Which utilization and service level lead to the maximum EVA?

Int. J. Production Economics 130 (2011) 16–26

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Which utilization and service level lead to the maximum EVA? Klaus Altendorfer n, Herbert Jodlbauer Upper Austrian University of Applied Sciences, Department of Operations Management, Wehrgrabengasse 1-3, A-4400 Steyr, Austria

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 November 2008 Accepted 7 October 2010 Available online 20 October 2010

In this paper a model for evaluating the influence of utilization, WIP, FGI, service level and production lead time on EVA (economic value added) is developed in order to link the available logistical key figures with a market perspective and discuss their influence on company value. The question answered in this paper is: What is the optimal utilization and service level of a production system in order to achieve the maximum possible EVA for a company? A single-product, single-machine, make-to-order production system with investment dependent machine capacity is modeled. The model combines a market share concept based on delivery/production lead time and service level with concepts describing the logistical relationships between WIP, utilization, production lead time and service level. In addition to the explanatory use of the model, it can provide support for strategic decisions concerning investing or divesting machinery. The main application of this model is in describing the link between capacity investment and company value comprehensively based on data available from cost accounting in real companies. Furthermore, this paper shows that high flexibility of personnel and machine capacity increases the maximum possible EVA of production systems even if this flexibility is linked to additional costs. & 2010 Elsevier B.V. All rights reserved.

Keywords: Make-to-order Economic value added Utilization Service level Production lead time

1. Introduction In the competitive environment in which manufacturing companies do business nowadays, one of the most important prerequisites of success is to keep the customers satisfied (Lambert and Pohlen, 2001; Cooper, 1993). If customer satisfaction is measured as the logistical performance of a company, assuming a constant product quality and make-to-order (MTO) production, this logistical performance is mainly dependent on promised delivery lead time and service level (Hegedus and Hopp, 2001; Ho and Zheng, 2004). In order to keep the capital employed low it is important to maintain a high utilization, which leads to low production costs per unit. Furthermore, the work in process (WIP) and the finished goods inventory (FGI) should be as low as possible in order to keep capital costs at a low level. Concerning logistical key figures there are, according to Hopp and Spearman (1996), three conflicting objectives of a manufacturing company these being high utilization, low inventory, and high service level. In this paper an additional objective of a manufacturing company, which is also discussed by Hegedus and Hopp (2001) and Ho and Zheng (2004), will be considered. This is short promised delivery lead time, which is defined as time span from request date to promised due date. Since these targets conflict with each other it

n

Corresponding author. Tel.: +43 7252 884 3150; fax: + 43 7252 884 3199. E-mail addresses: [email protected] (K. Altendorfer), [email protected] (H. Jodlbauer). 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.10.008

is necessary to find a compromise between short promised delivery lead time, low WIP and FGI, high utilization and a high service level (see also Raman and Kim, 2002 or Hopp and Spearman, 1996). There are many studies discussing one or more of these conflicts. For example Spearman et al. (1990) discuss how to reach a specified throughput with minimum WIP and introduce the constant work in process (CONWIP) methodology as a solution for this problem. Chang (1997) discusses job shop scheduling heuristics to balance the conflict between service level and mean lateness. Jodlbauer and Huber (2008) discuss different production planning methods under the aspect of WIP needed to achieve a specified service level. Koh and Bulfin (2004) discuss the influence of different production control strategies on the logistical key figure throughput as well as on operating costs (which are determined only by inventory holding costs) and net profit. In the research area of dispatching rules, Jones (1973) discusses their influence on utilization at a specified level of WIP and Schultz (1989) tries to determine a rule to minimize production lead time. However, all of these studies evaluate these figures as stand-alone variable which are not linked to the company value or to the market. From the inherent logistical relationships it is clear that the optimal utilization lies below 100% since production lead time reaches 1 otherwise (see e.g. Hopp and Spearman, 1996). The question answered in this paper is, given a certain cost structure, derived from the cost accounting of a company, what should the optimal utilization or equivalent capacity invested be? Furthermore, a topic directly linked to capacity investment is what the optimal service level should be (see Fischer et al., 2001), which is also answered.

K. Altendorfer, H. Jodlbauer / Int. J. Production Economics 130 (2011) 16–26

We assume a single-machine single-product MTO production system. The strength of the model developed in this paper is that optimal utilization and service level targets can be identified based on a certain cost structure known from the cost accounting and based on certain market assumptions derived from the sales department. Additionally, the influence on the EVA of the variation of WIP, which stems from the production system, and the variation of demand, which stems from market behavior, is discussed. The remainder of the paper is structured as follows. The relevant literature is reviewed in Section 2. The model comprehensively describing the composition of EVA with respect to the logistical key figures is introduced in Section 3. A numerical example is presented in Section 4 and we conclude in Section 5.

2. Literature review 2.1. Evaluation of investments One objective of this paper is to generate a framework which is practical applicable and can be intuitively understood by management. For this reason the Balanced Score Card by Kaplan and Norton (1996), the return on investment (ROI) and its decomposition in the DuPont system, which is described by Plewa and Friedlob (1996) and applied by Li et al. (2008), for example, in a manufacturing context, as well as the net present value (NPV) concept, discounted cash flow (DCF) concept, and the economic value added (EVA) concept have been reviewed. For the current application, the EVA concept, which was first presented by Stewart (1991) and is often also called economic profit plans (see Dutta and Reichelstein, 2005), seems to be the most appropriate one. It offers a holistic view of the evaluation of investments and has a nicely applicable decomposition structure which can be applied to identify the influence of single logistical key performance indicators on company value. It is applied by Lambert and Pohlen (2001), for example, for the performance evaluation of a supply chain and by Schnetzler et al. (2007) to break the goals of a company down to an operational level. 2.2. Logistical relationships The link between capacity available, and for this reason utilization, and service level is covered in Paraskevopoulos et al. (1991), Mapes (1993), Nyhuis and Wiendahl (2002), Yu (2001), Nieuwenhuyse et al. (2007), Lutz et al. (2003) as well as Jodlbauer (2008b) all of which show that an increase in capacity leads to an increase in service level either for make-to-stock (MTS) or for MTO production systems. The concept applied in this paper is the one presented in Jodlbauer (2008b) based on a capacity service level since it also includes the influence of random due dates. The relationship between utilization and WIP, a linear increase in utilization leads to a strictly convex increase in WIP, is shown in Medhi (1991), Hopp and Spearman (1996), Nyhuis and Wiendahl (2002), and Jodlbauer (2008a). In the concept of Jodlbauer (2008a), the function is based on the coefficient of variation of WIP which is easily observable in real production systems; this concept is applied in this study. The logistical principle that there is an inherent relationship between average production lead time, average WIP, and average throughput of a system is discussed in Little (1961), Souza et al. (2001), Hopp and Spearman (1996), Jodlbauer (2008a), and Nyhuis and Wiendahl (2002). 2.3. Market relationships A dependency of market share on the company performance (utility of the provided service to the customer) is described in

17

Cooper (1993) as well as Lilien et al. (1992) which introduce the multinomial logit concept. For example Ho and Zheng (2004) and Li and Lee (1994) apply this concept, which is also used in this paper, in a manufacturing context. Ho and Zheng (2004) use the multinomial logit concept with the satisfaction factors delivery lead time and service level, which are nearly equal to the logistical performance definition in this study. Also Bertrand and van Ooijen (2008) use the idea that longer lead times lead to higher costs, i.e. a lower customer utility, in their model optimizing the quoted lead time and WIP level in a CONWIP system. 2.4. Related studies concerning evaluation of logistical performance Some similar studies have already been performed by Lederer and Li (1997) which describe a method for calculating the profit of companies based on production rate and scheduling policies for different customer groups. This calculation is based on different production costs and different delivery lead times depending on the production rates. The delivery lead time is assumed to be negatively correlated to the prices, which leads to different profits for the companies with different delivery lead times. Some general strategies for firms are presented in their study but capital costs as well as service level costs are not included. Coelli et al. (2002) study the profit lost due to unused capacity taking into account the maximum possible capacity depending on fixed and variable input factors. This study does not consider topics like service level decrease or production lead time increase at higher capacity utilization. Zhang et al. (2004) describe a model for capacity extension in a multi-machine, multi-product production system without FGI but with lost sales. Investments are considered as well as demand uncertainty. The presented mathematical model provides a capacity plan minimizing total cost. Zhang et al. (2004) base their study on an operational time horizon and discuss the lost sales in the short run but do not consider the long term impact of production lead time and service level. A profit maximization problem including capacity costs and inventory costs based on a known production plan for aggregated product groups is set up in ¨ Zapfel (1998). Ballou (2006) states that the procedure of defining target values for logistical key figures like service level as well as production lead time, and then minimizing costs to reach these values lead to sub-optimal results. Raman and Kim (2002) study the influence of holding costs and flexible capacity of an apparel manufacturer. They conclude that an increase in capacity can reduce the working capital, and for this reason WIP and FGI, as well as costs for markdown and stockouts. Jodlbauer and Altendorfer (2010) describe the trade-off between capacity invested and inventory needed. They do not include the market share perspective.

3. Model development A model to describe the relationship between utilization, WIP, FGI, service level, production lead time, and EVA in a long-term equilibrium is introduced in this section. Five different concepts from literature are combined in this model. To integrate the market behavior the multinomial logit market concept from Cooper (1993) is adapted. In this multinomial logit market concept the maximum market volume is constant and the market share of an individual firm depends on the utility provided. The concept will be adapted to include production lead time and service level, see Section 3.4. Based on a constant coefficient of variation of demand and the mean value of demand derived from the market share the reachable service level is calculated depending on the average FGI. This is

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achieved by the application of the customer driven production planning concept presented in Jodlbauer (2008b). Within the model, the target utilization is predefined. Based on this predefined utilization the WIP needed to reach it is calculated according to the logistical key figure concept of Jodlbauer (2008a). In this logistical key figure concept the coefficient of variation of WIP leads, based on target utilization, to the average WIP needed. The sum of average WIP and average FGI combined with average throughput, which is equal to demand, lead to the average production lead time by using Little’s Law (see Little, 1961). The capital employed depends on the average WIP, the average FGI and the machining capacity available, which depends on target utilization and demand. According to this capital employed as well as some other cost and product price parameters the company value added will be calculated applying the EVA concept by Stewart (1991). The following figure shows the modeled production system and demonstrates how the concepts are related to each other (Fig. 1). The result will be a function for EVA with respect to utilization and service level which can only be evaluated numerically. An optimization problem is set up to determine which utilization and service level leads to the maximum EVA. All variables used are summarized in Appendix A. The following assumptions are made:

 In the current study a single-product single machinery type

  



 

production system will be discussed. The capacity of machinery is assumed to be investment dependent, which could be explained by having a group of equal machines. No setup times are taken into account and the average processing time for the product is constant over time. The pricing of one capacity unit of available machine capacity is different to the pricing of one capacity unit of available personnel capacity. Personnel capacity is assumed to be available at the level of maximum available machine capacity to be able to handle demand peaks. This assumption is consistent with Jodlbauer (2008b). No special production control strategy is modeled but all the influences from production control and the shop floor environment like machinery availability or deviation of single processing times are incorporated by the coefficient of variation of WIP. The market is modeled as mean demand and coefficient of variation of demand. The model is based on long-term equilibrium in the production and the market, which leads to equilibrium between the different figures of average utilization, average lead time,



  

average inventory, average service level, average market share, and EVA. Since interest for capital employed is also included in the model, the surveyed time interval is assumed to be a year. The N single periods of the time interval could be considered to be the days of the year. The calendar of production time, sales time, and interest rate time are set to be equal. All coefficients of variation are based on fluctuations occurring per period. The raw materials are assumed to be always available and no specific cash to cash cycle investigations are made.

3.1. Decomposition of EVA to logistical key figure influence In the current model the EVA, which is a widely used performance indicator in finance and decision sciences, is used to calculate the company value added related to the logistical key figures WIP, FGI, service level, production lead time, and capacity invested. Taxes, accruals, and other values from the financial statements not relevant for this study are neglected in the adapted concept from Stewart (1991) since they are not much influenced by the logistical relationships discussed in the current paper and they can vary greatly between companies and countries. The following directions of the influences of logistical key figures on the EVA can be stated:

 a lower inventory value leads to a lower capital employed and for this reason to lower cost of capital, which increases the EVA;

 a higher utilization leads to a lower capital employed in machinery and therefore to a higher EVA;

 the higher the utilization, the higher the WIP which is needed to





reach this utilization and the FGI needed to still keep the service level high will also be; this leads to more capital employed and for this reason to a reduction in EVA; according to the multinomial logit concept a shorter delivery lead time (here production lead time), which is dependent on the inventory, leads to a higher market share and more sales thus increasing EVA; according to the multinomial logit concept a higher service level leads to a higher market share and more sales thus increasing the EVA.

Since the calculation for the surveyed time interval is forward looking the result is an expected value for the EVA and its components. This will be omitted in further calculation. According

Logistical key figure concept for relationship between WIP and utilization

WIP

Machine

FGI

Customer driven production planning concept for relationship between utilization, FGI and service level Little’s Law for the relationship between WIP, FGI and production leadtime

Fig. 1. Model framework.

Market demand

Multinomial logit concept for relationship between service level, production leadtime and demand (market share)

Company Value

EVA concept to evaluate the investments in machining and inventory as well as the generated revenue for their impact on company value

K. Altendorfer, H. Jodlbauer / Int. J. Production Economics 130 (2011) 16–26

to Stewart (1991), the EVA e is the net operating profit after tax p minus the cost of capital cc needed to create this net operating profit after tax: e ¼ pcc

ð1Þ

3.1.1. Calculation of the net operating profit after tax The net operating profit after tax p is the revenue SI (as average sales per period S times price I) minus the average operating costs co times N periods in the survey time interval: p ¼ NðSIco Þ

ð2Þ

The average operating costs within one period co consist of depreciation of the machinery within one period cd, average additional variable costs for processing time within one period cv, average personnel costs within one period cp, and average material costs within one period cm: co ¼ cd þ cv þ cp þ cm

ð3Þ

The depreciation of the machinery cd depends on the average book value of machinery. The depreciation for one capacity unit of processing time cum is the depreciation of machinery cd divided by the average number of capacity units used during one period H: cum ¼

cd H

ð4Þ

The average number of capacity units used during one period H can be calculated depending on the targeted average utilization u, on the average sales per period S, and on the machine capacity needed to produce one piece Tm as follows: STm H¼ u

ð5Þ

Furthermore the depreciation for one product produced D is calculated depending on the machine capacity needed Tm, the depreciation for one capacity unit of processing time cum, and the targeted average utilization u: D ¼ cum

Tm u

ð6Þ

Combining (5) and (6) with (4) the following relationship between average sales per period S and depreciation for one product produced D can be derived: cd ¼ SD

ð7Þ

The fixed assets (average book value of machinery) aa can be calculated based on depreciation of machinery within one period cd, its economic life L and the number of periods within the surveyed time interval N. Under the assumption of linear depreciation and continuous reinvestment in machinery the following equation holds true (see also Rajan et al., 2007 for book values in reinvestment situations): c L aa ¼ N d 2

ð8Þ

The average additional variable costs for processing time within one period cv depend on the average sales per period S and the additional variable cost per piece Cv which could be tooling, energy, or runtime dependent maintenance and are not included in the personnel or material costs: cv ¼ SCv

ð9Þ

The average personnel costs within one period cp depend on the average sales per period S and the personnel cost of one product produced Cp: cp ¼ SCp

ð10Þ

19

The average material costs within one period cm depend on the average sales per period S and the material costs per piece Cm: cm ¼ SCm

ð11Þ

By means of (7), (9), (10), (11), and (3) the average operating costs within one period co can be calculated. 3.1.2. Calculation of the cost of capital The cost of capital within one period cc depends on the capital employed a within the production system and on the interest rate based on the weighted average cost of capital (WACC) iwacc calculated according to the capital asset pricing model (CAPM): cc ¼ aiwacc

ð12Þ

The interest rate based on the WACC iwacc depends on the shareholder equity m and on the desired return for this shareholder equity im as well as on the interest bearing liability b and the interest rate paid for borrowed capital ib. Neglecting the effect of tax and accounts receivable versus short term liabilities, the following equation for the interest rate based on the WACC iwacc can be derived from Miles and Ezzell (1980): iwacc ¼

mim þ bib a

ð13Þ

The capital employed a equals on the one hand the shareholder equity m plus the interest bearing liability b (non-interest bearing liability is not included in the calculation) and on the other hand the current assets aw plus the fixed assets (average book value of machinery) aa: a ¼ m þb ¼ aw þ aa

ð14Þ

The fixed assets (average book value of machinery) aa are calculated according to Eq. (8). The current assets aw can be calculated as the sum of the average value of WIP kw as well as the average value of FGI kf: aw ¼ kw þ kf

ð15Þ

According to throughput accounting (Corbett, 1998), it is assumed that the average value of WIP kw is only based on the material costs for one product Cm and the average WIP in pieces W but not on the value added: kw ¼ WCm

ð16Þ

The average value of FGI kf depends on the average FGI in pieces G, on the material costs per piece Cm, and on the value added during the production step V: kf ¼ GðCm þVÞ

ð17Þ

The value added during the production step V consists of the personnel cost of one product produced Cp, the additional variable cost per piece Cv, and the depreciation for one product produced D: V ¼ D þCp þCv

ð18Þ

To calculate the personnel cost of one product produced Cp it is necessary to detail the machine capacity assumptions first. The following chart visualizes which capacities are used in the current paper (Fig. 2). Based on the average machinery availability, the average available capacity is assumed to be 100%. Since this average utilizable capacity includes some scheduled maintenance and there is usually some flexibility to increase the capacity output for a short period of time the factor fo for the maximum available capacity is introduced. To enable this maximum available capacity, the personnel also have to be available for this time. On average the machinery is utilized with the average target utilization u in this paper.

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target utilization. Thirdly, the delta between the interest for shareholder equity and the interest for borrowed capital is added (could also be negative for lower equity capital costs). This value does not depend on the overall capital employed. Whether the interest rate for borrowed capital or for shareholder equity is higher has only marginal influence on the behavior of the model.

1.6 1.4

capacity

1.2

maximum available capacity (fo) average available capacity

1

average capacity used (u)

0.8 0.6

3.2. Logistical key figure concept and Little’s Law

0.4 0.2 0 2

0

4 6 8 time in periods [d]

average available capacity average capacity used

10

12

maximum available capacity current capacity needed

Fig. 2. Capacity assumptions.

The personnel cost of one product produced Cp depends on the machine capacity needed for one piece Tm, on the average target utilization u, on the relation factor between maximum capacity available on average and maximum capacity available due to flexibilities fo, and on the personnel cost of one capacity unit cup: Cp ¼ fo

Tm cup u

ð19Þ

The additional variable cost per piece Cv depends on the machine capacity needed for one piece Tm and on the additional variable costs for one capacity unit of machinery. This cost is for tooling, energy, or runtime dependent maintenance: Cv ¼ Tm cuv

ð20Þ

With Eqs. (12), (13), and (15) to (20) the cost of capital can be calculated. 3.1.3. Decomposition of the EVA on the input data The capital employed can be calculated from (8), and (14) to (17): c L a ¼ WCm þ GðCm þ VÞ þN d 2 which leads to the capital costs from (12) and (13):   c L cc ¼ mðim ib Þ þ WCm þGðCm þ VÞ þ N d ib 2

ð21Þ

ð22Þ

The operational costs can be calculated from (3) to (11) as co ¼ SðD þCp þCm þ Cv Þ and so the EVA is yielded as (with (19) and (20))    cum þ fo cup mðim ib Þ e ¼ NS ICm Tm cuv þ u      cum þfo cup cum Tm L ib þ NS  WCm þG Cm þ Tm cuv þ 2u u

ð23Þ

ð24Þ

Among the input data for Eq. (24) two groups can be distinguished. Parameters which are preset and assumed to remain constant (do not depend on the logistical relationships) and variables which are influenced by the logistical relationships discussed in this paper. The variables are average WIP in pieces W, average FGI in pieces G, average target utilization u and average sales per period S. The EVA decomposed to the input parameters and variables shows three different parts. Firstly the money inflow from the operation is calculated based on the average demand, the material costs, the personnel costs, and the variable costs. Secondly the interest that would be paid if all capital employed were borrowed is subtracted. This capital employed depends on the production costs of products, the WIP in pieces, the FGI in pieces, and the average

The logistical key figure concept of Jodlbauer (2008a) is applied to generate the link between utilization and WIP depending on the coefficient of variation of WIP. For the developed model the coefficient of variation is assumed to be a constant parameter. The following equation from Jodlbauer (2008a) gives an implicit function for the WIP in machining capacity units depending on the preset utilization: Z Tm 1 wðuÞ : u ¼ 1 Fðw, ðwaw Þ2 Þ ðtÞ dt Tm 0 wðuÞ WðuÞ ¼ ð25Þ Tm The average WIP in capacity units is denoted w, aw is the coefficient of variation of WIP in capacity units based on periods, and Fðw,ðwaw Þ2 Þ ðUÞ denotes the cumulative distribution function (cdf) of the WIP in capacity units based on periods. To solve this implicit equation (25) for WIP, a Newton method is used in the current model. For Fðw,ðwaw Þ2 Þ ðUÞ a lognormal distribution is assumed, since the WIP has to be a positive value and Jodlbauer (2008a) also argues for this distribution. Applying Little’s Law (see Little, 1961) leads to the average production lead time d depending on the WIP plus FGI in our model whereby the average sales per period S represent the throughput: dðG,W,SÞ ¼

GþW S

ð26Þ

Note that usually one could split up production lead time and FGI lead time (see Altendorfer and Jodlbauer, forthcoming), but both values are together referenced as production lead time in this model for simplicity reasons. 3.3. Customer driven production planning concept Depending on the variance in customer demand and on the capacities available, Jodlbauer (2008b) presents a function for a capacity oriented service level, which is applied in this paper and referred to as customer driven production planning concept. This is the probability that the capacity needed within more than one period of time is lower than the maximum available capacity in this number of periods. The service level is   STm sðu,SÞ ¼ FðSTm ,ðSTm ac Þ2 =fwaw Þ fo ð27Þ u Jodlbauer (2008b) applies a work ahead window work release policy with parameter fwaw based on ac being the coefficient of variation in capacity demand per period. The demand is assumed to be normally distributed since the capacity demand can be assumed to be the sum of multiple arbitrary distributions of single customer demands. Furthermore, in Bish et al. (2005) the applicability of the normal distribution is proposed because the probability of negative values is assumed to be negligible and only the right tail of the distribution function is used. Jodlbauer (2008b) shows that an increase in the work ahead window fwaw leads to an increase in the average FGI: fwaw ¼

G S

ð28Þ

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So the service level s can be calculated with a predefined average FGI in pieces G. 3.4. Multinomial logit concept In addition to the logistical relationships between utilization, WIP, FGI, production lead time, and service level, the market point of view is integrated by an evaluation of customer satisfaction or customer utility generated from the variables service level and production lead time. The multinomial logit concept is widely used (see Cooper, 1993; Lilien et al., 1992) and also Ho and Zheng (2004) apply an adapted version for a similar manufacturing context. The market share fs can be calculated as follows: expðb0 bL d þ bS sÞ fs ðd,sÞ ¼ expðb0 bL d þ bS sÞ þA Sðd,sÞ ¼ Sm fs ðd,sÞ

ð29Þ

b0, bl, and bs are parameterization variables describing the inherent utility of the product, the production lead time, and the service level, respectively. A describes the utility provided by the competitors in the market and Sm the whole market size in pieces per period. Eq. (29) shows that in our model the production lead time is included as a utility driver, whereas a comparison to Ho and Zheng (2004) shows that they apply the delivery lead time instead. Since in MTO production systems delivery lead time can be defined as production lead time plus an order preparation time, a linear relationship between production lead time and delivery lead time is assumed. For parsimonious modeling reasons no further parameter is introduced for this relationship since the qualitative behavior of Eq. (29) would not change. 3.5. Merging of the concepts—model generation Since some of Eqs. (25)–(29) explicitly define the relationships needed and others implicitly define them, the EVA can be written as a function of WIP, FGI, average sales, and service level, i.e. eðSðdðG,W,SÞ,sÞ,WðuÞ,GðsÞ,uÞ, which can numerically be reduced to a function depending on service level and utilization (eðs,uÞ). Fig. 3 shows how the concepts and variables are combined to reach this form of the EVA calculation. Furthermore, the additional parameters needed to integrate the different concepts to calculate the EVA value in the developed model are presented in Fig. 3. The link Parameters needed for WIP calculation: Tm, αw

Logistical key figure concept W(u)

Parameters needed for Service level calculation: Tm, f0, αc

Customer driven production planning concept s(S, G, u)

Parameters needed for FGI calculation: Tm

Little’s Law d(S, W, G)

Parameters needed for market share calculation: A, β0, βl, βs, Sm

Mulitnomial logit concept S(d, s)

21

between the parameters needed and the real company data is discussed in the next section. Applying Eqs. (24)–(29) leads to the following optimization problem which can numerically be solved and answers the research question stated: eðu,sÞ-max

ð30Þ

u,s

The influence of cost parameter changes, variation changes, and market sensitivity changes can also be discussed with the model to provide a comprehensive tool for evaluating the utilization and service level target for certain product groups.

4. Company data link to parameterization variables for practical application In this section the link between data available in companies and the parameters needed to calculate the presented model is provided. Especially the typical cost accounting data of a company is linked to the financial parameterization variables and the demand and production system information is linked to the logistical parameters needed. 4.1. Financial parameters The depreciation cost for one capacity unit of machinery cum is equal to the (current) investment cost of a single machine divided by the economic life of the machinery (in years) and the maximum possible units of capacity provided per year. The economic life of the machinery (in years) L is the time in years how long a machine can be utilized based on technology and on wear-down effects; it is usually available in cost accounting systems. The cost for one capacity unit of personnel cup is usually available in cost accounting systems or can be calculated as yearly gross wages for production employees (including all taxes) divided by the yearly working time (corrected by weekends, holidays, illness). The additional cost for one capacity unit of machinery cuv can either be found in a cost accounting system or it can be approximated as the sum of energy cost, tooling costs, and maintenance costs for one machine per year divided by the capacity units provided by this machine within the respective year. im and ib have to be defined by the finance department. Since these interest rates are often necessary to evaluate investments, they are available in most companies.

Additional Parameters needed for EVA calculation: N, I, Cm, m, im, ib, l, cum, cuv, cup,

EVA concept e(s, u)

Variables changed within optimization: s, u

Fig. 3. Logistical relationships and EVA.

Optimization value EVA max

22

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The material costs Cm can also be found in the cost accounting system or they can be calculated as the sum of all purchasing costs for the raw materials needed to produce one finished product. The price I and the shareholder equity m can be taken from sales and the balance sheet, respectively.

4.2. Logistics parameters The coefficient of variation of WIP aw (measured in capacity units) can be calculated based on historic data from the enterprise resource planning (ERP) system whereby the mean and variance of current WIP in capacity units is observed for a period of, for example, a year. This current WIP in capacity units is for each period calculated as the pieces released but not yet finished multiplied by their respective capacity demand. The coefficient of variation of capacity demand ac can also be calculated based on historic data from the ERP system. Analogues to aw, here the products ordered are accounted at their respective due date and multiplied with the capacity demand per product (for details on this see also Jodlbauer, 2008b). The machine capacity needed to produce one piece Tm clearly has to be known either from a cost accounting system or from the technical specifications of a product. The number of periods evaluated N can either be 365 to account for one year or the working days from the working calendar of the company e.g. 220 days (365 minus weekends and holidays).

4.3. Market parameters

5. Numerical example A numerical example of the application of the developed model is presented in this section. The curves for optimal utilization and optimal service level are calculated based on an example data set to describe their shape and some managerial implications of that. Furthermore, a sensitivity analysis concerning the parameters coefficient of variation of WIP, coefficient of variation of capacity demand, and an increase in capacity flexibility is provided. The following parameter set, which leads to a 20% market share with an average service level of 95% and an average production lead time of 20 periods, is tested: A ¼ 162, ac ¼ 1, aw ¼ 3, b0 ¼ 2, bL ¼ 0:01, bs ¼ 2, cum ¼ 30, cup ¼ 30, cuv ¼ 20, fo ¼ 1:1, ib ¼ 0:12, im ¼ 0:15, L ¼ 8, m ¼ 10,000, N ¼ 365, Sm ¼ 60, I ¼ 84, Cm ¼ 62, and Tm ¼ 0:1. The distribution of WIP is assumed to be lognormal and the distribution of customer demand is normally distributed. 5.1. Optimal utilization and service level Optimizing problem (30) only for service level and predefining the utilization leads to Fig. 4a. When only utilization is optimized and service level is predefined, Fig. 4b is generated. Fig. 4c shows the trajectory between service level and utilization under maximum EVA whereby the service level is optimized for a predefined utilization. For the test case, the maximum EVA can be reached with a utilization of 78% and a service level of 94%. As shown in Fig. 4a and b, there is a relatively broad range of utilization values but a relatively small range of service level values to achieve nearly the maximum EVA. Fig. 4b shows that service levels of nearly 100% are expensive to maintain and not optimal for this reason. Additionally, Fig. 4b indicates that a service level which

EVA [cu]

50000 45000 optimal point (max EVA) 40000 35000 30000 25000 20000 15000 10000 5000 0 40% 50% 60% 70% 80% utilization

service level

EVA [cu]

The market parameters cannot directly be derived from cost accounting or balance sheet data. Details on the parameterization of the multinomial logit concept can be found in Lilien et al. (1992). However, a simple strategy can be to identify certain market shares

from the sales department under certain service level and production lead time conditions to generate values for A, b0 , bL , bs , and Sm.

90%

100%

50000 45000 optimal point (max EVA) 40000 35000 30000 25000 20000 15000 10000 5000 0 70% 80% 90% 60% service level

1 current situation 0.9 optimal point (max EVA) 0.8 increase capacity 0.7 0.6 decrease FGI 0.5 0.4 0.3 0.2 0.1 0 40% 50% 60% 70% 90% 100% 80% utilization Fig. 4. Optimal utilization and service level.

100%

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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

utilization

optimal point (max EVA)

working point of production systems according Wiendahl

service level when EVA is maximized

0

1000

2000 WIP [cu]

3000

4000

Fig. 5. Service level versus WIP.

or some other capital intensive production facilities is considerably lower than that of companies with lower utilization. The trajectory can additionally be used to identify two improvement strategies when a production system finds its position to not be optimal. Especially when either service level or utilization are predefined as strategic decision, a target value for capacity or inventory can be identified by moving towards the trajectory. In the example provided in Fig. 4c this can be achieved by increasing capacity if service level is the strategic decision or decreasing FGI if utilization is the strategic decision. 5.2. Logistical key figures if EVA is maximized From the existing data, an interesting relationship between WIP (in cu) and the service level can be derived. This relationship, shown in Fig. 5, can be considered as an extension of the logistical relationships described by Hopp and Spearman (1996), Nyhuis and Wiendahl (2002), and Jodlbauer (2008a). The service level is linked to the existing logistical relationships based on a mathematical function with respect to maximum EVA. The information which can be derived from Fig. 5 is that in the studied combination of production system and market, the service level which leads to maximum EVA decreases fast with increasing WIP until a low service level is reached and approximately kept. This behavior as well as some further parameters for the market and the machines could also be examined in more detail in further research. According to Nyhuis and Wiendahl (2002), many production systems work with a high target utilization as denoted in Fig. 5 which leads to a gap between the high target value for service level and the optimal service level or between the high target value for utilization and the optimal utilization. To enable a better understanding of what happens within the production system when the utilization is increased, the WIP lead time as well as the FGI lead time are depicted separately and in combination in Fig. 6.

25

14 leadtime FGI [d]

leadtime WIP [d]

12 10 8 6 4 2

20 15

optimal point (max EVA)

10 5

optimal point (max EVA)

0 40%

50%

60%

70% 80% utilization

90%

100%

90%

100%

0 40%

50%

60%

25 leadtime WIP + FGI [d]

utilization / service level

is higher than the optimum reduces the EVA more than one which is lower by the same percentage. Relating these results to the success of concepts like World Class Manufacturing (see Schonberger, 1986), which propose to reduce utilization, shows that this model explains this utilization reduction as an attempt to maximize the EVA. Concerning the method of clustering customers and setting different service level targets (below 100%) as reported by Christopher (2005), this model again finds this service level reduction as an EVA maximizing behavior when done appropriately. The service level versus utilization trajectory provides the finding that a higher utilization requires a lower service level in the optimal case. This result confirms intuition since it seems obvious that a lower utilization leads to more flexibility for demand peaks and for this reason to lower inventories for the same service level. Furthermore, in real world companies it can be found that the service level of companies with a high utilization, like steel plants

20 15

23

optimal point (max EVA)

10 5 0 40%

50%

60%

70% 80% utilization

Fig. 6. Lead time versus utilization when EVA is maximized.

70% 80% utilization

90%

100%

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The WIP lead time (Fig. 6a) is independent of the EVA maximization and is a straightforward application of Jodlbauer (2008a). It is consistent with Hopp and Spearman (1996) as well as Nyhuis and Wiendahl (2002). The FGI lead time (Fig. 6b) increases to a peak and then drops down again. The peak in the graph is the point from which on it is cheaper to reduce the FGI than to try to maintain a high service level since capital costs and reduction of market share because of long production lead times become the dominant effects. This relationship is determined by the cost of capital, the market model evaluation, the production lead time, and the service level. Fig. 6c shows that the production lead time (sum of WIP and FGI lead time as defined in this paper) is dominated by the FGI part until the utilization reaches a level near 100% and then the WIP part dominates based on the limit for WIP being indefinite when utilization is 100%.

the customer demand is fluctuating much more than in the base situation. On the one hand, this has a major effect on the maximum EVA which reaches only a much lower level. On the other hand, the optimal utilization decreases to 73%. This decrease of utilization is needed to be able to react more flexibly to customers’ needs. An increase in the maximum capacity available in relation to the average capacity available fo (as shown in Fig. 7c), means that there is more capacity available for demand fluctuations, which is maintained by more personnel capacity. In the case of a 20% increase, as discussed in this sensitivity analysis, two effects occur:

 when the average utilization is low then the additional per

5.3. Sensitivity analysis

60%

70% 80% utilization

6. Conclusion Based on five different concepts describing logistical relationships and market behavior, a model to analyze what is the optimal

base situation

coefficient of variation of WIP

50%

The optimal utilization increases to 89%. This increase in maximum capacity available can be argued to be a result of personnel and machinery being more flexible. For a production system, the finding that with more flexible capacities higher target utilizations can be reached (when maximizing EVA) can be derived. This finding is consistent with the methodologies presented by concepts like World Class Manufacturing which propose to increase the flexibility of the workforce and adjust the capacity available to the capacity demand (Schonberger, 1986).

EVA

optimal point (max EVA) base situation

50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 40%

optimal point (max EVA) new situation

EVA

To improve the understanding of the developed model and the influence of the most important parameters, a sensitivity analysis for the parameters coefficient of variation of capacity demand ac, coefficient of variation of WIP aw, and maximum available capacity fo is conducted. Curves for maximum EVA with respect to utilization are compared. An increase of the WIP variation aw by 100%, which is discussed in the sensitivity analysis, could be caused by the production process being much less stable than in the base situation. As shown in Fig. 7a, this change has a very low effect on the maximum EVA as well as on the optimal utilization (which is 77% in this case in comparison to 78% in the base situation). This can be explained by the relatively low level of utilization which is optimal. An increase of the variation of the capacity needed ac by 100%, which is discussed in the sensitivity analysis (see Fig. 7b), means that

90%

100%

sonnel costs are dominant and the maximum EVA which can be reached is lower than in the base situation; at high levels of average utilization the increased ability to cope with demand fluctuations is dominant and for this reason the maximum EVA becomes even higher than in the base situation.

50000 45000 optimal point (max EVA) base situation base situation 40000 35000 optimal point (max EVA) new situation 30000 coefficient of 25000 variation of capacity demand doubled 20000 15000 10000 5000 0 50% 60% 70% 80% 90% 100% 40% utilization

EVA

maximum available capacity

increased by 20% (fo = 1, 3) 50000 optimal point (max EVA) new situation 45000 optimal point (max EVA) base situation 40000 35000 30000 base situation 25000 20000 15000 10000 5000 0 40% 50% 70% 80% 60% 90% 100% utilization

Fig. 7. Sensitivity analyses of the most important model parameters.

K. Altendorfer, H. Jodlbauer / Int. J. Production Economics 130 (2011) 16–26

Table A1

25

Table A1 (continued )

Symbol

Description

Symbol Description

Unit

cu pc h d

Currency unit (e.g. $ or h) Piece Capacity unit Period

L

1

Symbol Description

Unit

Financial variables a Capital employed aa Fixed assets (average book value of machinery) aw Current assets (average value of inventory) b Interest bearing liability cc Cost of capital within the evaluated time interval cd Depreciation of the machinery within one period cm Cm co cp Cp cum cup cuv cv Cv D e I ib im iwacc kf kw m p V

cu cu cu cu cu cu/ d Average material costs within one period cu/ d Material cost for one product produced cu/ pc Average operating costs within one period cu/ d Average personnel costs within one period cu/ d Personnel cost for one product produced cu/ pc Depreciation cost for one capacity unit of machinery cu/ h Cost of one capacity unit of personnel cu/ h Additional cost for one capacity unit of machinery (variable costs cu/ like energy, tooling or runtime dependent maintenance) h Average additional variable costs for processing (only when cu/ machine is running) within one period d Additional variable costs per piece (tooling, energy) cu/ pc Depreciation for one product produced cu/ pc Economic value added (EVA) within the surveyed time interval cu Money income per product (price) cu/ pc Interest rate which has to be paid for liability 1 Interest rate which has to be earned for the shareholder equity 1 Interest rate according to weighted average cost of capital 1 (WACC) Average value of finished goods inventory (FGI) cu Average value of work in process (WIP) cu Shareholder equity (money invested in the business) cu Net operating profit after tax within the evaluated time interval cu value added during the processing step cu

Market variables A Parameterization variable for the market share function describing the utility of the competitors in the market ac Coefficient of variation of capacity demand based on periods fs Market share (depending on the service level and production lead time) S Average number of products sold per period Sm

b0 bl bs

u w W

Average target utilization Average WIP in capacity units Average WIP in pieces

N s

d 1 h/ pc 1 h pc

utilization and service level for maximum EVA was developed for a one machinery type, single product MTO production system. Furthermore, a transformation list of cost parameters needed to calculate this model based on real company data is provided to ensure the applicability of the model. The logistical relationships between utilization, inventory, and production lead time have been extended by an EVA optimal service level. A numerical example shows that with such a holistic view on the production system, the optimal utilization should be rather low supporting concepts like World Class Manufacturing proposing to accept lower utilizations. Furthermore, the optimal service level is found to be considerably below 100%, supporting diversified service level targets in companies. One insight is that an increase in maximum possible personnel capacity in relation to the average available (machine) capacity implies that a higher average (machine) utilization becomes optimal for maximizing EVA. For management this means that it can be good to invest in the flexibility of the workforce without changing the average work time when machines are available. From the sensitivity analysis it is found that a decrease in demand fluctuation leads to an increase in EVA and a decrease in fluctuations on the shop floor (modeled as WIP fluctuation) also leads to an increase in EVA. Further research should be conducted on the logistical relationships including service level with respect to maximum EVA in a multi-machine system. Another field of further research is the integration of setup times, the extension of the model to a multiproduct surrounding, and the modeling of price elasticity.

Appendix A. Definition of variables 1 1 1

pc/ d Average sales of the whole market (all competitors) per period pc/ d Parameter for the market share function describing the inherent 1 utility of the product Parameter for the market share function describing the 1/d importance of production lead time for the customers Parameter for the market share function describing the 1 importance of service level for the customers

Production variables Coefficient of variation of WIP in capacity units based on periods d Average production lead time (WIP and FGI) fo Relationship factor between maximum available capacity and average available capacity (fo Z 1) fwaw Work ahead window resulting from FGI G Average FGI in pieces H Average number of capacity units for machining used during one period

aw

Tm

Economic life of the machinery (as a multiple of the evaluated time interval) Number of periods in the evaluated time interval Average service level of the production system in the evaluated time interval Machine capacity needed to produce one piece

1 d 1 d pc h/d

The following units are used. See Table A1 for the units used. References Altendorfer, K., Jodlbauer, H. An analytical model for service level and tardiness in a single machine MTO production system. International Journal of Production Research, doi:10.1080/00207541003660176. Ballou, R.H., 2006. Revenue estimation for logistics customer service offerings. International Journal of Logistics Management 17, 21–37. Bertrand, J.W.M., van Ooijen, H.P.G., 2008. Optimal work order release for make-toorder job shops with customer order lead-time costs, tardiness costs and work-in-process costs. International Journal of Production Economics 116, 233–241. Bish, E.K., Muriel, A., Biller, S., 2005. Managing flexible capacity in a make-to-order environment. Management Science 51, 167–180. Chang, F.-C.R., 1997. Heuristics for dynamic job shop scheduling with real time updated queuing time estimates. International Journal of Production Research 35 (3), 651–665. Christopher, M., 2005. Logistics and Supply Chain Management: Creating ValueAdding Networks. Prentice Hall, Harlow a. o,. Coelli, T., Grifell-Tatje´, E., Perelman, S., 2002. Capacity utilisation and profitability: a decomposition of short-run profit efficiency. International Journal of Production Economics 79, 261–278.

26

K. Altendorfer, H. Jodlbauer / Int. J. Production Economics 130 (2011) 16–26

Cooper, L.G., 1993. Market-share models. In: Eliashberg, J., Lilien, G.L. (Eds.), Marketing, Handbooks in Operations Research and Management Science, vol. 3. Amsterdam. Corbett, T., 1998. Throughput Accounting. Great Barrington. Dutta, S., Reichelstein, S., 2005. Accrual accounting for performance evaluation. Review of Accounting Studies 10, 527–552. Fischer, M., Herrmann, A., Huber, F., 2001. Return on Customer Satisfaction—Wie ¨ rentable sind Maßnahmen zur Steigerung der Zufriedenheit. Zeitschrift fur Betriebswirtschaft, Heft 10, 1161–1190. Hegedus, M.G., Hopp, W.J., 2001. Due date setting with supply constraints in systems using MRP. Computers and Industrial Engineering 39, 293–305. Ho, T.H., Zheng, Y.-S., 2004. Setting customer expectation in service delivery: an integrated marketing-operations perspective. Management Science 50, 479–488. Hopp, W.J., Spearman, M.L., 1996. Factory Physics—Foundations of Manufacturing Management. Irwin/McGraw-Hill, New York,. Jodlbauer, H., 2008a. A time continuous analytic production model for service level, WIP, lead-time and utilization. International Journal of Production Research 46, 1723–1744. Jodlbauer, H., 2008b. Customer driven production planning. International Journal of Production Economics 111, 793–801. Jodlbauer, H., Altendorfer, K., 2010. Trade-off between capacity invested and inventory needed. European Journal of Operational Research 203, 118–133. Jodlbauer, H., Huber, A., 2008. Service level performance of MRP, KANBAN, CONWIP and DBR due to parameter stability and environmental robustness. International Journal of Production Research 46, 2179–2195. Jones, C.H., 1973. An economic evaluation of job shop dispatching rules. Management Science 20 (3), 293–307. Kaplan, R.S., Norton, D.P., 1996. The Balanced Scorecard—Translating Strategy Into Action. Harvard Business Scholl Press, Boston,. Koh, S.-G., Bulfin, R.L., 2004. Comparison of DBR with CONWIP in an unbalanced production line with three stations. International Journal of Production Research 42 (2), 391–404. Lambert, D.M., Pohlen, T.L., 2001. Supply chain metrics. The International Journal of Logistics Management 12 (1), 1–19. Lederer, P.J., Li, L., 1997. Pricing, production, scheduling, and delivery-time competition. Operations Research 45, 407–421. Li, J., Min, K.J., Otake, T., Voorhis, T.V., 2008. Inventory and investment in setup and quality operations under Return on Investment optimization. European Journal of Operational Research, 593–605. Li, L., Lee, Y.S., 1994. Pricing and delivery-time performance in a competitive environment. Management Science 40, 633–646. Lilien, G.L., Kotler, P., Moorthy, S.K., 1992. Marketing Models. Prentice-Hall, New Jersey.

Little, J.D.C., 1961. A proof for the queuing formula L¼ lW. Operations Research 9 (3), 383–387. ¨ Lutz, S., Lodding, H., Wiendahl, H.-P., 2003. Logistics-oriented inventory analysis. International Journal of Production Economics 85, 217–231. Mapes, J., 1993. The effect of capacity limitations on safety stock. International Journal of Operations and Production Management 13, 26–33. Medhi, J., 1991. Stochastic Models in Queuing Theory. Academic Press, Boston, MA,. Miles, J.A., Ezzell, J.R., 1980. The weighted average cost of capital, perfect capital markets, and project life: a clarification. Journal of Financial and Quantitative Analysis 15, 719–730. Nieuwenhuyse, I.V., Vandaele, N., Rajaram, K., Karmarkar, U.S., 2007. Buffer sizing in multi-product multi-reactor batch processes: impact of allocation and campaign sizing policies. European Journal of Operational Research 179, 424–443. Nyhuis, P., Wiendahl, H.-P., 2002. Logistische Kennlinien, Grundlagen, Werkzeuge und Anwendungen, 2. Auflage. Springer Verlag, Berlin a. o,. Paraskevopoulos, D., Karakitsos, E., Rustem, B., 1991. Robust capacity planning under uncertainty. Management Science 37, 787–800. Plewa, F.J., Friedlob, G.T., 1996. Understanding Return on Investment. John Wiley and Sons,. Raman, A., Kim, B., 2002. Quantifying the impact of inventory holding cost and reactive capacity on an apparel manufacturer’s profitability. Production and Operations Management 11, 358–373. Rajan, M.V., Reichelstein, S., Soliman, M.T., 2007. Conservatism, growth and return on investment. Review of Accounting Studies 12, 325–370. ¨ Schnetzler, M.J., Sennheiser, A., Schonsleben, P., 2007. A decomposition-based approach for the development of a supply chain strategy. International Journal of Production Economics 105, 21–42. Schonberger, R.L., 1986. World Class Manufacturing. The Free Press, A Division of Macmillan Publishing Co., Inc.,. Schultz, C.R., 1989. An expediting heuristic for the shortest processing time dispatching rule. International Journal of Production Research 27 (1), 31–41. Souza, G.C., Wagner, H.M., Whybark, D.C., 2001. Evaluating focused factory benefits with queueing theory. European Journal of Operational Research 128, 597–610. Spearman, M.L., Woodruff, D.L., Hopp, W.J., 1990. CONWIP: a pull alternative to kanban. International Journal of Production Research 28 (5), 879–894. Stewart, B.G., 1991. The Quest for Value, The EVA Management Guide. HarperBusiness. ¨ die TerminabYu, K.-W., 2001. Terminkennlinie—Eine Beschreibungsmethodik fur ¨ Hannover, VDIweichung im Produktionsbereich, Diss, Reihe 2. Universitat ¨ Verlag, Dusseldorf,. ¨ Zapfel, G., 1998. Customer-order-driven production: an economical concept for responding to demand uncertainty? International Journal of Production Economics 56/57 699–709. Zhang, F., Roundy, R., C - akanyildirim, M., Huh, W.T., 2004. Optimal capacity expansion for multi-product, multi-machine manufacturing systems with stochastic demand. IIE Transactions 36, 23–36.