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Evaluation of postponement structures to accommodate mass customization
Journal of Operations Management 23 (2005) 305–318 www.elsevier.com/locate/dsw
Evaluation of postponement structures to accommodate mass customization Jack C.P. Sua,*, Yih-Long Changb, Mark Fergusonb a
The University of New Mexico, Anderson School of Management, Albuquerque, NM 87131, USA b College of Management, Georgia Institute of Technology, Atlanta, GA 30332-0520, USA Available online 23 December 2004
Abstract In order to meet increasing customer demands for more diverse product offerings, firms are revising their supply chain structures to accommodate mass customization. The revised structures often involve delaying the delivery of the products until after the customer orders arrive, termed time postponement (TP), or delaying the differentiation of the products until later production stages, termed form postponement (FP). We develop models representing possible implementations of the TP and FP structures and compare their performance in total supply chain cost and expected customer waiting times. We find that once the number of different products increases above some threshold level, the TP structure is preferred under both performance metrics. For the most general model, a numerical experiment was designed to investigate how different factors affect the performance of the TP and FP structures. Through this experiment we show that higher arrival time and process time variations make the FP structure more favorable while increases in the number of products and higher interest rates make the TP structure more favorable. We also offer guidance to managers using either structure on where to allocate resources for performance improvement. For example, to improve the customer waiting times under the FP structure, increasing the coverage of the generic component and reducing the number of products provide larger benefits than reducing the variability of the arrival and process times. # 2004 Elsevier B.V. All rights reserved. Keywords: Supply chain management; Operations strategy; Mass customization; Postponement
1. Introduction Companies are providing a larger degree of product customization to fulfill the needs of increasingly differentiated customer segments. The Internet helps * Corresponding author. E-mail addresses: [email protected] (Jack C.P. Su), [email protected] (Y.-L. Chang), [email protected] (M. Ferguson).
make this possible by providing companies with a low cost platform to interact with their customers. McCarthy (2000) described a Hong Kong-based Internet site where customers can design their own watches. Other examples of industries providing more customization include: eyeglasses (Gilmore and Pine, 1997), color paints (Pagh and Cooper, 1998), and automobiles (Pine et al., 1993). To offer greater variety in a cost efficient way (also referred to as mass customization), various supply
0272-6963/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jom.2004.10.016
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chain structures have been explored. Many of these structures involve either delaying the delivery of the products until after the customer orders arrive or delaying the differentiation of the products until later stages of the supply chain. Zinn and Bowersox (1988) labeled the former as time postponement (TP) and the later as form postponement (FP). They show that postponement structures allow firms to meet the increased customized demands with lower inventory levels in the case of TP, or with shorter lead-times in the case of FP. In a recent review paper on postponement, van Hoek (2001) states: ‘‘Postponement is consistently mentioned as one of the central features of mass customization." Given their apparent advantages and widespread use in industry, each of these structures deserves a critical review and comparison. Employing TP involves delaying the manufacturing and shipping of the product until after the customer orders are received, also commonly referred to as a ‘‘make-to-order’’ approach. Production and distribution of the product, as such, is most often centralized in a single facility. An example of a company using TP is Bang and Olufsen, a high-end television and stereosystem manufacturer based in Denmark. All Bang and Olufsen products are made-to-order at a centralized plant and shipped directly to customers. The need for holding safety stock is eliminated when using TP and customers must be willing to wait the entire manufacturing lead-time for their customized products. In contrast to TP, employing FP involves shipping the products in a semi-finished state from the manufacturing facility to a downstream facility where final customization occurs. In order to delay the final customization of the product, the firm stocks a generic (semi-finished) component from which it draws upon for final assembly. Note that FP is not necessarily an assemble-to-order (ATO) process. An ATO process does not hold inventory of the finished product while the FP structure described here holds finished-goods inventory for each distinct product at the product’s respective point of customization. A classic example of a company using FP is Hewlett-Packard’s (HP) postponement of the final assembly of their DeskJet printers to their local distribution centers (Lee et al., 1993). Even though the localization of the printers was postponed, the regional distribution centers still
produced the localized printers in a make-to-stock fashion. Research on postponement dates back to Bucklin (1965), who was the first to mention the term ‘‘postponement’’ but did not provide any analytical results. Christopher (1992) provided case studies of how postponement works in the European market and Lee et al. (1993) presented the HP DeskJet printer case involving multiple international markets. In both cases, the authors found that significant supply chain savings could be achieved by redesigning the product or process to delay the differentiation decision, resulting in shorter lead-times, and thus, lower safety stocks. Feitzinger and Lee (1997), Lee and Tang (1997), and Grag and Tang (1997) provided analytical models measuring the costs and benefits of delayed differentiation, a type of FP. They showed that reductions in safety stock levels due to risk-pooling is the key benefit while the cost of designing and manufacturing the generic component is the main drawback. Zinn and Bowersox (1988), Cooper (1993), and Pagh and Cooper (1998) overview different types of postponement structures and discuss their potential benefits but do not provide models to compare the structures analytically. Although the viability of various postponement structures has been discussed, the environments where one type of postponement structure may be better than another have not received sufficient attention. Also, despite the fact that increasing product proliferation is often a major factor behind a firm’s decision to incorporate a postponement structure, its impact on the choice of what type of structure to implement has not been addressed. In this paper, we seek to fill these gaps. We compare the TP structure and the FP structure by using queuing models and derive conditions under which each structure is preferred. In addition, we show how product proliferation affects the supply chain performance of both structures. Two performance measures are evaluated. The first is the total supply chain cost, which includes both the amortized fixed cost and the periodic operating cost. The second is the expected customer waiting time, i.e., the time to fulfill the orders. These two measures are important evaluation criteria for most supply chain managers (Morash, 2001). While cost is a common performance measure, Baljko (2003) shows that delivery speed
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(referred to as supply chain agility) can also be a source of competitive advantage. We find that once the number of products increases above some threshold level, the TP structure is preferred under both performance metrics. We prove this analytically for the case of exponential arrival and process times and show it numerically for the general distribution case. For the general arrival and process time situation, we use G/G/1 approximations and design a numerical experiment to investigate how different factors affect the performance of the TP and FP structures. Through this experiment, we show that higher arrival time and process time variations make the FP structure more favorable while increases in the number of products and higher interest rates make the TP structure more favorable. We also offer guidance to managers using FP on where to allocate resources for performance improvement. For example, to improve the customer waiting times, increasing the coverage of the generic component and reducing the number of products provide larger benefits than reducing the variability of the arrival and process times. The remainder of this paper is organized as follows. In Section 2 we model both structures as M/M/1 systems and analyze how product proliferation impacts the choice between the two structures. In Section 3 we generalize the arrival and process time assumptions and present G/G/1 approximations for each structure. In Section 4 we compare the two structures through a numerical study and give managerial insights on when each structure is preferred. In Section 5 we summarize the study and discuss potential areas for future research.
2. M/M/1 models Consider a firm that supplies a product family consisting of N different customized products. Because all products belong to the same product family, we assume a common distribution for their process times along with negligible changeover times between products. This assumption is suitable for many business applications. For example, Dell Computer promises the same lead-time regardless of the computer configuration chosen (Dell.com). It is reasonable to assume that the cycle times to put in a larger or smaller hard drive come from the same
307
distribution and the changeover times between assembling different configurations are minimal. For both structures, we assume that the raw materials are always available and waiting at the beginning of the supply chain since our study focuses on the choice of internal supply chain structures. We also assume that a waiting order will not consume any raw material or components until it is processed. For the purpose of a fair comparison, we assume that both structures face the same demand. Lastly, we assume that the demand arrivals and the production process both follow random Poisson processes. This assumption is later relaxed when we present the G/G/1 models. In the TP structure, the products are manufactured in a make-to-order (MTO) fashion and shipped directly to customers from a centralized facility following the order receipts (Zinn and Bowersox, 1988). We model the TP structure as a multi-class single server queuing system with exponential interarrival times and exponential service times (i.e. a multi-class M/M/1 system). There are N types of customer orders (in our case, N different product types) for one unit each, arriving at the centralized facility where the service rule is First Come First Serve. The arrival processes are assumed independent and the interarrival times for the type k orders, 1 k N, come from a Poisson process with a mean arrival rate of lk. The processing rates for all products are i.i.d. random variables from a Poisson distribution with a mean rate of m. This structure is illustrated in Fig. 1. The FP structure consists of two general stages. At Stage 1, the generic component is made-to-stock at a centralized facility. Since Stage 1 produces a single generic component and there is no setup cost, a basestock control policy is optimal for managing the component inventory (Zipkin, 2000). Thus, Stage 1 is analyzed as a single class, single server base-stock system, i.e., an M/M/1 base-stock system (Buzacott and Shanthikumar, 1993). Final customizations are then made-to-stock at Stage 2, consisting of a dedicated facility for each of the N different product configurations. Our motivation for this supply chain structure comes from the HP DeskJet printer postponement example where the production line at a regional distribution center is dedicated to the product distributed in that region and the final product is madeto-stock. The FP structure is illustrated in Fig. 2.
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Fig. 1. The TP structure.
To evaluate the two supply chain structures, two performance measures are used: total cost (TC) and expected customer waiting time (ET). For the TP structure, the total cost (TCTP) for each period includes the amortized fixed cost (FTP), the production cost, and a work-in-process (WIP) holding cost. For the FP structure, Stage 1 cost (CFP,1) for each period includes the production cost for the generic component and the holding costs for both the WIP inventory and the finished generic component. Stage 2 cost (CFP,2) for each period includes the production cost for the final assembly as well as the associated holding costs for the WIP inventory and the finished customized products. To implement the FP structure, we assume the firm invests a fixed cost to develop and design the generic component and to replicate the processing equipment at each location needed for the second stage localization. This amortized fixed cost for each period
is represented by FFP. In general, FFP is greater than FTP because of the increased expense of redesigning the product for delayed differentiation. Since the raw material cost will be the same for both structures we do not include it in our model. 2.1. The TP structure The expected waiting time for the type k product in the TP structure (ETTP,k) can be derived using a birth– death process (Gross and Harris, 1985, p. 77), giving: 1 : ETTP ¼ PN m k¼1 lk
(1)
For the single server system, the average WIP for a product is equal to the percentage of time the server is dedicated to it. Hence, we use the system’s utilization, rk = lk/m, to represent the average amount of WIP
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309
Fig. 2. The FP structure.
inventory for product k. The total cost of the TP structure is the sum of fixed cost, WIP holding cost, and production cost: TCTP ¼ FTP þ
N N X X rk wk þ lk ck ; k¼1
(2)
k¼1
where wk and ck are the average unit WIP holding cost and the unit production cost for the kth product, respectively. We separate these two costs because the unit production cost is incurred for each unit produced but the WIP holding cost varies with the average number of units in the system. 2.2. The FP structure
Assume that orders for the generic component arrive with a mean rate of lg and are processed with a mean rate of mg. The average utilization of Stage 1 server is rg = lg/mg. For the generic component, let hg be the per unit holding cost for the finished generic component inventory, wg be the unit holding cost of the WIP inventory, cg the per unit production cost, and zg the base-stock level. Note that a zg = 0 is equivalent to a pure just-in-time implementation. The following expected waiting time and expected inventory level for Stage 1 and Stage 2 (Eqs. (3), (4), (6) and (7)) are based on the analysis of Buzacott and Shanthikumar (1993). The expected waiting time for Stage 1 is z
As with the TP structure, we assume exponential interarrival times and exponential process times.
ETFP;1 ¼
rgg : m g lg
(3)
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Let E[I] be the expected inventory level of the generic component, where rg z ð1 rgg Þ (4) E½I ¼ zg 1 rg is made up of the base-stock level minus the expected production orders. The cost at Stage 1 is CFP;1 ¼ hg E½I þ rg wg þ lg cg :
(5)
The first term of (5) is the generic component inventory holding cost, the second term is the average WIP holding cost (for the single server system, the average WIP for a product is equal to the percentage of time the server is dedicated to it), and the last term is the production cost. At Stage 2, each product type is customized by a dedicated production line. We model this stage as N single-class M/M/1 base-stock systems, analyzed the same way as Stage 1. For a type k product, let zk be the base-stock level, lk the mean arrival rate, and m0 the mean production rate. The utilization of the server for type k product is rk = lk/m0 . The expected waiting time for product k at Stage 2 is ETFP;2;k ¼
rzkk : m 0 lk
(6)
Let E[Ik] be the expected inventory level for product k at Stage 2, where rk E½Ik ¼ zk ð1 rzkk Þ: (7) 1 rk For a type k product, let hk be the unit holding cost, vk the average unit WIP holding cost, and bk the per unit production cost. The total cost over all locations at Stage 2 is CFP;2 ¼
N X ðE½Ik hk þ rk vk þ bk lk Þ:
(8)
k¼1
The first term of (8) is the total holding cost for finished products, the second term is the WIP holding cost, and the last term is the production cost. The total expected waiting time for product k under the FP structure is the sum of the waiting times for both stages ETFP;k ¼ ETFP;1 þ ETFP;2;k z
¼
rzk rgg þ 0 k m g l g m lk
(9)
and the total cost for the FP structure is TCFP ¼ FFP þ CFP;1 þ CFP;2 :
(10)
2.3. Effect of product proliferation Product proliferation results when companies customize their products for smaller customer groups or segments. In this section, we study how product proliferation affects the cost and the responsiveness of the TP and FP structures. In order to isolate the impact of a change in the number of products from the impact of a change in the facility’s utilization, we assume a constant overall utilization for the supply chain. To do so, we use a throttle demand rate where the total demand and total process capacity are held constant to maintain a constant system utilization rate, even though the total number of products may vary. In the absence of such control, an increase in the number of products may worsen the performance simply as a consequence of the increased load on the facility. Thus, the throttle demand rate removes the effect of an increased utilization rate, allowing us to truly study the effect of increasing the number of products. To facilitate mathematical analysis and to isolate the effect of product proliferation from the effect of asymmetry in the system, we also assume symmetric production, i.e., all the parameters of the different products are the same. Under this assumption, the subscript k of all parameters disappears. For example, lk = l, vk ¼ v, and ck = c. Gupta and Srinivasan (1998) use both the throttle demand rate and symmetric production assumptions to study the effect of product proliferation for a single stage queuing system. Without loss of generality, we normalize the total demand rate for the N products to equal 1. This allows us to simplify our notation and does not affect the performance of our models because we adjust our utilizations accordingly. Since the total demand rate for the N products is 1, the mean time between arrivals for each product is N or (l = 1/N). In the TP structure, the system utilization rate, r, is expressed as PN r¼ l =m ¼ Nl=m ¼ 1=m. This implies that k¼1 k the mean process time for each product (1/m) is also r. To make a meaningful comparison between the TP and FP structures, the same demand rate is employed
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for both structures and we adjust the process times to ensure that both structures have the same capacity. In the FP structure, the mean time between arrivals at the generic component stage is 1 since it includes the demand of all N products. The mean time between arrivals for each product at the second stage is N since each product has a dedicated production line. For the process time of the FP structure, let r be the mean total processing time of both stages (this ensures that both structures have the same total capacity). Let r, 0 r 1 represent the percentage of the mean total processing time consumed by the generic component, i.e. mg = 1/rr. The parameter r may also be thought of as the percentage of generic component coverage. At Stage 2, we divide the capacity available into N dedicated lines, each taking N(1 r)r time units to finish the final customization, or m0 = 1/N(1 r)r. Based on the above assumptions and definitions, we derive the following lemmas before stating our main result on the effect of product proliferation. Lemma 1. As N increases, the expected waiting time of the TP structure stays constant. Proof. Applying the symmetric production system assumption to (1), lk = l, the total expected waiting time for the TP structure becomes ETTP ¼
1 1 r ¼ ¼ : m Nl 1=r 1 1 r
Thus, ETTP is not a function of N.
Proof. For the FP structure, under symmetric production, from (9), the total expected waiting time becomes z
ETFP ¼
rgg ðl=m0 Þz : þ 0 mg l g m l
ETFP ¼
ðrrÞzg þ1 N½ð1 rÞrzþ1 þ : 1 rr 1 ð1 rÞr
Thus, as the number of products (N) increases, the expected waiting time of the FP structure (ETFP) increases monotonically. & Lemma 4. The cost of Stage 1 of the FP structure is constant with respect to N. Proof. Substituting rg = rr, lg = 1, mg = 1/rr, l = 1/ N, and m0 = 1/N(1 r)r into Eq. (4) gives Stage 1 cost of the FP structure of rr z ð1 ðrrÞ Þ hg þ rrwg þ cg : CFP;1 ¼ zg 1 rr (16) Thus, CFP,1 is not a function of N.
Proof. Under symmetric production, lk = l, and ck = c. From (2), the total expected cost for the TP structure becomes
CFP;2 ¼ NE½Ih þ N
(12)
Substituting l = 1/N and m = 1/r into (12), we get Thus, TCTP is not a function of N.
&
Lemma 5. The cost of Stage 2 of the FP structure increases monotonically in N. Proof. The symmetric reduces (8) to
TCTP ¼ FTP þ rw þ c:
(15)
(11)
&
l w þ Nlc: m
(14)
From the throttle demand rate and the equal capacity assumption, we get rg = rr, lg = 1, mg = 1/ rr, l = 1/N, and m0 = 1/N(1 r)r. Substituting these values into (14) gives
Lemma 2. As N increases, the expected cost of the TP structure stays constant.
TCTP ¼ FTP þ N
311
(13) &
Lemma 3. The expected waiting time of the FP structure increases monotonically in N.
where E½I ¼ z
production
l v þ Nbl; m0
assumption
(17)
z l=m0 l 1 : m0 1 l=m0
Substituting l = 1/N and m0 = 1/N(1 r)r into (17) gives ð1 rÞr ð1 ð1 rÞrÞz h CFP;2 ¼ N z 1 ð1 rÞr þ Nð1 rÞrv þ b:
(18)
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Thus, as the number of products (N) increases, Stage 2 cost of the FP structure (CFP,2) increases monotonically. & Lemma 6. The total cost of the FP structure increases monotonically in N. Proof. Since TCFP = FFP + CFP,1 + CFP,2, from Lemmas 4 and 5, the total cost of the FP structure (TCFP) increases monotonically in N. & Based on the lemmas given above, we conclude with the following proposition. Proposition 1. As N increases, there exists a threshold value of N above which TCTP < TCFP and ETTP < ETFP. Proof. As N increases, Lemmas 1 and 2 state that the expected waiting time (ETTP) and expected cost (TCTP) of the TP structure stay constant. From Lemmas 3 and 6, the expected waiting time (ETFP) and expected cost (TCFP) of the FP structure are monotonically increasing in N. Therefore, as N increases, there exists a threshold value of N above which TCTP < TCFP and ETTP < ETFP. & Example 1. We now give a numerical example to demonstrate the result stated in Proposition 1. First, let r = 0.5, r = 0.3, FTP = 10, and FFP = 12. For the TP structure, let w = 0.05, and c = 1. For Stage 1 of the FP structure, let zg = 2, hg = 0.03, wg = 0.015, and cg = 0.3. For Stage 2 of the FP structure, let z = 1, h = 0.1, v = 0.065, and b = 0.7. Fig. 3 is a plot of the total cost and customer waiting time as the number of products offered, N, increases from 1 to 8. An increase in the number of products greater than or equal to 6 results in the TP structure requiring less cost and having a shorter customer waiting time than the FP structure. Thus, the TP structure dominates the FP structure on both performance dimensions once the number of products exceeds 5. Intuitively, increasing the number of products could complicate the operation of the supply chain and worsen its performance. However, under the throttle demand and zero changeover time/cost assumptions, our analysis shows that the cost and time of the TP
Fig. 3. The effect of product proliferation.
structure stay constant as N increases. Gupta and Srinivasan (1998) also find that under the throttle demand assumption, conditions exist where an increase in the number of products decreases the number of back-orders and thus, reduces the expected customer waiting time. In our models, increasing the number of products in the FP structure requires that the capacity at Stage 2 be divided into equal amounts for each dedicated line. Thus, the pooling effect is lost in the FP structure (resulting in an increase in the WIP and final product inventory levels as well as the average number of back-orders) but not in the TP structure where all capacity is centralized. Therefore, as N increases the cost and time of the FP structure also increases.
3. G/G/1 models The M/M/1 models provide a means to study the effect of product proliferation on the choice between the TP and FP structures. However, more detail is needed to perform sensitivity analysis on how changes in the interarrival time variation and process time variation affect the choice of structure. The exponential distribution only has one parameter that determines both the mean and the variance. It does not allow us to change the variance without changing the mean. For this reason, we also model our supply chain structures using G/G/1 queuing systems.
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3.1. The G/G/1 approximation of the TP structure Let l and m be the mean arrival rate and mean process rate for a product, r = Nl/m be the overall system utilization, and s 2d and s 2p be the variances of the interarrival times and process times, respectively. There are several G/G/1 approximations available (Marchal, 1976; Shore, 1988). We tested both and found their results to be very close. To our knowledge, there is no published study stating that one approximation is better than another. Therefore, we use the one from Shore (1988). From Shore’s approximation, the expected number of customers in the system is ( )( ) r2 ð1 þ m2 s 2p Þ l2 s 2d þ r2 m2 s 2p L¼ þ r: (19) 2ð1 rÞ 1 þ r2 m2 s 2p By applying Little’s law, the expected customer waiting time using the TP structure is (( ) r2 ð1 þ m2 s 2p Þ 1 ETTP ¼ Nl 1 þ r2 m2 s 2p ( ) l2 s 2d þ r2 m2 s 2p
þ rg: (20) 2ð1 rÞ Similar to the M/M/1 model, the total cost of the TP structure is TCTP ¼ FTP þ rw þ Nlc:
(21)
3.2. The G/G/1 approximation of the FP structure The G/G/1 model for the FP structure is based on the approximation developed by Buzacott and Shanthikumar (1993, p. 106). Like the M/M/1 model, we first analyze Stage 1 where the production and stocking of the generic component occurs. 3.2.1. Stage 1 Let lg and mg be the mean arrival rate and mean processing rate for the generic component, and s 2d;g and s 2p;g be variances of the interarrival times and process times. Define rg = lg/mg to be the utilization of Stage 1, and following the notation of Buzacott and Shanthikumar (1993), let L¼
L rg ; L
where (
L ¼
r2g ð1 þ m2g s 2p;g Þ
)(
313
l2g s 2d;g þ r2g m2g s 2p;g
1 þ r2g m2g s 2p;g
)
2ð1 rg Þ
þ rg : (23)
The expected number of back-orders of the generic component, E[B], is E½B ¼
1 X
nrg ð1 LÞLn1þz ¼
n¼1
rg Lzg : 1L
(24)
The expected waiting time for Stage 1, using Little’s law, is ETFP;1 ¼
1 E½B: mg
(25)
Let E[I] be the expected inventory level: E½I ¼
zX g 1
fnð1 rg Þrg Lzg n1 g þ ð1 rg Þzg
n¼1
(26)
¼
ð1 rg Þrg Lzg 2 f1 zg ð1=LÞzg 1 þ ðzg 1Þð1=LÞzg g ð1 ð1=LÞÞ2
þð1 rg Þzg : (27)
Similar to (4), the cost of Stage 1 is CFP;1 ¼ E½Ihg þ rg wg þ lg cg :
(28)
3.2.2. Stage 2 Let l and m0 be the mean arrival rate and mean process rate for a product at each dedicated line of Stage 2 and s 2d and s 2p be the variances of the interarrival times and process times. Similar to Stage 1, the approximate expected waiting times for a product at Stage 2 is ETFP;2 ¼
rLz m0 ð1 LÞ
;
(29)
where r = l/m0 , L = (L* r)/L*, and L ¼ fr2 ð1 þ m0 2s 2p Þ=ð1 þ r2 m0 2s 2p Þgfðl2 s 2d þ r2 m0 2s 2p Þ=2ð1 rÞg þ r: Similar to (7), the cost of Stage 2 is
(22)
CFP;2 ¼ NðE½Ih þ rv þ blÞ;
(30)
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where E½I ¼
z1 X
fnð1 rÞrLzn1 g þ ð1 rÞz
n¼1
¼
ð1rÞrLz2 f1 zð1=LÞz1 þðz 1Þð1=LÞz g ð1 1=LÞ2 þ ð1 rÞz:
The total expected waiting time for a product under the FP structure is ETFP ¼ ETFP;1 þ ETFP;2
(31)
and the total cost is TCFP ¼ FFP þ CFP;1 þ CFP;2 :
(32)
4. Structure comparisons Using the G/G/1 approximations, we can evaluate the impact of customer arrival time variation and process time variation on the cost and the waiting time of the two structures. To compare the total costs and waiting times, we substitute in the parameter values for a particular scenario into Eqs. (19)–(32) to see which structure provides the lowest cost and/or shortest waiting time for those particular data values. However, there are many factors affecting the costs and waiting times and isolating the effect of each one analytically is intractable. Therefore, we design a numerical experiment to provide a comparison of the two structures under a wide range of parameter values. Six factors are included in the experiment: utilization rate, arrival time variation, process time variation, interest rate, percentage of generic component coverage, and the number of products. We choose the interest rate as a factor and assume that the holding costs for both the generic component and the WIP inventory are directly proportional to the interest rate. Any change in the interest rate changes the two holding cost proportionately, thus allowing us to analyze their impact through the use of a single factor. There are other factors that are not included because their effects on the costs and waiting times are straightforward. These include the fixed cost, the production cost, and the base-stock levels. We measured performance through changes in the total costs and the expected waiting times. Initial tests
showed that the utilization rate had the greatest impact of all the model parameters and significantly confounded the effects of the other factors. Therefore, we created three separate experiments corresponding to low, medium, and high utilization rates. Each experiment covers the other five factors, at three levels for each factor. A full factorial experiment would require 35 different runs. By using the Taguchi’s L18(21 37) orthogonal array (Phadke, 1989), the number of experimental runs is significantly reduced to only 18 for each experiment. Taguchi’s L18(21 37) orthogonal array is designed to test the significance of up to eight different variables. Since our experiment only has five factors in each experiment, the remaining three are set as dummy factors. Each factor has three levels: low, medium, and high. Values were chosen to cover the ranges of most realistic scenarios. The values selected for each factor are summarized in Table 1. Based on the factor levels, the other model parameters such as the demand rate (l), process rate (m), holding cost (h), and WIP cost (w) were set according to the throttle demand rate, symmetric production, and equal capacity assumptions described in Section 2.3. The two response variables are the expected customer waiting times given by (18) and (31) and the total costs given by (19) and (32). ANOVAs were performed to test the significance of the factors and the results are summarized in Table 2. From the results in Table 2, we make observations to describe the impact of the design factors on structure performances. The first four observations are intended to inform firms of the environments where one supply chain structure may be more attractive than the other. Observation 1. Under medium to high utilization levels, higher arrival time variation significantly increases the expected waiting time of the TP structure (ETTP) but not that of the FP structure (ETFP). An increase in the arrival time variation significantly increases the expected waiting time of the TP structure at all utilization levels but only increases the expected waiting time of the FP structure at low utilization levels. The FP structure is more robust to the increases of arrival time variation. This is due to the stock of generic components that provide a
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315
Table 1 Factors and their level values Factors
Levels
Utilization rate Coefficient of variation of times between arrivals (%) Coefficient of variation of process times (%) Interest rate (%) Percentage of generic component coverage, r Number of products
Low
Medium
High
0.5 10 10 5 30 2
0.75 200 50 25 50 8
0.97 400 100 50 70 16
Table 2 Results of ANOVA analysis (P-values) Utilization
Cost of FP L
M
Time of FP H
L
M
Cost of TP H
L
M
Time of TP H
"(a) 0.030
Arrival time variation Process time variation Interest rate
"(b) 0.001
"(b) 0.002
"(b) 0.002
Percentage of coverage Number of products
"(b) 0.006
"(b) 0.006
"(b) 0.006
"(b) 0.000 #(a) 0.017 "(a) 0.016
#(a) 0.021 "(a) 0.026
"(b) 0.000
L
M
H
"(b) 0.000 "(b) 0.000
"(b) 0.000 "(b) 0.000
"(b) 0.000 "(b) 0.000
"(b) 0.000
#(a) 0.028 "(a) 0.042
(") An increase in factor increases the value of the output; (#) an increase in factor decreases the value of the output; (a) P-value less than 0.05 but greater than 0.01; (b) P-value less than 0.01.
buffering effect. Thus, as the inter-arrival times become more variable, the FP structure becomes more attractive.
Observation 3. A higher percentage of generic component coverage (r) significantly decreases the expected waiting time of the FP structure (ETFP).
Observation 2. Higher process time variation significantly increases the expected waiting time of the TP structure (ETTP) but not that of the FP structure (ETFP).
A higher percentage of generic component coverage significantly reduces the expected waiting time of the FP structure but has no significant effect on its cost. The magnitude of the reduction is increasing in the utilization rate. Hence, a company seeking to reduce its customer waiting times and operating in an FP structure under high utilizations should consider delaying the differentiation of its products as long as possible. Of course, the reduction in waiting times must be balanced against the possible increase in the fixed cost for redesigning the product or process. The result is shown in Fig. 4.
More variability in the process times significantly increases the expected waiting time of the TP structure but has no significant impact on that of the FP structure. Similar to Observation 1, the FP structure is more robust to increases in the variation because of its generic component inventory buffer. Hence, an increase in the process time variability makes the FP structure more attractive. Combining Observations 1 and 2 suggests that companies in a highly uncertain environment should consider an FP structure.
Observation 4. Increasing the number of products (N) significantly increases both the cost and the
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Fig. 4. Effect of generic component coverage on waiting time of FP.
expected waiting time of the FP structure but not those of the TP structure.
structure, seeking to allocate resources in order to improve performance.
Increasing the number of products significantly increases the expected waiting time and expected cost of the FP structure but has no significant impact on the TP structure. Hence, increasing the number of products makes the TP structure more attractive under both performance metrics. This result, shown in Fig. 5, is consistent with our analysis of product proliferation (stated in the proposition) using the M/ M/1 models. Some companies may already be established in a particular supply chain structure and are more interested in improving the performance of the structure they currently have. The next observation provides guidance to firms, operating in an FP
Observation 5. In the FP structure, increasing the percentage of the generic component coverage (r) and reducing the number of products (N) significantly improve the expected waiting times. In contrast, lowering the arrival time and process time variations does not significantly improve the waiting times except when the utilization level is low. Increasing the generic component coverage and reducing the number of different products offer significant improvement to the customer waiting times of the FP structure. Alternatively, a decrease in the arrival time variation does not significantly improve the waiting times except under low utilization
Fig. 5. Effect of product proliferation.
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317
Fig. 6. The effect of interest rate on structure costs.
levels. A decrease in the process time variation does not significantly improve the waiting times under any utilization level. Hence, if a firm desires to improve its responsiveness in the FP structure, allocating resources to product improvement (i.e., increasing r by a better designed generic component or reducing N by designing a product suitable for multiple market segments/regions) is more effective than process improvement (i.e., reducing the variation in arrival times and process times). The last observation compares the robustness of the two structures to external shocks (in our case, increases in the firms’ interest rates). Observation 6. Increases in interest rate significantly increases both the cost of the TP and FP structures. However, it has a larger impact on the FP structure than on the TP structure. An increase in the interest rate significantly impacts the costs of both the TP and FP structures. However, by investigating the detailed results of its effect as shown in Fig. 6, we see that the slope of the cost increase for the FP structure is greater than the slope of the cost increase for the TP structure. This is because the FP structure (a make-to-stock structure) has more inventory than the TP structure (a make-to-order structure). Therefore, higher interest rates make the TP structure more favorable. 5. Conclusions and future research The trend of increasing product customization provides many challenges for supply chain designers. A common response to these challenges is to incorporate some form of postponement. In this
paper, we develop models representing two possible mass customization postponement structures, TP and FP, and study their performance in terms of total supply chain cost and the expected customer waiting times. We find that once the number of products increases above some threshold level, the TP structure is preferred under both performance metrics. We prove this analytically for the case of exponential arrival and process times and show it numerically for the general distribution case. For the general arrival and process time situations, we use the G/G/1 approximations and design a numerical experiment to investigate how different factors affect the performance and attractiveness of the TP and FP structures. Our experiment shows that higher arrival time and process time variation makes the FP structure more favorable while an increase in the number of products and higher interest rates make the TP structure more favorable. Our research also provides guidance for managers regarding the allocation of resources for process improvement. We find that increasing the coverage of the generic component and reducing the number of products provide a larger impact on improving the customer waiting times of the FP structure than reductions in the variability of the arrival and process times. Our models and findings have several limitations. First, there are many supply chain configurations that incorporate TP and FP. We only explore limited instances of each structure. Our TP structure assumes that all production occurs at a centralized, single processing center while our FP structure assumes that all production of the generic component occurs at a single processing center while customization for each unique final product occurs at separate processing facilities. While the basic tradeoff of TP and FP is
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captured, different ways of configuring the supply chain for TP and FP may result in different managerial insights. Second, to ensure a fair comparison between the two structures, we assume a throttle demand rate so that the total system utilization is the same under both structures. When this assumption is invalid, firms can use the given expected waiting times and cost equations directly to determine which supply chain structure best fits their needs. Third, we assume that the customized products are in the same product family so the changeover times between them are negligible. Our models for the TP structure will need to be modified if changeover times between customized products are significant. There are several opportunities to extend our study. First, we used expected cost and expected waiting time as performance measures. The variance of the cost and waiting time could also be important in some business applications and the models can be extended to study these new measures. Second, the optimal coverage of the generic component and the optimal number of products may be interesting to some managers. Determining the optimal decision variables will involve more detail regarding the relationship between the fixed cost and the amount of redesign effort required. Third, we assumed there is only one product family. Including multiple product families could lead to some interesting extensions including partial demand substitution and savings incurred by sharing common components (product platforming). Fourth, we assumed a constant unit production cost. In practice, high arrival and process time variation could increase production cost by increasing the possibility of rush orders and overtime requirements to meet demand. This could be an interesting extension to be addressed.
References Baljko, J., 2003. Built for speed — when putting the reams of supply chain data they’ve amassed to best use, companies are discovering that agility counts. EBN Manhasset 1352, 25. Bucklin, L.P., 1965. Postponement, speculation and the structure of distribution channels. Journal of Marketing Research 2 (1), 26–31.
Buzacott, J., Shanthikumar, J.G., 1993. Stochastic Models of Manufacturing Systems. Prentice-Hall, Upper Saddle River, NJ, pp. 103–106. Christopher, M., 1992. Logistics and Supply Chain Management. Pitman, London. Cooper, J.C., 1993. Logistics structures for global business. International Journal of Physical Distribution and Logistics Management 23 (4), 12–23. Feitzinger, E., Lee, H.L., 1997. Mass customization at Hewlett Packard: the power of postponement. Harvard Business Review 75 (1), 116–120. Gilmore, H., Pine, B.J., 1997. The four faces of mass customisation. Harvard Business Review 75 (1), 91–101. Grag, A., Tang, C.S., 1997. On postponement structures for product families with multiple points of differentiation. IIE Transactions 29 (8), 641–650. Gross, D., Harris, C., 1985. Fundamentals of Queuing Theory. Wiley, New York. Gupta, D., Srinivasan, M.M., 1998. Note: how does product proliferation affect responsiveness? Management Science 44 (7), 1017–1020. Lee, H.L., Billington, C., Carter, B., 1993. Hewlett Packard gains control of inventory and service through design for localization. Interfaces 23 (4), 1–11. Lee, H.L., Tang, C.S., 1997. Modeling the costs and benefits of delayed product differentiation. Management Science 43 (1), 40–53. Marchal, W.C., 1976. An approximation formula for waiting time in single-server queues. AIIE Transition 8, 473–474. McCarthy, F.T., 2000. All yours. The Economist 355 (8164), 57– 58. Morash, E.A., 2001. Supply chain strategies, capabilities, and performance. Transportation Journal 41 (1), 37–54. Pagh, J.D., Cooper, M.C., 1998. Supply chain postponement and speculation structures: how to choose the right structure? Journal of Business Logistics 19 (2), 13–34. Phadke, M.S., 1989. Quality Engineering Using Robust Design. Prentice-Hall, Englewood Cliffs, NJ. Pine, B.J., Victor, B., Boynton, A.C., 1993. Making mass customization work. Harvard Business Review 71 (5), 108–116. Shore, H., 1988. Simple approximations for the GI/G/c queue. II. The moments, the inverse distribution function and the loss function of the number in the system and of the queue delay. The Journal of the Operational Research Society 39 (4), 381– 391. van Hoek, R.I., 2001. The rediscovery of postponement: a literature review and directions for research. Journal of Operations Management 19 (2), 161–184. Zinn, W., Bowersox, D.J., 1988. Planning physical distribution with the principle of postponement. Journal of Business Logistics 9 (2), 117–136. Zipkin, P., 2000. Foundations of Inventory Management. McGrawHill, New York.
Evaluation of postponement structures to accommodate mass customization Jack C.P. Sua,*, Yih-Long Changb, Mark Fergusonb a
The University of New Mexico, Anderson School of Management, Albuquerque, NM 87131, USA b College of Management, Georgia Institute of Technology, Atlanta, GA 30332-0520, USA Available online 23 December 2004
Abstract In order to meet increasing customer demands for more diverse product offerings, firms are revising their supply chain structures to accommodate mass customization. The revised structures often involve delaying the delivery of the products until after the customer orders arrive, termed time postponement (TP), or delaying the differentiation of the products until later production stages, termed form postponement (FP). We develop models representing possible implementations of the TP and FP structures and compare their performance in total supply chain cost and expected customer waiting times. We find that once the number of different products increases above some threshold level, the TP structure is preferred under both performance metrics. For the most general model, a numerical experiment was designed to investigate how different factors affect the performance of the TP and FP structures. Through this experiment we show that higher arrival time and process time variations make the FP structure more favorable while increases in the number of products and higher interest rates make the TP structure more favorable. We also offer guidance to managers using either structure on where to allocate resources for performance improvement. For example, to improve the customer waiting times under the FP structure, increasing the coverage of the generic component and reducing the number of products provide larger benefits than reducing the variability of the arrival and process times. # 2004 Elsevier B.V. All rights reserved. Keywords: Supply chain management; Operations strategy; Mass customization; Postponement
1. Introduction Companies are providing a larger degree of product customization to fulfill the needs of increasingly differentiated customer segments. The Internet helps * Corresponding author. E-mail addresses: [email protected] (Jack C.P. Su), [email protected] (Y.-L. Chang), [email protected] (M. Ferguson).
make this possible by providing companies with a low cost platform to interact with their customers. McCarthy (2000) described a Hong Kong-based Internet site where customers can design their own watches. Other examples of industries providing more customization include: eyeglasses (Gilmore and Pine, 1997), color paints (Pagh and Cooper, 1998), and automobiles (Pine et al., 1993). To offer greater variety in a cost efficient way (also referred to as mass customization), various supply
0272-6963/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jom.2004.10.016
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chain structures have been explored. Many of these structures involve either delaying the delivery of the products until after the customer orders arrive or delaying the differentiation of the products until later stages of the supply chain. Zinn and Bowersox (1988) labeled the former as time postponement (TP) and the later as form postponement (FP). They show that postponement structures allow firms to meet the increased customized demands with lower inventory levels in the case of TP, or with shorter lead-times in the case of FP. In a recent review paper on postponement, van Hoek (2001) states: ‘‘Postponement is consistently mentioned as one of the central features of mass customization." Given their apparent advantages and widespread use in industry, each of these structures deserves a critical review and comparison. Employing TP involves delaying the manufacturing and shipping of the product until after the customer orders are received, also commonly referred to as a ‘‘make-to-order’’ approach. Production and distribution of the product, as such, is most often centralized in a single facility. An example of a company using TP is Bang and Olufsen, a high-end television and stereosystem manufacturer based in Denmark. All Bang and Olufsen products are made-to-order at a centralized plant and shipped directly to customers. The need for holding safety stock is eliminated when using TP and customers must be willing to wait the entire manufacturing lead-time for their customized products. In contrast to TP, employing FP involves shipping the products in a semi-finished state from the manufacturing facility to a downstream facility where final customization occurs. In order to delay the final customization of the product, the firm stocks a generic (semi-finished) component from which it draws upon for final assembly. Note that FP is not necessarily an assemble-to-order (ATO) process. An ATO process does not hold inventory of the finished product while the FP structure described here holds finished-goods inventory for each distinct product at the product’s respective point of customization. A classic example of a company using FP is Hewlett-Packard’s (HP) postponement of the final assembly of their DeskJet printers to their local distribution centers (Lee et al., 1993). Even though the localization of the printers was postponed, the regional distribution centers still
produced the localized printers in a make-to-stock fashion. Research on postponement dates back to Bucklin (1965), who was the first to mention the term ‘‘postponement’’ but did not provide any analytical results. Christopher (1992) provided case studies of how postponement works in the European market and Lee et al. (1993) presented the HP DeskJet printer case involving multiple international markets. In both cases, the authors found that significant supply chain savings could be achieved by redesigning the product or process to delay the differentiation decision, resulting in shorter lead-times, and thus, lower safety stocks. Feitzinger and Lee (1997), Lee and Tang (1997), and Grag and Tang (1997) provided analytical models measuring the costs and benefits of delayed differentiation, a type of FP. They showed that reductions in safety stock levels due to risk-pooling is the key benefit while the cost of designing and manufacturing the generic component is the main drawback. Zinn and Bowersox (1988), Cooper (1993), and Pagh and Cooper (1998) overview different types of postponement structures and discuss their potential benefits but do not provide models to compare the structures analytically. Although the viability of various postponement structures has been discussed, the environments where one type of postponement structure may be better than another have not received sufficient attention. Also, despite the fact that increasing product proliferation is often a major factor behind a firm’s decision to incorporate a postponement structure, its impact on the choice of what type of structure to implement has not been addressed. In this paper, we seek to fill these gaps. We compare the TP structure and the FP structure by using queuing models and derive conditions under which each structure is preferred. In addition, we show how product proliferation affects the supply chain performance of both structures. Two performance measures are evaluated. The first is the total supply chain cost, which includes both the amortized fixed cost and the periodic operating cost. The second is the expected customer waiting time, i.e., the time to fulfill the orders. These two measures are important evaluation criteria for most supply chain managers (Morash, 2001). While cost is a common performance measure, Baljko (2003) shows that delivery speed
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(referred to as supply chain agility) can also be a source of competitive advantage. We find that once the number of products increases above some threshold level, the TP structure is preferred under both performance metrics. We prove this analytically for the case of exponential arrival and process times and show it numerically for the general distribution case. For the general arrival and process time situation, we use G/G/1 approximations and design a numerical experiment to investigate how different factors affect the performance of the TP and FP structures. Through this experiment, we show that higher arrival time and process time variations make the FP structure more favorable while increases in the number of products and higher interest rates make the TP structure more favorable. We also offer guidance to managers using FP on where to allocate resources for performance improvement. For example, to improve the customer waiting times, increasing the coverage of the generic component and reducing the number of products provide larger benefits than reducing the variability of the arrival and process times. The remainder of this paper is organized as follows. In Section 2 we model both structures as M/M/1 systems and analyze how product proliferation impacts the choice between the two structures. In Section 3 we generalize the arrival and process time assumptions and present G/G/1 approximations for each structure. In Section 4 we compare the two structures through a numerical study and give managerial insights on when each structure is preferred. In Section 5 we summarize the study and discuss potential areas for future research.
2. M/M/1 models Consider a firm that supplies a product family consisting of N different customized products. Because all products belong to the same product family, we assume a common distribution for their process times along with negligible changeover times between products. This assumption is suitable for many business applications. For example, Dell Computer promises the same lead-time regardless of the computer configuration chosen (Dell.com). It is reasonable to assume that the cycle times to put in a larger or smaller hard drive come from the same
307
distribution and the changeover times between assembling different configurations are minimal. For both structures, we assume that the raw materials are always available and waiting at the beginning of the supply chain since our study focuses on the choice of internal supply chain structures. We also assume that a waiting order will not consume any raw material or components until it is processed. For the purpose of a fair comparison, we assume that both structures face the same demand. Lastly, we assume that the demand arrivals and the production process both follow random Poisson processes. This assumption is later relaxed when we present the G/G/1 models. In the TP structure, the products are manufactured in a make-to-order (MTO) fashion and shipped directly to customers from a centralized facility following the order receipts (Zinn and Bowersox, 1988). We model the TP structure as a multi-class single server queuing system with exponential interarrival times and exponential service times (i.e. a multi-class M/M/1 system). There are N types of customer orders (in our case, N different product types) for one unit each, arriving at the centralized facility where the service rule is First Come First Serve. The arrival processes are assumed independent and the interarrival times for the type k orders, 1 k N, come from a Poisson process with a mean arrival rate of lk. The processing rates for all products are i.i.d. random variables from a Poisson distribution with a mean rate of m. This structure is illustrated in Fig. 1. The FP structure consists of two general stages. At Stage 1, the generic component is made-to-stock at a centralized facility. Since Stage 1 produces a single generic component and there is no setup cost, a basestock control policy is optimal for managing the component inventory (Zipkin, 2000). Thus, Stage 1 is analyzed as a single class, single server base-stock system, i.e., an M/M/1 base-stock system (Buzacott and Shanthikumar, 1993). Final customizations are then made-to-stock at Stage 2, consisting of a dedicated facility for each of the N different product configurations. Our motivation for this supply chain structure comes from the HP DeskJet printer postponement example where the production line at a regional distribution center is dedicated to the product distributed in that region and the final product is madeto-stock. The FP structure is illustrated in Fig. 2.
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Fig. 1. The TP structure.
To evaluate the two supply chain structures, two performance measures are used: total cost (TC) and expected customer waiting time (ET). For the TP structure, the total cost (TCTP) for each period includes the amortized fixed cost (FTP), the production cost, and a work-in-process (WIP) holding cost. For the FP structure, Stage 1 cost (CFP,1) for each period includes the production cost for the generic component and the holding costs for both the WIP inventory and the finished generic component. Stage 2 cost (CFP,2) for each period includes the production cost for the final assembly as well as the associated holding costs for the WIP inventory and the finished customized products. To implement the FP structure, we assume the firm invests a fixed cost to develop and design the generic component and to replicate the processing equipment at each location needed for the second stage localization. This amortized fixed cost for each period
is represented by FFP. In general, FFP is greater than FTP because of the increased expense of redesigning the product for delayed differentiation. Since the raw material cost will be the same for both structures we do not include it in our model. 2.1. The TP structure The expected waiting time for the type k product in the TP structure (ETTP,k) can be derived using a birth– death process (Gross and Harris, 1985, p. 77), giving: 1 : ETTP ¼ PN m k¼1 lk
(1)
For the single server system, the average WIP for a product is equal to the percentage of time the server is dedicated to it. Hence, we use the system’s utilization, rk = lk/m, to represent the average amount of WIP
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309
Fig. 2. The FP structure.
inventory for product k. The total cost of the TP structure is the sum of fixed cost, WIP holding cost, and production cost: TCTP ¼ FTP þ
N N X X rk wk þ lk ck ; k¼1
(2)
k¼1
where wk and ck are the average unit WIP holding cost and the unit production cost for the kth product, respectively. We separate these two costs because the unit production cost is incurred for each unit produced but the WIP holding cost varies with the average number of units in the system. 2.2. The FP structure
Assume that orders for the generic component arrive with a mean rate of lg and are processed with a mean rate of mg. The average utilization of Stage 1 server is rg = lg/mg. For the generic component, let hg be the per unit holding cost for the finished generic component inventory, wg be the unit holding cost of the WIP inventory, cg the per unit production cost, and zg the base-stock level. Note that a zg = 0 is equivalent to a pure just-in-time implementation. The following expected waiting time and expected inventory level for Stage 1 and Stage 2 (Eqs. (3), (4), (6) and (7)) are based on the analysis of Buzacott and Shanthikumar (1993). The expected waiting time for Stage 1 is z
As with the TP structure, we assume exponential interarrival times and exponential process times.
ETFP;1 ¼
rgg : m g lg
(3)
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Let E[I] be the expected inventory level of the generic component, where rg z ð1 rgg Þ (4) E½I ¼ zg 1 rg is made up of the base-stock level minus the expected production orders. The cost at Stage 1 is CFP;1 ¼ hg E½I þ rg wg þ lg cg :
(5)
The first term of (5) is the generic component inventory holding cost, the second term is the average WIP holding cost (for the single server system, the average WIP for a product is equal to the percentage of time the server is dedicated to it), and the last term is the production cost. At Stage 2, each product type is customized by a dedicated production line. We model this stage as N single-class M/M/1 base-stock systems, analyzed the same way as Stage 1. For a type k product, let zk be the base-stock level, lk the mean arrival rate, and m0 the mean production rate. The utilization of the server for type k product is rk = lk/m0 . The expected waiting time for product k at Stage 2 is ETFP;2;k ¼
rzkk : m 0 lk
(6)
Let E[Ik] be the expected inventory level for product k at Stage 2, where rk E½Ik ¼ zk ð1 rzkk Þ: (7) 1 rk For a type k product, let hk be the unit holding cost, vk the average unit WIP holding cost, and bk the per unit production cost. The total cost over all locations at Stage 2 is CFP;2 ¼
N X ðE½Ik hk þ rk vk þ bk lk Þ:
(8)
k¼1
The first term of (8) is the total holding cost for finished products, the second term is the WIP holding cost, and the last term is the production cost. The total expected waiting time for product k under the FP structure is the sum of the waiting times for both stages ETFP;k ¼ ETFP;1 þ ETFP;2;k z
¼
rzk rgg þ 0 k m g l g m lk
(9)
and the total cost for the FP structure is TCFP ¼ FFP þ CFP;1 þ CFP;2 :
(10)
2.3. Effect of product proliferation Product proliferation results when companies customize their products for smaller customer groups or segments. In this section, we study how product proliferation affects the cost and the responsiveness of the TP and FP structures. In order to isolate the impact of a change in the number of products from the impact of a change in the facility’s utilization, we assume a constant overall utilization for the supply chain. To do so, we use a throttle demand rate where the total demand and total process capacity are held constant to maintain a constant system utilization rate, even though the total number of products may vary. In the absence of such control, an increase in the number of products may worsen the performance simply as a consequence of the increased load on the facility. Thus, the throttle demand rate removes the effect of an increased utilization rate, allowing us to truly study the effect of increasing the number of products. To facilitate mathematical analysis and to isolate the effect of product proliferation from the effect of asymmetry in the system, we also assume symmetric production, i.e., all the parameters of the different products are the same. Under this assumption, the subscript k of all parameters disappears. For example, lk = l, vk ¼ v, and ck = c. Gupta and Srinivasan (1998) use both the throttle demand rate and symmetric production assumptions to study the effect of product proliferation for a single stage queuing system. Without loss of generality, we normalize the total demand rate for the N products to equal 1. This allows us to simplify our notation and does not affect the performance of our models because we adjust our utilizations accordingly. Since the total demand rate for the N products is 1, the mean time between arrivals for each product is N or (l = 1/N). In the TP structure, the system utilization rate, r, is expressed as PN r¼ l =m ¼ Nl=m ¼ 1=m. This implies that k¼1 k the mean process time for each product (1/m) is also r. To make a meaningful comparison between the TP and FP structures, the same demand rate is employed
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for both structures and we adjust the process times to ensure that both structures have the same capacity. In the FP structure, the mean time between arrivals at the generic component stage is 1 since it includes the demand of all N products. The mean time between arrivals for each product at the second stage is N since each product has a dedicated production line. For the process time of the FP structure, let r be the mean total processing time of both stages (this ensures that both structures have the same total capacity). Let r, 0 r 1 represent the percentage of the mean total processing time consumed by the generic component, i.e. mg = 1/rr. The parameter r may also be thought of as the percentage of generic component coverage. At Stage 2, we divide the capacity available into N dedicated lines, each taking N(1 r)r time units to finish the final customization, or m0 = 1/N(1 r)r. Based on the above assumptions and definitions, we derive the following lemmas before stating our main result on the effect of product proliferation. Lemma 1. As N increases, the expected waiting time of the TP structure stays constant. Proof. Applying the symmetric production system assumption to (1), lk = l, the total expected waiting time for the TP structure becomes ETTP ¼
1 1 r ¼ ¼ : m Nl 1=r 1 1 r
Thus, ETTP is not a function of N.
Proof. For the FP structure, under symmetric production, from (9), the total expected waiting time becomes z
ETFP ¼
rgg ðl=m0 Þz : þ 0 mg l g m l
ETFP ¼
ðrrÞzg þ1 N½ð1 rÞrzþ1 þ : 1 rr 1 ð1 rÞr
Thus, as the number of products (N) increases, the expected waiting time of the FP structure (ETFP) increases monotonically. & Lemma 4. The cost of Stage 1 of the FP structure is constant with respect to N. Proof. Substituting rg = rr, lg = 1, mg = 1/rr, l = 1/ N, and m0 = 1/N(1 r)r into Eq. (4) gives Stage 1 cost of the FP structure of rr z ð1 ðrrÞ Þ hg þ rrwg þ cg : CFP;1 ¼ zg 1 rr (16) Thus, CFP,1 is not a function of N.
Proof. Under symmetric production, lk = l, and ck = c. From (2), the total expected cost for the TP structure becomes
CFP;2 ¼ NE½Ih þ N
(12)
Substituting l = 1/N and m = 1/r into (12), we get Thus, TCTP is not a function of N.
&
Lemma 5. The cost of Stage 2 of the FP structure increases monotonically in N. Proof. The symmetric reduces (8) to
TCTP ¼ FTP þ rw þ c:
(15)
(11)
&
l w þ Nlc: m
(14)
From the throttle demand rate and the equal capacity assumption, we get rg = rr, lg = 1, mg = 1/ rr, l = 1/N, and m0 = 1/N(1 r)r. Substituting these values into (14) gives
Lemma 2. As N increases, the expected cost of the TP structure stays constant.
TCTP ¼ FTP þ N
311
(13) &
Lemma 3. The expected waiting time of the FP structure increases monotonically in N.
where E½I ¼ z
production
l v þ Nbl; m0
assumption
(17)
z l=m0 l 1 : m0 1 l=m0
Substituting l = 1/N and m0 = 1/N(1 r)r into (17) gives ð1 rÞr ð1 ð1 rÞrÞz h CFP;2 ¼ N z 1 ð1 rÞr þ Nð1 rÞrv þ b:
(18)
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Thus, as the number of products (N) increases, Stage 2 cost of the FP structure (CFP,2) increases monotonically. & Lemma 6. The total cost of the FP structure increases monotonically in N. Proof. Since TCFP = FFP + CFP,1 + CFP,2, from Lemmas 4 and 5, the total cost of the FP structure (TCFP) increases monotonically in N. & Based on the lemmas given above, we conclude with the following proposition. Proposition 1. As N increases, there exists a threshold value of N above which TCTP < TCFP and ETTP < ETFP. Proof. As N increases, Lemmas 1 and 2 state that the expected waiting time (ETTP) and expected cost (TCTP) of the TP structure stay constant. From Lemmas 3 and 6, the expected waiting time (ETFP) and expected cost (TCFP) of the FP structure are monotonically increasing in N. Therefore, as N increases, there exists a threshold value of N above which TCTP < TCFP and ETTP < ETFP. & Example 1. We now give a numerical example to demonstrate the result stated in Proposition 1. First, let r = 0.5, r = 0.3, FTP = 10, and FFP = 12. For the TP structure, let w = 0.05, and c = 1. For Stage 1 of the FP structure, let zg = 2, hg = 0.03, wg = 0.015, and cg = 0.3. For Stage 2 of the FP structure, let z = 1, h = 0.1, v = 0.065, and b = 0.7. Fig. 3 is a plot of the total cost and customer waiting time as the number of products offered, N, increases from 1 to 8. An increase in the number of products greater than or equal to 6 results in the TP structure requiring less cost and having a shorter customer waiting time than the FP structure. Thus, the TP structure dominates the FP structure on both performance dimensions once the number of products exceeds 5. Intuitively, increasing the number of products could complicate the operation of the supply chain and worsen its performance. However, under the throttle demand and zero changeover time/cost assumptions, our analysis shows that the cost and time of the TP
Fig. 3. The effect of product proliferation.
structure stay constant as N increases. Gupta and Srinivasan (1998) also find that under the throttle demand assumption, conditions exist where an increase in the number of products decreases the number of back-orders and thus, reduces the expected customer waiting time. In our models, increasing the number of products in the FP structure requires that the capacity at Stage 2 be divided into equal amounts for each dedicated line. Thus, the pooling effect is lost in the FP structure (resulting in an increase in the WIP and final product inventory levels as well as the average number of back-orders) but not in the TP structure where all capacity is centralized. Therefore, as N increases the cost and time of the FP structure also increases.
3. G/G/1 models The M/M/1 models provide a means to study the effect of product proliferation on the choice between the TP and FP structures. However, more detail is needed to perform sensitivity analysis on how changes in the interarrival time variation and process time variation affect the choice of structure. The exponential distribution only has one parameter that determines both the mean and the variance. It does not allow us to change the variance without changing the mean. For this reason, we also model our supply chain structures using G/G/1 queuing systems.
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3.1. The G/G/1 approximation of the TP structure Let l and m be the mean arrival rate and mean process rate for a product, r = Nl/m be the overall system utilization, and s 2d and s 2p be the variances of the interarrival times and process times, respectively. There are several G/G/1 approximations available (Marchal, 1976; Shore, 1988). We tested both and found their results to be very close. To our knowledge, there is no published study stating that one approximation is better than another. Therefore, we use the one from Shore (1988). From Shore’s approximation, the expected number of customers in the system is ( )( ) r2 ð1 þ m2 s 2p Þ l2 s 2d þ r2 m2 s 2p L¼ þ r: (19) 2ð1 rÞ 1 þ r2 m2 s 2p By applying Little’s law, the expected customer waiting time using the TP structure is (( ) r2 ð1 þ m2 s 2p Þ 1 ETTP ¼ Nl 1 þ r2 m2 s 2p ( ) l2 s 2d þ r2 m2 s 2p
þ rg: (20) 2ð1 rÞ Similar to the M/M/1 model, the total cost of the TP structure is TCTP ¼ FTP þ rw þ Nlc:
(21)
3.2. The G/G/1 approximation of the FP structure The G/G/1 model for the FP structure is based on the approximation developed by Buzacott and Shanthikumar (1993, p. 106). Like the M/M/1 model, we first analyze Stage 1 where the production and stocking of the generic component occurs. 3.2.1. Stage 1 Let lg and mg be the mean arrival rate and mean processing rate for the generic component, and s 2d;g and s 2p;g be variances of the interarrival times and process times. Define rg = lg/mg to be the utilization of Stage 1, and following the notation of Buzacott and Shanthikumar (1993), let L¼
L rg ; L
where (
L ¼
r2g ð1 þ m2g s 2p;g Þ
)(
313
l2g s 2d;g þ r2g m2g s 2p;g
1 þ r2g m2g s 2p;g
)
2ð1 rg Þ
þ rg : (23)
The expected number of back-orders of the generic component, E[B], is E½B ¼
1 X
nrg ð1 LÞLn1þz ¼
n¼1
rg Lzg : 1L
(24)
The expected waiting time for Stage 1, using Little’s law, is ETFP;1 ¼
1 E½B: mg
(25)
Let E[I] be the expected inventory level: E½I ¼
zX g 1
fnð1 rg Þrg Lzg n1 g þ ð1 rg Þzg
n¼1
(26)
¼
ð1 rg Þrg Lzg 2 f1 zg ð1=LÞzg 1 þ ðzg 1Þð1=LÞzg g ð1 ð1=LÞÞ2
þð1 rg Þzg : (27)
Similar to (4), the cost of Stage 1 is CFP;1 ¼ E½Ihg þ rg wg þ lg cg :
(28)
3.2.2. Stage 2 Let l and m0 be the mean arrival rate and mean process rate for a product at each dedicated line of Stage 2 and s 2d and s 2p be the variances of the interarrival times and process times. Similar to Stage 1, the approximate expected waiting times for a product at Stage 2 is ETFP;2 ¼
rLz m0 ð1 LÞ
;
(29)
where r = l/m0 , L = (L* r)/L*, and L ¼ fr2 ð1 þ m0 2s 2p Þ=ð1 þ r2 m0 2s 2p Þgfðl2 s 2d þ r2 m0 2s 2p Þ=2ð1 rÞg þ r: Similar to (7), the cost of Stage 2 is
(22)
CFP;2 ¼ NðE½Ih þ rv þ blÞ;
(30)
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where E½I ¼
z1 X
fnð1 rÞrLzn1 g þ ð1 rÞz
n¼1
¼
ð1rÞrLz2 f1 zð1=LÞz1 þðz 1Þð1=LÞz g ð1 1=LÞ2 þ ð1 rÞz:
The total expected waiting time for a product under the FP structure is ETFP ¼ ETFP;1 þ ETFP;2
(31)
and the total cost is TCFP ¼ FFP þ CFP;1 þ CFP;2 :
(32)
4. Structure comparisons Using the G/G/1 approximations, we can evaluate the impact of customer arrival time variation and process time variation on the cost and the waiting time of the two structures. To compare the total costs and waiting times, we substitute in the parameter values for a particular scenario into Eqs. (19)–(32) to see which structure provides the lowest cost and/or shortest waiting time for those particular data values. However, there are many factors affecting the costs and waiting times and isolating the effect of each one analytically is intractable. Therefore, we design a numerical experiment to provide a comparison of the two structures under a wide range of parameter values. Six factors are included in the experiment: utilization rate, arrival time variation, process time variation, interest rate, percentage of generic component coverage, and the number of products. We choose the interest rate as a factor and assume that the holding costs for both the generic component and the WIP inventory are directly proportional to the interest rate. Any change in the interest rate changes the two holding cost proportionately, thus allowing us to analyze their impact through the use of a single factor. There are other factors that are not included because their effects on the costs and waiting times are straightforward. These include the fixed cost, the production cost, and the base-stock levels. We measured performance through changes in the total costs and the expected waiting times. Initial tests
showed that the utilization rate had the greatest impact of all the model parameters and significantly confounded the effects of the other factors. Therefore, we created three separate experiments corresponding to low, medium, and high utilization rates. Each experiment covers the other five factors, at three levels for each factor. A full factorial experiment would require 35 different runs. By using the Taguchi’s L18(21 37) orthogonal array (Phadke, 1989), the number of experimental runs is significantly reduced to only 18 for each experiment. Taguchi’s L18(21 37) orthogonal array is designed to test the significance of up to eight different variables. Since our experiment only has five factors in each experiment, the remaining three are set as dummy factors. Each factor has three levels: low, medium, and high. Values were chosen to cover the ranges of most realistic scenarios. The values selected for each factor are summarized in Table 1. Based on the factor levels, the other model parameters such as the demand rate (l), process rate (m), holding cost (h), and WIP cost (w) were set according to the throttle demand rate, symmetric production, and equal capacity assumptions described in Section 2.3. The two response variables are the expected customer waiting times given by (18) and (31) and the total costs given by (19) and (32). ANOVAs were performed to test the significance of the factors and the results are summarized in Table 2. From the results in Table 2, we make observations to describe the impact of the design factors on structure performances. The first four observations are intended to inform firms of the environments where one supply chain structure may be more attractive than the other. Observation 1. Under medium to high utilization levels, higher arrival time variation significantly increases the expected waiting time of the TP structure (ETTP) but not that of the FP structure (ETFP). An increase in the arrival time variation significantly increases the expected waiting time of the TP structure at all utilization levels but only increases the expected waiting time of the FP structure at low utilization levels. The FP structure is more robust to the increases of arrival time variation. This is due to the stock of generic components that provide a
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315
Table 1 Factors and their level values Factors
Levels
Utilization rate Coefficient of variation of times between arrivals (%) Coefficient of variation of process times (%) Interest rate (%) Percentage of generic component coverage, r Number of products
Low
Medium
High
0.5 10 10 5 30 2
0.75 200 50 25 50 8
0.97 400 100 50 70 16
Table 2 Results of ANOVA analysis (P-values) Utilization
Cost of FP L
M
Time of FP H
L
M
Cost of TP H
L
M
Time of TP H
"(a) 0.030
Arrival time variation Process time variation Interest rate
"(b) 0.001
"(b) 0.002
"(b) 0.002
Percentage of coverage Number of products
"(b) 0.006
"(b) 0.006
"(b) 0.006
"(b) 0.000 #(a) 0.017 "(a) 0.016
#(a) 0.021 "(a) 0.026
"(b) 0.000
L
M
H
"(b) 0.000 "(b) 0.000
"(b) 0.000 "(b) 0.000
"(b) 0.000 "(b) 0.000
"(b) 0.000
#(a) 0.028 "(a) 0.042
(") An increase in factor increases the value of the output; (#) an increase in factor decreases the value of the output; (a) P-value less than 0.05 but greater than 0.01; (b) P-value less than 0.01.
buffering effect. Thus, as the inter-arrival times become more variable, the FP structure becomes more attractive.
Observation 3. A higher percentage of generic component coverage (r) significantly decreases the expected waiting time of the FP structure (ETFP).
Observation 2. Higher process time variation significantly increases the expected waiting time of the TP structure (ETTP) but not that of the FP structure (ETFP).
A higher percentage of generic component coverage significantly reduces the expected waiting time of the FP structure but has no significant effect on its cost. The magnitude of the reduction is increasing in the utilization rate. Hence, a company seeking to reduce its customer waiting times and operating in an FP structure under high utilizations should consider delaying the differentiation of its products as long as possible. Of course, the reduction in waiting times must be balanced against the possible increase in the fixed cost for redesigning the product or process. The result is shown in Fig. 4.
More variability in the process times significantly increases the expected waiting time of the TP structure but has no significant impact on that of the FP structure. Similar to Observation 1, the FP structure is more robust to increases in the variation because of its generic component inventory buffer. Hence, an increase in the process time variability makes the FP structure more attractive. Combining Observations 1 and 2 suggests that companies in a highly uncertain environment should consider an FP structure.
Observation 4. Increasing the number of products (N) significantly increases both the cost and the
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Fig. 4. Effect of generic component coverage on waiting time of FP.
expected waiting time of the FP structure but not those of the TP structure.
structure, seeking to allocate resources in order to improve performance.
Increasing the number of products significantly increases the expected waiting time and expected cost of the FP structure but has no significant impact on the TP structure. Hence, increasing the number of products makes the TP structure more attractive under both performance metrics. This result, shown in Fig. 5, is consistent with our analysis of product proliferation (stated in the proposition) using the M/ M/1 models. Some companies may already be established in a particular supply chain structure and are more interested in improving the performance of the structure they currently have. The next observation provides guidance to firms, operating in an FP
Observation 5. In the FP structure, increasing the percentage of the generic component coverage (r) and reducing the number of products (N) significantly improve the expected waiting times. In contrast, lowering the arrival time and process time variations does not significantly improve the waiting times except when the utilization level is low. Increasing the generic component coverage and reducing the number of different products offer significant improvement to the customer waiting times of the FP structure. Alternatively, a decrease in the arrival time variation does not significantly improve the waiting times except under low utilization
Fig. 5. Effect of product proliferation.
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317
Fig. 6. The effect of interest rate on structure costs.
levels. A decrease in the process time variation does not significantly improve the waiting times under any utilization level. Hence, if a firm desires to improve its responsiveness in the FP structure, allocating resources to product improvement (i.e., increasing r by a better designed generic component or reducing N by designing a product suitable for multiple market segments/regions) is more effective than process improvement (i.e., reducing the variation in arrival times and process times). The last observation compares the robustness of the two structures to external shocks (in our case, increases in the firms’ interest rates). Observation 6. Increases in interest rate significantly increases both the cost of the TP and FP structures. However, it has a larger impact on the FP structure than on the TP structure. An increase in the interest rate significantly impacts the costs of both the TP and FP structures. However, by investigating the detailed results of its effect as shown in Fig. 6, we see that the slope of the cost increase for the FP structure is greater than the slope of the cost increase for the TP structure. This is because the FP structure (a make-to-stock structure) has more inventory than the TP structure (a make-to-order structure). Therefore, higher interest rates make the TP structure more favorable. 5. Conclusions and future research The trend of increasing product customization provides many challenges for supply chain designers. A common response to these challenges is to incorporate some form of postponement. In this
paper, we develop models representing two possible mass customization postponement structures, TP and FP, and study their performance in terms of total supply chain cost and the expected customer waiting times. We find that once the number of products increases above some threshold level, the TP structure is preferred under both performance metrics. We prove this analytically for the case of exponential arrival and process times and show it numerically for the general distribution case. For the general arrival and process time situations, we use the G/G/1 approximations and design a numerical experiment to investigate how different factors affect the performance and attractiveness of the TP and FP structures. Our experiment shows that higher arrival time and process time variation makes the FP structure more favorable while an increase in the number of products and higher interest rates make the TP structure more favorable. Our research also provides guidance for managers regarding the allocation of resources for process improvement. We find that increasing the coverage of the generic component and reducing the number of products provide a larger impact on improving the customer waiting times of the FP structure than reductions in the variability of the arrival and process times. Our models and findings have several limitations. First, there are many supply chain configurations that incorporate TP and FP. We only explore limited instances of each structure. Our TP structure assumes that all production occurs at a centralized, single processing center while our FP structure assumes that all production of the generic component occurs at a single processing center while customization for each unique final product occurs at separate processing facilities. While the basic tradeoff of TP and FP is
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captured, different ways of configuring the supply chain for TP and FP may result in different managerial insights. Second, to ensure a fair comparison between the two structures, we assume a throttle demand rate so that the total system utilization is the same under both structures. When this assumption is invalid, firms can use the given expected waiting times and cost equations directly to determine which supply chain structure best fits their needs. Third, we assume that the customized products are in the same product family so the changeover times between them are negligible. Our models for the TP structure will need to be modified if changeover times between customized products are significant. There are several opportunities to extend our study. First, we used expected cost and expected waiting time as performance measures. The variance of the cost and waiting time could also be important in some business applications and the models can be extended to study these new measures. Second, the optimal coverage of the generic component and the optimal number of products may be interesting to some managers. Determining the optimal decision variables will involve more detail regarding the relationship between the fixed cost and the amount of redesign effort required. Third, we assumed there is only one product family. Including multiple product families could lead to some interesting extensions including partial demand substitution and savings incurred by sharing common components (product platforming). Fourth, we assumed a constant unit production cost. In practice, high arrival and process time variation could increase production cost by increasing the possibility of rush orders and overtime requirements to meet demand. This could be an interesting extension to be addressed.
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