INTRODUCTION
Supply Chain Management (SCM) encompasses materials/supply management from
raw material to finished product (Tan et al., 1998).
A supply chain contains four levels, supplier, manufacturer, distributor, and
consumer, where each may be comprised of numerous facilities (Beamon,
1999).
A shorter leadtime implies better customer service, less inventory, and higher
efficiency, and thus is more and more important for obtaining competitive advantage
and increased market shares (Wedel and Lumsden, 1995).
Taking madetoorder manufacturing as an example, 54% of the delivery time is
waiting, which suggest that there is significant potential for improvement (Jahnukainen
and Lahti, 1999).
The definition of a supply chain has changed along with the various technology
breakthroughs seen in the last few decades. In the early and middle 1990’s,
a supply chain was defined as a group of firms/organizations which function
as a network flowing from raw material to final product or service (Ellram,
1991). With the rise of the Internet, business entities within the supply
chain became more strategically allied and began to exchange more information
to accelerate business processes.
Disregarding the finer points of these changes in definition, a supply chain
is commonly seen as being organized into several groups for specific purposes,
which are raw material supplier, subcomponent supplier, assembler/manufacturer,
distribution providers, and customer/consumer (Thomas and
Griffin, 1996; Kopczak, 1997). Beamon
(1999) defined that a supply chain contained the suppliers, manufacturers,
distributors and consumers, and they were grouped differently depending on whether
they play as a supplier, producer, wholesaler, or retail outlet.
Shin et al. (2000) constructed a supply chain
measurement model in terms of supplier and buyer performance. Supplier performance
includes cost, quality, delivery reliability, leadtime, and ontime delivery.
Beamon (1998) presented a different measurement approach
based on both qualitative and quantitative aspects. Furthermore, Beamon
(1999) also identified output and flexibility as the major performance measurements.
Accordingly, most of the available performance measurement models have been
costrelated. Lawrence (1999) argued that the cost of
safety stock and stock out were influenced by leadtime and variability, as
well as the results of Gilbert and Ballou (1999) study.
In addition, Tyworth and Zeng (1998) found that the
expected total annual logistics cost is the sum of transportation, holding,
ordering, and shortage costs, in which transportation cost is further related
to the freight rate, annual demand, and weight of goods. The application of
SCM or cost reduction is often found in the management literature (Ahmadi
and Teimouri, 2008; Ebrahimipoor et al., 2009;
Emongor and Kirsten, 2006; Hemalatha
and Vivekanandan, 2008; Kocsoy et al., 2008;
Lee et al., 2008; Alqedra
et al., 2011; Reaz et al., 2009; Shafia
et al., 2009; Shirazi et al., 2008).
The aim of this study was to understand how purchasing leadtime at the manufacturing
level influenced the overall cost of the supply chain. A cost model constructed
in this study was used to analyze the effects arising from a reduction in purchasing
leadtime. Furthermore, a case study of flexible Printed Circuit Boards (PCB)
was included to illustrate this approach.
THE OPTIMAL EXPECTED TOTAL COST REDUCTION MODEL
This study investigates how a manufacturer can reduce the costs resulting from the vendor’s delivery leadtime which is identical to manufacturer’s purchasing leadtime. Utilizing the proposed optimal expected total cost reduction model, guidelines are developed for an incentive program in which vendors will be motivated to reduce the leadtime for each purchase. This model is constructed under the following conditions (1) material will be brought solely from a single vendor, (2) the quality of material from this vendor is acceptable and constant, (3) the vendor is able to reduce the purchasing leadtime at a constant ratio of β (0≤β≤1) when encouraged by the incentive program, (4) the quality of products manufactured is acceptable and constant and (5) the manufacturer has to use the fastest transportation method to ensure ontime delivery. The Expected Delivery Time (EDT) of a manufacturer in a supply chain is composed of the following three major elements, as shown in Fig. 1:
• 
Expected leadtime of purchasing (ELTP): The expected time
frame from placing an order to the receipt of raw material 
• 
Expected leadtime of manufacturing (ELTM): The expected time frame from
the receipt of material to the finished products being shipped 
• 
Leadtime of transportation (LTT): The time frame from shipment to the
receipt by customers 
The top of Fig. 1 represents the EDT of a manufacturer that
purchases from a supplier with the regular ELTP.

Fig. 1: 
The structure of manufacturer’s expected delivery time
(EDT) 
The bottom represents the EDT of a manufacturer who purchases from the same
supplier after conducting ELTP reduction by β. In order to objectively
compare the manufacturer’s cost of purchasing from the same supplier before
and after this reduction, the manufacturer’s EDTs remain identical, regardless
of the changes in the ELTP. As a result, when the manufacturer purchases from
a supplier with reduced ELTP, the ELTM and/or the LTT tend to have more flexibility
to respond to the changes in the schedule.
The following symbols and notations used throughout this study are as follows:
b 
: 
Direct labor cost (amount per thousand units) 
C 
: 
Cost of the material (amount per item) 
D 
: 
Annual demand of the material (units per year) 
d 
: 
Daily demand of the material (units per day) 
E_{(Z)} 
: 
Unit normal loss integral 
e 
: 
Equipment depreciation (amount per thousand units) 
F_{i} 
: 
Freight rate of approach i where i = 1, 2, 3, …, n (amount per kg) 
I 
: 
Holding cost (expressed as a percentage of the item cost) 
k 
: 
Stock out cost (amount per order) 
P 
: 
Daily shipment (thousand units per day) 
Q 
: 
Economic Order Quantity (EOQ) after the ELTP has been reduced by β
(units per order) 
q 
: 
Economic Order Quantity (EOQ) before the ELTP has been reduced (units
per order) 
S 
: 
Ordering cost (amount per order) 
s 
: 
Working days (days per year) 
T_{i} 
: 
Transportation leadtime for approach i where i = 1, 2, 3, …, n (days) 
t_{i} 
: 
Increased transportation leadtime, compared with the first approach
when using approach i where i = 1, 2, 3, …, n (days) 
w 
: 
Weight per thousand units (kg) 
Z 
: 
The number of standard deviation 
β 
: 
Leadtime reduction ratio for each purchase (percentage) 
σ^{2}_{d} 
: 
Variance of daily material demand 
σ^{2}_{LTP} 
: 
Variance of purchasing leadtime 
λ 
: 
Daily demand of product (thousand units per day) 
μ 
: 
Daily production capacity (thousand units per day) 
μ_{i} 
: 
Daily production capacity when using transportation approach i (thousand
units per day) 
When the EDT remained, any changes in ELTP, ELTM and LTT might influence the
total cost. For a given β, the reduced leadtime is (1β) ELTP and
the standard deviation and variance are (1β)σ_{LTP} and (1β)^{2}
σ^{2}_{LTP}, respectively. The above change will result
in (1) cost reduction in relevant inventory, (2) cost reduction in transportation
method and (3) cost reduction in capacity.
The effect of a reduction in ELTP on expected relevant inventory cost: The influence of a reduction in ELTP on the inventory cost is explored in this subsection where the cost structure is based on the following assumptions:
• 
The demand is continuous and given 
• 
The purchasing leadtime and demand are both based on normal distribution 
• 
The ordering cost is constant 
• 
The back order is not allowed 
• 
The holding cost is linear and 
• 
The leadtime can be reduced by a ratio of β for each purchase 
Based on the relevant cost model presented by Lawrence
(1999) and Ballou (1992), the following equations
are developed by this study where the Expected Relevant Inventory Cost (ERIC)
before ELTP reduction can be obtained as follows:
where, q (EOQ) is:
and Safety Stock (ss) is:
According to Eq. 1, the first term is the cost of order processing, where the period can be of any length. However, it must be long enough to last through a purchasing cycle. Yearly demand is a common choice for this cycle which can be divided by q (EOQ) to obtain the number of orders placed in a year. In the second term, the cost of holding average inventory is presented where q divided by two represents average inventory. The next term is the cost of holding safety stock. The final term is the cost of stock outs, where the combined term of:
represents the expected numbers of stock outs during an order cycle. When Z
is 1.645 for the desired service level of 95%, E_{(Z)} is then equal
to 0.0211 (Ballou, 1992).
According to the above when the purchasing leadtime is reduced by β for each purchase, the ERIC, q, and ss would be reformulated as follows:
where, Q (EOQ) is:
and Safety Stock (SS) is:
When comparing Eq. 1 and 4, one can see
that when the ELTP is reduced, EOQ will also decrease. This thus results in
an increase in the cost of order processing and a decrease in the cost of holding
average inventory. In addition, the reduction in both ELTP and variance will
cause the cost of holding safety stock and stock outs to decrease.
Based on the above, if provided with the purchasing leadtime reduced by β for each purchase, the Expected Cost Reduction of Relevant Inventory (ECRRI) can be obtained by subtracting Eq. 4 from 1, as follows:
In Eq. 7, the q, ss, Q, and SS are those stated in Eq.
2, 3, 5 and 6. The
first term presents the cost difference of orders processing in Eq.
4 and 1 which is always a negative value to illustrate
the increasing cost.
The effect of a reduction in ELTP on transportation cost: According
to Tyworth and Zeng (1998), the freight rate and weight
affect the transportation cost. The assumptions of transportation are as follows:
• 
The transportation cost is weight related 
• 
The freight rate is based on transportation time which normally requires
more money to deliver with in a shorter time, and 
• 
There are n available transportation methods 
According to the above, the first transportation method (T_{1}), the most expensive and fastest way to deliver products, has been normally selected to avoid any delay. The reduction in transportation cost comes from extra transportation time being allowed, which results from the reduced ELTP, provided there is a fixed EDT. The extra transportation time obtained, t_{i}, can be expressed as:
where, LTT_{i} is the leadtime of transportation approach i.
Accordingly, t_{i} can be employed to utilize other flexible transportation approaches with less cost. The Cost Reduction of Transportation approach i (CRT_{i}) can be formulated as the equation below, which also uses the most expensive freight rate, F_{1} as the basis for comparisons:
where, s is the number of working days in a year.
When a transportation approach with less cost is adopted, a cost benefit, CRT_{i}, can be achieved. The optimal approach i happens while the sum of CRT_{i} and the Expected Cost Reduction of Capacity for approach i (ECRC_{i}) reaches a maximum value.
The effect of a reduction in ELTP expected capacity cost: The required
production capacity can be analyzed based on the M/M/1 queuing model presented
by Gilbert and Ballou (1999). The assumptions of the
queuing model are as follows:
• 
The processing times are exponentially distributed 
• 
The arrival of material is a Poisson process 
• 
There is only one set of production equipment available and 
• 
The finished products must be shipped instantly 
According to the M/M/1 queuing model, the ELTM can be obtained as follows:
then,
As shown in Fig. 1, based on the ELTP being reduced by a ratio of β and the LTT increased by t_{i}, the Expected LeadTime of Manufacturing for approach i (ELTM_{i}) can be formulated as follows:
Assuming constant demand, the following equations can be derived using the M/M/1 queuing model and daily production capacity for approach i (μ_{i}) can be obtained with the following equation:
Replacing ELTM_{i} in Eq. 13 for that in Eq.
12 when ELTP is reduced by a ratio of β and LTT is increased by t_{i},
Eq. 13 can be further updated to:
From Eq. 11 and 14, the following can
be obtained:
where, Δμ_{i} refers to the reduction in capacity for approach i.
Maintaining the excess capacity leads to cost increases due to production equipment,
labor force, and storage space (Lawrence, 1999). Since
the cost of space is very difficult to measure, only equipment and direct labor
costs are considered in this study. The ECRC_{i} can thus be obtained,
as follows:
In Eq. 16, multiplying the reduction of capacity for approach i (Δμ_{i}) by the sum of unit equipment and direct labor cost (e+b) gives the daily capacity cost reduction for approach i. Replacing the Δμ_{i} in Eq. 15 for that from 15, then:
From Eq. 17, the equipment investment and labor cost are reduced when the ELTM increases.
The optimal expected total cost reduction modeling: Based on the above
equations derived, leadtime reduction ratio, β, for each purchase will
lead to cost reductions for ECRRI, CRT_{i} and ECRC_{i}. From
Eq. 7, 9 and 16, the
Expected Total Cost Reduction of approach i (ETCR_{i}) in a year can
be obtained. Furthermore, the Optimal Expected Total Cost Reduction (OETCR)
in a year resulting from ELTP reduction, when using approach i, is given as
follows:
Subject to
In the Eq. 18, there is a tradeoff between CRT_{i} and ECRC_{i}. The longer the t_{i} is, the greater the OETCR becomes. Since the growth of ECRC_{i} is limited, only one t_{i} exists for a given OETCR. If the first approach has been selected, the reduced ELTP can be achieved by utilizing ECRC_{i} instead of CRT_{i}.
CASE STUDY
A flexible Printed Circuit Board (PCB) manufacturing company located in Taiwan, which is a supplier to notebook PC, printer, hard disk drive, and digital camera manufacturers, has been investigated to verify the proposed approach. Similar to other electronic companies, the subject company has to deal with short delivery times and rush orders, which often results in excess inventory and capacity. Accordingly, the subject company would like to aggressively reduce the ELTP to pursue more cost effective operations.
Optimal expected total cost reduction model solution: The flexible PCB production flow is shown in Fig. 2 which includes design, front processes, patterning, lamination, surface treatment, and back processes. During the patterning process, etching has always been a bottleneck due to low yield. Cover lay is the main raw material, which has to be purchased in rolls. The subject company’s detailed information is listed in Table 1.
As to the CRT_{i}, it takes 1.6 rolls of cover lay for every 1,000
pieces output. Accordingly, 12.8 rolls are needed for the daily 8,000 output,
281.6 rolls for monthly (22 working days) production, and 3,380 rolls for annual
demand (D). Based on Eq. 12, the EOQ can be obtained as 30
rolls. As mentioned before, if the desired service level is 95%, then, the Z
and E_{(Z)} are 1.645 and 0.0211, respectively. As to the stock out
cost per order (k), three scenarios are presented. First, the customer requests
a stock out item and is willing to wait based on the regular leadtime. Second,
the customer requests a stock out item and is unable to wait for the regular
leadtime, and so the company has to initiate an expedited order. Third, the
sale will be lost when the material is stock out (Lawrence,
1999).

Fig. 2: 
The Supply Chain of the Flexible PCB Processing 
Table 1: 
Information about the Flexible PCB manufacturing company 

Table 2: 
The ECRRI in different β levels 

CR_{1}: Cost reduction of orders processing; CR_{2}:
Cost reduction of holding average inventory; CR_{2}: Cost reduction
of holding average inventory; CR_{4}: Expected cost reduction of
stock out 
In case of the first and second scenarios, the added ordering costs will be
20 and 50%, respectively. Under the third circumstance, the cost of the lost
sale for the company is $1,000. Based on the Table 1, the
expected stock out cost is equal to $108.58, considering the probability for
each scenario provided. Accordingly, Eq. 14 is used to obtain
the ECRRI for different β, and these are summarized in Table
2.
As for the ECRC_{i}, air freight is used to transport products from Taiwan to Japan in order to meet limited time frame. The product weighs two kgs per 1,000 pieces. There are three approaches to be considered. The freight rate of the first is $8.696 (F_{1}) per kg, which takes only two days (T_{1}); the second is $6.667 (F_{2}) per kg, with three days (T_{2}) needed; and the third is $5.507 (F_{3}) per kg in four days (T_{3}). Therefore, the CRT_{i} of each transportation approach for different β can be obtained with Eq. 9.
As for the ECRC_{i}, if the daily output (λ) is 8,000 pieces,
this is also number of the shipping units. To manage rush orders and variations
in quality, the daily capacity (μ) has to be increased to the level of
12,000 pieces, which results in an ELTM of 0.25 day in Eq. 10.
Table 3: 
Maximum cost reduction of i for different β levels 

β: Percentage of leadtime reduction ratio for each purchase 
Table 4: 
Scenarios analysis of case study 

β: Percentage of leadtime reduction ratio for each purchase;
R*: Percentage of the OETCR to total annual purchased amount ($2,028,000) 
Since the manufacturing equipment costs $85,000 and the depreciation period
is three years, the equipment cost per 1,000 pieces share (e) is $13.415. Under
current operational arrangements, the equipment requires five operators with
a wage of $20 per operator per day. The direct labor cost per 1,000 pieces (b)
is thus equal to $12.5. As a result, the ECRC_{i} of each transportation
approach for different β can be obtained from Eq. 17.
Consequently, given the ELTP reduction ratio, β, the variance can be lowered proportionally. By substituting β with 10, 20, and 30% in Eq. 18, Table 2 can be obtained, where the ETCR_{i} reaches its most costeffective status with 10% ELTP reduction when i equals one. As β becomes 20 and 30%, the maximum ETCR_{i} (OETCR) occurs when i is equal to two and three, respectively. Table 3 also reveals a tradeoff between ECRC_{i} and ECRC_{i}. When β equals 10%, if the one day saving in ELTP can be applied to the ECRC_{i}, the cost can be reduced by $21,893 while the CRT_{i} reduces it by only $8,571. When utilizing the time saved in ECRC_{i}, an i equal one becomes the most cost effective option when β equals 10%. Accordingly, it also results in i equals two and three with a β of 20 and 30%, respectively, to achieve a similar outcome. More information about i with different levels of β is given in Table 4.
Vendor policy: The vendor can usually be motivated to reduce the leadtime
for each purchase through the utilization of the proposed total cost reduction
model. For a manufacturer, the ELTP varies from one vendor to another, and thus
different cost reductions can be achieved.
Table 5: 
Sensitivity analysis in OETCR 

β: Percentage of leadtime reduction ratio for each purchase 
Table 6: 
Sensitivity analysis in R^{*} 

β: Percentage of leadtime reduction ratio for each purchase 
R* the maximum benefit ratio from ELTP reduction, provides a reference for
the manufacturer to share profits with suppliers. As to vendor policy, an incentive
feedback program is worth establishing. Table 4 offers the
feedback guidelines with respect to various vendors’ time reductions for
delivery to encourage continuous improvement. Moreover, vendors can use these
guidelines to enhance their managerial and manufacturing performance in order
to obtain incentives from a reduction in ELTP.
Sensitivity analysis: The sensitivity analysis is used to explore the major factors of cost reduction when the ELTP is reduced at different levels of β. ELTP and variance reduction against cost reduction is presented by assuming that both ELTP and variance have three levels of 10, 20, and 30. In Table 5 and 6, the cost reduction and reduced ratios are listed. In Table 6 it can be seen that the cost reduction is mainly influenced by ELTP with a lower β. Taking β at 10% and ELTP at 20 as an example, the cost reduction rates under different variance levels are 1.62, 1.64, and 1.67, respectively, which demonstrate similar results. On the other hand, as to a fixed σ^{2}_{LTP} of 20 with different ELTP at 10, 20, and 30, the cost reduction rates are 1.18, 1.64 and 1.85, respectively. Accordingly, the cost reduction depends mainly on the ELTP, to which β makes only a minor contribution.
In contrast, with the same ELTP level of 20 with β at 100%, the cost reduction rates are 2.92, 3.22, and 3.45 at various σ^{2}_{LTP} levels. In addition, as to a fixed σ^{2}_{LTP} of 20, the cost reduction rates are 3.18, 3.22, and 3.25 when β is equal to 100% for different ELTP levels. Accordingly, the cost reduction is mainly affected by the variance of the ELTP instead of ELTP itself when β is close to 100%. When β increases, the variance decreases dramatically, which also leads to a significant improvement in ECRRI. Furthermore, CRT_{i} and ECRC_{i} are mainly affected by the reduced ELTP.
Although β can increase up to 100%, there exists only three possible transportation approaches, which limit the reduction scale of CRT_{i}. In addition, it is clear that ECRC_{i} can not be improved significantly based on the results of scenario analysis. The situation described above can be explained by Table 4, where the ECRRI is mainly influenced by the reduction in variance, while the CRT_{i} and the ECRC_{i} are mainly influenced by the ELTP.
CONCLUSIONS
This study focuses on variation in supply chain cost when the ELTP can be reduced with the required EDT unchanged. An illustrative case study of a flexible PCB company validates the proposed model through sensitivity analysis. The following conclusions can be presented:
• 
With regard to the cost reduction, a reduction in ELTP leads
to lower expected total cost, which jointly comes from the reductions in
expected relevant inventory cost, transportation cost, and expected capacity
cost 
• 
There exists a tradeoff between transportation cost and expected capacity
cost 
Overall, an improved ELTP can reduce manufacturing cost, and the savings cab be shared with vendors through an incentive feedback program. Accordingly, the total cost in the supply chain tends to become lower, which will definitely enhance firm competitiveness.
ACKNOWLEDGMENTS
This study is partially supported by the National Science Council of Taiwan under grant NSC 942416H218008.