom mentioned. Furthermore, ABChas been criticized for its failure to incorporate constraints intoproduction-mix decisions (Kee and Schmidt, 2000). On account ofthis, Kee (1995) began to integrate ABC with TOC in the product-mix decision analysis. Several researchers proposed variousmathematical programming models in succession to conduct theproduct-mix decision analysis under ABC (Kee, 1995; Malik andSullivan, 1995; Yahya-Zadeh, 1998; Kee and Schmidt, 2000; Tsaiet al., 2012c).

According to TOC, the performance of any production system isdetermined by its slowest process (Goldratt et al., 1986; Yahya-

W.-H. Tsai et al. / Journal of CleZadeh, 1998). Thus, managers should focus their attention oncapacity constraint resources (CCRs) and removing bottleneckprocesses (Onwubolu and Mutingi, 2001). Since TOC treats over-head and operating expenses as given, TOC can also be viewed as ashort-run optimization procedure for managing resources andopening bottlenecks, with the goal of maximizing throughput(Holmen, 1995). The ABC and TOC approaches appear to comple-ment one another in addressing short-run operational and long-run cost management problems (Kee, 1995; Lockhart and Taylor,2007). Several researchers have suggested that TOC should beused for short-term production-mix decisions where costs arepredominantly xed (Noreen et al., 1995) and that ABC should beused to determine any increases or decreases in capacity andproducts because all costs tend toward being variable in the longterm.

The following steps, called the TOC procedure, provide on-goingimprovement to the throughput of a system (Goldratt, 1990):

1. Identify the systems constraints.2. Decide how to exploit the systems constraints.3. Subordinate everything else to the above decision.4. Elevate the systems constraints.5. If in the previous steps, a constraint has been broken, go back to

step 1.

The above ve steps of the TOC can be applied to the product-mix decision problem. Through the cycle of these ve steps, TOCsuccessively relieves bottlenecks and their associated constraintsby expanding the obtainable resources (capacities) or by improvingthe companys operations (Tsai and Lin, 1990; Tsai et al., 2011a). Inaddition, the product-mix decision problem that is solved usingTOC can also be formulated as a linear programming (LP) model(Tsai and Lin, 1990; Luebbe and Finch, 1992; Plenert, 1993; Tsaiet al., 2011b, 2012a).

As compared to Kee (1995), the model proposed in this paperhas the following additional characteristics: (1) considering Envi-ronmental Regulatory Cost (xed cost), Volatile Organic Com-pounds (VOCs) emission cost (piecewise linear cost) and theassociated constraints to restrain the VOCs emission quantity, (2)considering the facility-level activity cost increasing with a step-wise xed cost function, and (3) considering the capacity expan-sions for direct labor hours and machine hours.

In terms of point (3) mentioned above, regarding capacityexpansion, we consider capacity expansion for direct labor hours byusing overtime work with higher wage rates, which can beformulated as the piecewise linear cost function. Herein, we alsoconsider capacity expansion for machine hours by renting ma-chines or by buying machines, which can be formulated as astepwise linear cost function. Currently, this method is applied invarious research topics (Tsai and Kuo, 2004; Tsai and Lai, 2007; Tsaiet al., 2007, 2008, 2010).

2.3. Priming and top coating processes and activities in theautomotive industry

Many products and parts manufactured in the metal industriesare required to receive both priming and top coating processes.Typical primer-top coat technologies are adopted for miscellaneousmetal work pieces, plastic part, and the automotive industry. Thetypical sequence of operations performed by such a primer-topcoatsystem in the automotive industry includes multiple stages, asshown in Fig. 1.

In the beginning of a primer-topcoat process, the incomingmetal component parts or metalwork pieces for the car body areoften cleaned (e.g., degreased or steam-cleaned) and are passed

Production 57 (2013) 178e187 179through a zinc phosphate stage before being immersed in a large

decision. The cost elements related to the product-mix decisionmodel are described below:

1. Total revenue:

The terms in Eq. (1) represent the total revenue of bid prices forproducts.

Xn

i1PiXi (1)

2. Total direct labor cost:

ner Production 57 (2013) 178e187electro deposition tank in which a cathodic or anodic primer isapplied. After using dry-off ovens, the work pieces with electro-deposited primer are cured in a baking oven at temperaturesranging from 300 to 400 F. In the sealers and sound deadeningphase, the metal work pieces receive a polyvinyl chloride (PVC)coating that provides sound-deadening attributes. After undergo-ing light sanding, a second coat of primer is applied and then themetal work pieces are again dried and cured in a baking oven. In thetop coating and/or clear coating phase, the metal work pieces enterthe top coating spray booth and a basecoat, a solid color top coat orawet-on-wet clear coat may be applied. Eventually, the metal workpieces enter the nal baking oven in which the top coats are cured.

Given the importance of the primer-top coat process in theautomotive industry, new GMTs that prevent pollution are impor-tant issues for operations. Facilities typically use new GMTs such asthermal oxidizers, catalytic incinerators, and carbon absorbers, or acombination of these technologies, to control VOCs. Below, we willdescribe the elements of product cost that will be used in devel-oping the product-mix decision model under ABC systems.

2.4. Product-mix decision model with capacity expansions

In this section, we develop a product-mix decision model usingthe primer-top coat system as an example. In addition to theassumption about the primer-top coat process, the product-mixdecision model presented includes the following assumptions:

1. The activities in this green, multi-product primer-topcoat sys-tem have been classied as unit-level, batch-level, product-level, and facility-level activities. The related resource drivers

Fig. 1. A typical process for applying a primer-topcoating system in the automotiveindustry.

W.-H. Tsai et al. / Journal of Clea180and activity drivers have also been chosen by the companysABC team through an ABC study.

2. The unit selling prices are constant within the relevant range.3. The specic process is regarded as a stepwise xed cost that

varies with machine hours.4. Machine hour resources can be expanded by renting or pur-

chasing additional machines.5. Direct labor resources can be expanded by using overtimework

or additional night shifts with higher wage rates.6. VOC emissions are taxed at different rates, which are depen-

dent on emission quantities, and the cost of VOC emissions isregarded as a piecewise variable cost.

3. A mathematical programming model

The following is a discussion on capacity expansions, capacityconstraints and VOC emission costs, which are incorporated intothemathematical programmingmodel for determining the optimalWe assume that direct labor resources can be expanded usingovertime work or additional night shifts, or by hiring workers at ahigher wage rate. The total direct labor cost function will be apiecewise linear function, as shown in Fig. 2. The available normaldirect labor hours are LH1 and the direct labor hours can beexpanded to LH2 with the total direct labor cost being LC1 and LC2 atLH1 and LH2, respectively.

Thus, the total direct labor cost and associated constraints are asfollows (Tsai and Lin, 1990; Tsai et al., 2011b):

Total direct labor cost LC1m1 LC2m2 (2)Constraints:

TL LH1m1 LH2m2 (3)

m0 h1 0 (4)

m1 h1 h2 0 (5)

m2 h2 0 (6)

m0 m1 m2 1 (7)

h1 h2 1 (8)

(h1, h2) is an SOS1 set of 0e1 variables, within which exactly onevariable must be non-zero; (m0, m1, m2) is an SOS2 set of non-negative variables, within which at most two adjacent variables,in the order given to the set, can be non-zero (Beale and Tomlin,1970; Williams, 1985); TL is the total direct labor hours we need,and its function depends on the case under study.

3. Stepwise machine cost:

The total machine cost is regarded as a common xed cost, andits cost function is assumed to be a stepwise function (as shown inFig. 2. Piecewise direct labor cost.

Fig. 3) that varies with machine hours, as observed from prior costbehavior analysis. The total machine cost is dened as FC0 underthe current capacity of MH0 machine hours. If the capacity is suc-cessively expanded to MH1, MH2,., MHt machine hours, then thetotal machine cost increases to FC1, FC2,.,FCt, respectively. Let lih bethe requirement of machine hours for one unit of product i. Thus,the total machine cost and associated machine hour constraints areas follows (Tsai and Lin, 1990):

Total machine cost Xt

k0FCkqk (9)

Constraints:Xn

lihXi Xt

MHkqk (10)

2 2 3

Total Direct Labor Cost Total Unit Level Activity Cost Total Batch Level Activity Cost Total Product Level Activity Cost Total Facility Level Activity Cost Total VOCs Emission Cost

Xn

i1PiXi

Xn

i1

Xs

m1CmaimXi LC1m1 LC2m2

Xn

i1

XjU

djlijXi Xn

i1

XjB

djdijBij Xn

i1

XjP

djrijRi Xt

k0FCkqk

VOP1a1 VOP2a2 VOP3a3

W.-H. Tsai et al. / Journal of Cleaneri1 k0

Xt

k0qk 1 (11)

(q0, q1,.,qt) is an SOS1 set of 0e1 variables, within which exactlyone variable must be non-zero (Beale and Tomlin, 1970; Williams,1985). When qm 1 (m s 0), the capacity needs to be expandedto the mth level, i.e. MHm machine hour.

4. Environmental and social cost e VOC emission costs:

Even though new GMTs can reduce emissions, there are stillsmall amounts of VOC emissions from the topcoat spray processes.The emission costs are measured by the life cycle assessment (LCA)method (Tsai et al., 2011a). LCA is a method of comparison ofenvironmental impacts of products, technologies or services with aview of their whole life cycle. The VOC emissions to all areas of theenvironment during product production, use and disposal areconsidered. FollowingWard and Chapmans (1995) approaches, Eq.(12) is used to quantize the VOC emissions. VOC emissions are alsoassumed to be taxed at different rates depending on the quantity ofthese. Hence, the total VOCs emission cost function will be apiecewise linear function (see Fig. 4). With increasing VOC emis-sions, taxationwill be increased. The quantity of VOC emissions canbe increased from VOQ1 to VOQ2 and VOQ3. Therefore, the total VOCemission cost is VOP1, VOP2, and VOP3 at VOQ1, VOQ2 and VOQ3,respectively (Tsai et al., 2011b).

The total VOC emission costs and associated constraints are asfollows:

Total VOC emission costs VOP1a1 VOP2a2 VOP3a3(12)

VOC emission constraints:

Cost

Machine Hour Fig. 3. Stepwise machine costs.a3 u3 0 (17)

a0 a1 a2 a3 1 (18)

u1 u2 u3 1 (19)

Similarly, (u1, u2, u3) is also an SOS1 set of 0e1 variables,within which exactly one variable must be non-zero; (a0, a1, a2,a3) is an SOS2 set of non-negative variables, within which atmost two adjacent variables, in the order given to the set, can benon-zero. TVOC in Eq. (13) is the total quantity of VOC emissions;the function of TVOC will depend on the case problem. [Note thatthe function of TVOC in Section 4. Numerical example is(2X1 X2 X3), which means that the quantity of VOC emissionsfor one unit of Products 1, 2 and 3 are 2, 1, and 1, respectively.]

3.1. Integrated cost models

The model for product-mix decision making with capacity ex-pansions under activity-based costing is as follows:

Maximize:

p Total Revenue Total Direct Material Cost TVOC VOQ1a1 VOQ2a2 VOQ3a3 (13)

a0 u1 0 (14)

a1 u1 u2 0 (15)

a u u 0 (16)

Cost

VOC emissionsquantity (metric ton)0

Fig. 4. VOCs emission costs.

Production 57 (2013) 178e187 181(20)

nerSubject to:

Direct material constraints:

Xn

i1aimXi Qm; m 1;2;.; s (21)

Direct labor constraints:

TL LH1m1 LH2m2 (22)

m0 h1 0 (23)

m1 h1 h2 0 (24)

m2 h2 0 (25)

m0 m1 m2 1 (26)

h1 h2 1 (27)Batch-level activity constraints:

Xi sijBij; i 1;2;.;n; jB (28)

Xn

i1dijBij Tj; jB (29)

Product-level constraints:

Xi DiRi; i 1;2;.;n (30)

Xn

i1riRi Vj (31)

Machine hour constraints:

Xn

i1lihXi

Xt

k0MHkqk 0 (32)

Xt

k0qk 1 (33)

VOC emissions constraints:

TVOC VOQ1a1 VOQ2a2 VOQ3a3 (34)

a0 u1 0 (35)

a1 u1 u2 0 (36)

a2 u2 u3 0 (37)

a3 u3 0 (38)

a0 a1 a2 a3 1 (39)

u1 u2 u3 1 (40)

Xi 0; i 1;2;.;n

Bij 0; i 1;2;.;n jB

W.-H. Tsai et al. / Journal of Clea182(m0, m1, m2), (a0, a1, a2, a3): SOS2 set of non-negative variables.(h1, h2), qk (k 0, 1,.,t), (u1, u2, u3): SOS1 set of 0e1 variables.h1, h2, Ri (i 1, 2,.,n), qk (k 0, 1,.,t), u1, u2, u3: 0e1 variables.where

p e the companys prot;Xi e the production quantity of product i;Pi e the unit selling price of product i;Cm e the unit cost of the mth material;aim e the requirement of the mth material for one unit ofproduct i;LH1 e the available normal direct labor hours;LC1 e total direct labor cost in LH1;LC2 e total direct labor cost in LH2;dj e the actual running activity cost per activity driver for ac-tivity j;lij e the requirement of the activity driver of unit-level activity j(j U) for one unit of product i;dij e the requirement of the activity driver of batch-level activityj (j B) for product i;Bij e the number of batches of batch-level activity j (j B) forproduct i;rij e the requirement of the activity driver of product-level ac-tivity j (j P) for product i;sije the number of units per batch of batch-level activity j (j B)for product i;Ri e the indicator for producing product i (Ri 1) or not pro-ducing product i (Ri 0);TL e total direct labor hours;MHk e the available direct machine hours;VOP1 e total VOC emissions cost in VOQ1;VOP2 e total VOC emissions cost in VOQ2;VOP3 e total VOC emissions cost in VOQ3;TVOC e the total quantity of VOC emissions;VOQ1 e the total quantity of VOC emissions from productexecution (must increase the carbon tax rate);VOQ2 e the total quantity of VOC emissions from productexecution (must increase the carbon tax rate);VOQ3 e the total quantity of VOC emissions from productexecution (must increase the carbon tax rate);qk e an SOS1 (special ordered set of type 1) set of 0e1 variables,within which exactly one variable must be non-zero (Beale andTomlin, 1970; Williams, 1985), qk 1 (k s 0) means that thecapacity needs to be expanded to the kth level, i.e.,MHkmachinehours;h1, h2; u1, u2, u3 e an SOS1 (special ordered set of type 1) set of0e1 variables, within which exactly one variable must be non-zero (Beale and Tomlin, 1970; Williams, 1985);m0, m1, m2; a0, a1, a2, a3 e an SOS2 (special ordered set of type 2)set of non-negative variables, within which at most two adja-cent variables, in the order given to the set, can be non-zero(Beale and Tomlin, 1970; Williams, 1985);Di e the maximum demand of product i;Vj e the capacity limit of the activity driver of product-levelactivity j (j P);Tje the capacity limit of the activity driver of batch-level activityj (j B);Qm e the available quantity of the material.

Eq. (20) is theprot function (p) tobemaximized in themodel. Therst term Pni1 PiXi of Eq. (20) is Total Revenue, and is described inEq. (1). The second term Pni1

Psm1 cmaimXi of Eq. (20) is Total

Direct Material Cost and the associated constraints are in Eq. (21),where the available quantity of themthmaterial isQm. The third term(LC1m1 LC2m2) of Eq. (20) is Total Direct Labor Cost and the associated

Production 57 (2013) 178e187constraints are in Eqs. (22)e(27), which come from Eqs. (3)e(8).

ith product and Eq. (31) is the constraint related to the capacity

anerlimit of the activity driver of product-level activity j (j P) (Vj). The

seventh termPt

k0 FCkqk

of Eq. (20) is Total Facility-level Ac-

tivity Cost and the associated constraints are in Eqs. (32) and (33)which correspond to Eqs. (10) and (11). The machine hoursrequired increase proportionally with the production quantity, butthe cost of this is a stepwise xed cost function. This is the typicalexample of theory of constraints.

The eighth term (VOP1a1 VOP2a2 VOP3a3) of Eq. (20) is TotalVOC Emissions Cost and the associated constraints are in Eqs. (34)e(40) as described earlier in this section for Eqs. (12)e(19). TVOC inEq. (34) is the total quantity of VOC emissions, and the function ofTVOC will depend on the case problem.

As for the constraints in the model, some constraints are usedfor constructing the specic cost functions like piecewise linearfunctions and stepwise linear functions. However, the laborresource constraint is hidden in the formulations. Some constraintsare the real constraints for resources, like Eqs. (21), (29), (31) and(32) for setting up the resource limits of materials, of the activitydrivers of batch-level activities and product-level activities, and ofmachine hours, respectively.

As mentioned in Section 2.2 the theory of constraints (TOC), wecan relax the bottleneck resources by using themethods of capacityexpansions for the specic resources. This will be done in the post-optimal analyses. However, the model proposed in this paperincorporating the possible levels of capacity expansions for thevarious resources. Then it can, simultaneously, consider more thanone resource constraints.

4. Numerical example

A numerical example is presented to illustrate the application ofa mathematical programming model to determine the optimalproduct-mix under activity-based costing. Company A manufac-tures metal component parts for the automotive industry.Numerous environmental problems are preventing the Companyfrom getting its nished components to the market. Company Anow has applied GMTs to produce their products and has overcomethe following environmental problems:

(1) Solid sludge from the metal pretreatment process requires thedisposal of relatively large volumes of poisonous waste.

(2) Large volumes of rinse water from the topcoating spray boothfor topcoating and/or clear coating need more special treat-ment due to the local water treatment plants requirements.

(3) The nishedmetal component parts do not have the same glossThe fourth term Pni1PjU

djlijXi of Eq. (20) is Total Unit-level

Activity Cost, which may have specic associated constraints (notshown in the model), for a specic case problem. Strictly speaking,direct material and direct labor costs are unit-level costs whichincrease with the production quantity. The fth termPni1

PjB

djdijBij of Eq. (20) is Total Batch-Level Activity Cost and

the associated constraints are in Eqs. (28) and (29), where Tj is thecapacity limit of the activity driver of batch-level activity j (j B) inEq. (29) and sijBij is the upper limit of the ith products quantityfrom the perspective of the jth batch-level activity in Eq. (28). Thesixth term Pni1

Pjp

djrijRi of Eq. (20) is Total Product-Level Ac-

tivity Cost and the associated constraints are in Eqs. (30) and (31). IfRi 1, this means that the ith product will be produced in theperiod, Eq. (30) is the constraint related to the demand limit of the

W.-H. Tsai et al. / Journal of Cleand the quality of the coating is unstable.Despite using electrostatic turbo bells, the transfer efciency isstill too low for such paint spray guns. Thus, VOC emissions alreadycome near the permitted cap and are almost double what wasoriginally estimated when the permits were applied for.

Assume that Company A is considering producing products 1,2 and 3 (i 1, 2, 3) by using new GMTs and that these productsneed three different kinds of direct materials (m 1, 2, 3).Company A needs to calculate the following essential costs inproducing these products: (1) unit-level costs and activities:manufacturing costs include machine costs, labor costs and ma-terial costs; (2) batch-level costs: inventory handling costs, car-bon absorption costs and setup costs; (3) product-level costs:design costs; (4) facility-level costs: environment regulatory costsand VOC emissions costs. The related data for this example arepresented in Table 1. Environmental Regulatory Cost, which refersto the costs associated with handling regular inspections, dis-charging waste and ensuring that processes are in compliancewith the Environmental standard value specication according tothe laws and regulations of local government, is a xed cost andso can be expressed with a constant (12,000 in this example).Company A has to decide the optimal quantity of products withits current capacity. By using Eqs. (20)e(40) and the example datain Table 1, the green product-mix decision model for the exampleis formulated as follows:

Maximize

p Total Revenue Total Direct Material Cost Total Direct Labor Cost Total Unit Level Activity Cost Total Batch Level Activity Cost Total Product Level Activity Cost Total Facility Level Activity Cost Total VOCs Emission Cost

Xn

i1PiXi

Xn

i1

Xs

m1CmaimXi LC1m1 LC2m2

Xn

i1

XjU

djlijXi Xn

i1

XjB

djdijBij Xn

i1

XjP

djrijRi Xt

k0FCkqk

VOP1a1 VOP2a2 VOP3a3 200X1 230X2 250X3 10*6 2*5 1*2 3*1X1

10*7 2*9 1*2 3*1X2 10*8 2*10 1*2 3*2X3 120;000m1 220;000m2 2*5 4*6X1 2*5 4*7X2 2*5 4*8X3 100*2B13 100*2B23 100*2B33 2*10B14 2*10B24 2*20B34 15*2B15 15*2B25 15*4B35 100*20R1 100*10R2 100*30R3 40;000q0 75;000q1 120;000q2 100;000a1 150;000a2 195;000a3 12;000

91X1 99X2 100X3 120;000m1 220;000m2 200B13 200B23 200B33 20B14 20B24 40B34 30B15 30B25 60B35 2000R1 1000R2 3000R3 40;000q0 75;000q1 120;000q2 100;000a1 150;000a2 195;000a3 12;000:

Subject to:

Production 57 (2013) 178e187 183Direct material constraints:

C2

H2

OP3OQ

3

ner6X1 7X2 8X3 120;000

5X1 9X2 10X3 100;000

Table 1Example data.

Maximum demand jSelling priceDirect material (Unit-level) m 1 $10/unit

m 2 $2/unitm 3 $1/unitm 4 (Disposal ofhazardous material)

$3/unit

Unit-level activity Machine hours $2 1Labor hours $4 2

Batch-level activityInventory handling Handling hours $100 3

Carbon adsorption Machine hours $2 4

Setup Setup hours $15 5

Product- level activity e Design Drawings $100 6Facility-level cost

(Excluding regulatory costs)FC0 $40,000 FC1 $75,000 F

Machine hours MH0 20,000 MH1 30,000 MEnvironment regulatory cost Total cost $12,000Direct labor constraint-cost LC1 $120,000 LC2 $ 220,000Labor hours LH1 30,000 LH2 50,000Wage rate r1 $4/h r2 $5/hVOCs emission constraintCost VOP1 $100,000 VOP2 $150,000 VEmission quantities VOQ1 10,000 VOQ2 12,500 VTax rate T1 $10/ton T2 $20/ton T

W.-H. Tsai et al. / Journal of Clea1842X1 2X2 2X3 50;000

X1 X2 2X3 40;000Stepwise facility-level machine hour constraints:

5X1 5X2 5X3 20;000q0 30;000q1 40;000q2 0

q0 q1 q2 1Direct labor constraints:

6X1 7X2 8X3 30;000m1 50;000m2 0

m0 h1 0

m1 h1 h2 0

m2 h2 0

m0 m1 m2 1

h1 h2 1VOC emissions constraints:

2X1 X2 X3 10;000a1 12;500a2 14;000a3 0a0 u1 0a1 u1 u2 0

a2 u2 u3 0

Product 1 Product 2 Product 3 Available capacity

Di 3000 2500 5000Pi 200 230 250ai1 6 7 8 W1 120,000ai2 5 9 10 W2 100,000ai3 2 2 2 W3 50,000ai4 1 1 2 W4 40,000

li1 5 5 5li2 6 7 8

di3 2 2 2 T3 900si3 10 10 30di4 10 10 20 T4 18,000si4 4 4 8di5 2 2 4 T5 3000si5 5 5 10ri6 20 10 20 V6 55

$120,000

40,000

$195,000 vi 2 1 13 14,000$30/ton

Production 57 (2013) 178e187a3 u3 0

a0 a1 a2 a3 1

u1 u2 u3 1Batch-level inventory handling activity constraints:

X1 10B13 0

X2 10B23 0

X3 30B33 0

2B13 2B23 2B33 900;Batch-level carbon adsorption activity constraints:

X1 4B14 0

X2 4B24 0

X3 8B34 0

10B14 10B24 20B34 18;000;Batch-level setup activity constraints:

X1 5B15 0

problem by utilizing the software, LINGO 13.0, and obtain thefollowing optimal solutions.

X1 3000 X2 0 X3 4000q0 0 q1 0 q2 1m0 0 m1 0 m2 1h1 0 h2 1 R0 0R1 1 R2 0 R3 1a1 1 a2 0 a3 0u1 1 u2 0 u3 0B13 300 B23 0 B33 134B14 750 B24 0 B34 500B 600 B 0 B 400

anerdepartment to provide cost data for direct materials, and the ac-counting department to provide information on unit-level, batch-According to the results, the optimal quantity of green product-mix is (X1, X2, X3) (3000, 0, 4000), which requires 50,000 units(6 3000 7 0 8 4000) of the rst kind of material, 55,000units (5 3000 9 0 10 4000) of the second kind ofmaterial, 14,000 units (2 3000 2 0 2 4000) of the thirdkind of material, 35,000 (5 3000 5 0 5 4000) machinehours, 50,000 (6 3000 7 0 8 4000) direct labor hours,and 10,000 (2 3000 1 0 1 4000) VOC emissionsquantities. The total prot p is $52,200. This means that the ma-chine capacity does not exceed 40,000 h or that the company has torent machines, that the direct labor capacity is equal to 50,000 la-bor hours and that the VOC emissions are equal to 10,000 tons ofemission quantity which is in the upper limit of the rst range ofVOC emission cost function.

Company A has adopted ABC. Therefore, some related ABC datacan be obtained directly from the accounting department of Com-pany A. We can also ask about the related business units to providerelated data required in the product-mix decision models. Forexample, we can ask the production department to provide infor-mation concerning maximum demand, the sales department toprovide information concerning selling price, the purchasing

15 25 35X2 5B25 0

X3 10B35 0

2B15 2B25 4B35 3000;Product-level constraints:

X1 3000R1 0

X2 2500R2 0

X3 5000R3 0

20R1 10R2 20R3 55

Xi 0; i 1;2;3

Bij 0; i 1;2;3; j 3;4;5;(h1, h2), (q0, q1, q2), (u1, u2, u3): SOS1 set of 0e1 variables.h1, h2, R1, R2, R3, q0, q1, q2, u1, u2, u3: 0e1 variables.This is amixed-integer programming (MIP)model.We solve this

W.-H. Tsai et al. / Journal of Clelevel, product-level and facility-level activity costs obtained fromthe ABC study. As for the Environmental Regulatory cost and VOCemissions, we can invite the HSE management department toprovide information, and can also ask the human resourcesdepartment to provide related direct labor cost information.However, the most direct, and fastest, method is to invite the de-cision maker to request business units to submit related data to theaccounting department for collection, and then provide this infor-mation for the study.

In addition, VOCs can also be obtained from the emission costanalysis of the government unit or the company. Furthermore,additional overtime situations and related operation activities,caused by production capacity expansion, can also be provided bythe production department of Company A.

Using the TOC procedure, the constraints are identied and usedso that new GMTs are used most protably. Company A is able tochoose products that produce the least amount of VOC emissionssince the TOC approach fosters the selection of optimal product-mix, which emits fewer VOC emissions. In effect, when theoptimal product-mix is chosen, the output volumes of product 2 arezero. This means that there is an unsatised demand for product 2in the market, and Company A may increase the price of product 2to reect its environmental costs. Although investments in newGMTs can be very expensive, by adopting the TOC procedure, asound environmental investment by Company A can maximizetheir prots.

5. Discussion

It seems that the model proposed in this paper will select aproduct mix with higher pollution with the only objective ofmaximizing the prot of a product mix based on the most con-strained resources. Although themodel does not explicitly select anoptimal product mix that emits fewer VOC emissions, we can usethe related constraints to restrain VOC emission quantity withincertain limits. As a matter of fact, it is impractical to aim to mini-mize VOC emission quantity or cost. Alternatively, we can set up agoal programming model to maximize the operating prot, tominimize deviation from the VOC emission quantity target, andmeet other objectives. In the numerical example presented inSection 4, it was assumed that the total VOC emissions cost functionwould be a piecewise linear function. The unit cost for VOC emis-sions (i.e. tax rate) will increase with increasing VOC emissionsfrom $10/ton, $20/ton to $30/ton within the different ranges ofemission quantity [0,10,000], [10,000,12,500] and [12,500,14,000],respectively. This constraint will restrain the product-mix solutionto emit the VOCs within the upper limit of the rst range. Other-wise, the tax rate will increase double. Managers may want tosearch for new GMTs with fewer VOC emissions from the top coatspray processes to simultaneously increase operating prots and tomaintain corporate social responsibility.

6. Conclusion

In this paper, we considered the capacity expansions for ma-chine hours and direct labor hours. We also used piecewise andstepwise linear functions to approximate the non-linear direct la-bor costs and machine costs. Specically, we further extended thepiecewise linear function to quantize the VOC emissions so that wecould depict the total VOC emissions cost function, which in turnhelps to build a product-mix model using the green, multi-productprimer-topcoat system under ABC. Limited by cost considerations,the prots combination also undergoes certain changes along withadjustment, such that a maximum prot combination is calculatedaccording to the conditions. Compared with early scholars andearly articles that only use gures for description, such as Kee

Production 57 (2013) 178e187 185(1995), this study has explored a detailed mathematical

uating the product-mix decision. Future research may attempt toextend these techniques to different industries and diverse activ-

tives to make the model more realistic.

nerAcknowledgment

We would like to thank the National Science Council of Taiwanfor nancially supporting this research under Grant No. NSC100-2410-H-008-007-MY3.

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A product-mix decision model using green manufacturing technologies under activity-based costing1 Introduction2 Background2.1 Activity-based costing (ABC)2.2 The theory of constraints (TOC)2.3 Priming and top coating processes and activities in the automotive industry2.4 Product-mix decision model with capacity expansions

3 A mathematical programming model3.1 Integrated cost models

4 Numerical example5 Discussion6 ConclusionAcknowledgmentReferences