(P = 9,600, r = 90%, b = 0.152003)
1. Introduction
The research on supply chain management evolved from two separate paths:
purchasing and supply perspective of the manufacturers, and
transportation and logistics perspective of the distributors.
The former is the same as supplier base integration, which deals with traditional purchasing and supply management focusing on inventory and cycle time reduction. The latter concentrates on the logistics system for effective delivery of goods from supplier to customer. Supply chain management focuses on matching supply with demand to improve customer service without increasing inventory by eliminating inefficiencies and hidden operating costs throughout the whole process of materials flow. An essential concept of supply chain management is thus the coordination of all the activities from the material suppliers through manufacturer and distributors to the final customers. Recently, many researchers (for example, Weng, 1997, Lee and Whang, 1999, Cachon and Lariviere, 2005, Gerchak and Wang, 2004, Davis and Spekman, 2004, Yao and Chiou, 2004, Chang et al., 2008 among others) have examined theoretical, as well as practical, issues involving buyer-supplier coordination. The research findings claim that well coordinated supply chains have the potential for companies competing in a global market to gain a competitive advantage, especially in situations involving outsourcing, which is becoming increasingly common.
The current chapter discusses, from the perspective of supplier base integration, supply chain coordination for a make-to-order environment in which manufacturing (or assembly) and shipping capacity is ready. The managers have purchase orders in hand and the choice of flexible production and delivery policies in filling the order. For the benefits of operational efficiency, the supplier adopts the policy of frequent shipments of manufactured parts and products in small lots. In the case of standard-size container shipping, each container has limited space, and the manufacturer should split the orders into multiple containers over time. This can be extended to the situation where the manufacturer may have to use multiple companies (different trucks) to ship the entire orders. For the buyer, it is important to work closely with the supplier to facilitate frequent delivery schedules so that the supplier is able to meet the buyer’s requirements while still remaining economically viable. Obviously, this collaboration is an example of vendor managed inventory (VMI) system that requires well-managed cooperation between buyer and supplier in terms of sharing information on demand and inventory. While using the multiple delivery models, it is assumed that the vendor has the flexibility to select its own production policy. It can produce all units in a single setup or multiple setups to respond to a buyer’s order. The existing literature, however, has not focused on comparisons between single-setup-multiple-delivery (SSMD) and multiple-setup-multiple-delivery (MSMD) policies. Although the SSMD policy is well accepted and gaining popularity, the MSMD policy has been largely disregarded due to the likelihood of high setup costs. However, when we factor in setup reduction through learning and the reduction of necessary inventory space, the MSMD may be just as viable, or even the better option in certain situations. For example, suppose in a make-to-order environment that the supplier receives customer orders frequently through the Internet and has cost/time efficient setup operation, then it is natural for the supplier to choose the MSMD policy over the SSMD policy, since the MSMD policy would help the company keep a low inventory and provide fast delivery to its customers, obviously enhancing the supplier’s competitive advantage. This advantage will be apparent especially for the companies in high tech industries, where the product’s life cycle tends to be shorter. This is also true of companies in the food industry, where the demand is always for fresh products. See David Blanchard, 2007 for more examples.
In this study, we extend the models that focused on the supplier’s production policy (See Kim et al., 2008, and Kim and Ha, 2003). Kim et al., 2008 assumed in their MSMD model that the setup reduction through learning is restricted to one single lot and the learning starts anew for the next lot. In our first extension, however, we relax that assumption and allow that the setup reduction through learning is continued and accumulated throughout the subsequent production lots. The second extension of the model is that the MSMD model is allowed to have unequal setups and deliveries, while retaining the assumption of the MSMD model that the learning on setup reduction is confined to each lot alone and does not continue across lots. In other words, the model allows the number of setups to be unequal to the number of deliveries in each lot. This model may provide greater flexibility to the supplier in determining the production policy compared to the MSMD model or the SSMD model. Numerical examples are presented for illustration.
Although our goal is to elaborate on the entire supply chain synchronization, our discussion is limited to a relatively simple situation, i.e., single buyer and single supplier, under deterministic conditions for a single product that may account for a significant portion of the firm's inventory expenses. It is hoped that the result can be extended to a supply chain where multiple products and multiple parties are involved. In the following sections, the chapter discusses the supply chain coordination issue, from the perspective of supplier base integration, for a make-to-order environment in which manufacturing (or assembly) and shipping capacity is ready. The supplier has the flexibility to select its own production policy, producing all units of demand in either a single setup or multiple setups to respond to a buyer’s order, and also to choose a shipping policy of single or multiple deliveries for a given lot. Not much research in the existing literature has focused on comparisons between single-setup-multiple-delivery (SSMD) and multiple-setup-multiple-delivery (MSMD) policies. This study compares the SSMD and the MSMD policies, where frequent setups give rise to learning in the supplier's setup operation. A multiple delivery policy shows a strong and consistent cost-reducing effect on both the buyer and the supplier, in comparison to the traditional lot-for-lot approach. This paper extends the MSMD model in two directions:
Modified MSMD Model
multiple-setup-multiple-delivery with allowance for unequal number of setups and deliveries, and
Modified MSMD Model
multiple-setup-multiple-delivery with allowance for cumulative learning on setups over the subsequent production cycles.
Numerical illustrations are provided to compare the performance of the proposed models.The concluding section summarizes and discusses the implications of the results obtained.
2. Assumptions of the models and notation
When the buyer orders a quantity,
Lot for Lot, i.e., single-setup-single-delivery (SSSD),
SSMD, or
MSMD.
In the latter two cases, the order quantity,
If the MSMD policy is chosen, on the other hand, the supplier can meet the buyer’s demand with lower inventories than in the case of the SSMD policy. But he will incur higher setup costs due to more frequent setups. Also, there will be opportunity costs for the supplier that account for the capacity foregone by having more frequent setups than with the SSMD policy for a given order quantity. However, the MSMD policy may give rise to learning effects on setup operations, which in turn will reduce setup time and cost. The reduced setup time (and cost) will eventually benefit the supplier in the long run. It is reasonable for the buyer and the supplier to share this opportunity cost, because both the buyer and supplier can benefit from such a policy: the supplier achieves setup reduction via the learning effect on setup operations, and the buyer receives the benefits of multiple deliveries, i.e., lower inventories.
Once a long-term contract between buyer and supplier is agreed upon, both parties work in a cooperative manner to coordinate supply with actual customer demand. Their effective linkage in this manner will eventually make any practice of frequent delivery in small lot sizes beneficial to both parties. In this study, market demand rate, production rate, and delivery time are assumed to be constant and deterministic. It is also assumed that all cost parameters, including unit price, are known and constant, and neither quantity-discount nor backorders are allowed. The following notations are adopted:
α=the proportion of the fixed part of the total setup cost,
3. Single-Setup-Multiple-Delivery (SSMD) model
In the SSMD model, the order quantity is produced with one setup and shipped through multiple deliveries over time. The multiple deliveries are to be arranged in such a way that each succeeding delivery arrives at the time that all inventories from the previous delivery have just been depleted. As mentioned earlier, the buyer's total cost consists of ordering and holding costs, as well as transportation costs, incurred during the multiple deliveries as:
And the supplier's cost function includes a setup and order handling cost, and a holding cost:
The aggregate total cost function for both parties is as follows:
Note that
policy. The fact that the second derivatives of Equation (3) (with respect to
The expression for optimal order (contract) quantity for SSMD is almost identical to the supplier’s independent Economic Production Quantity (EPQ) model, except that the buyer’s ordering cost,
4. Multiple-Setup-Multiple-Delivery (MSMD) model
In the SSMD model, as shown in the earlier section, the supplier maintains large inventories and incurs high inventory holding costs due to the small delivery lot sizes over the multiple shipments. If the supplier, however, chooses the MSMD policy to set up the production process more frequently and to produce the exact quantity to be shipped on every setup, it can meet the buyer’s demand with lower average inventory than in the case of the SSMD policy. But the supplier in this MSMD case consumes more capacity hours due to frequent setups, which incurs higher setup costs in the long run. However, if the supplier’s capacity is greater than the threshold level (
We now assume that the system has no constraint on capacity for setting up
In Equation (5) above, α is the fixed cost portion of the setup cost. The setup cost has two components: fixed (or machine) and variable (or human) setup operation. And the learning effect is applied to the variable setup cost only. Without multiple setups, i.e., if
The integrated total cost function for both parties is as shown below:
Since the terms reflecting learning effects in Equation (6) bring step functions into the equation, derivatives with respect to
Integration for
If the MSMD policy is chosen, the supplier can meet the buyer’s demand with lower inventories than in the case of the SSMD policy, although more frequent setups will incur higher setup costs. A comparison of the integrated total costs for both SSMD and MSMD policies in Equations (3) and (8) would be sufficient in leading the supplier to an informed decision. However, since it is difficult to make an algebraic comparison of the two total costs due to the complexities of the expressions, Kim et al., 2008 suggested a brief guideline to help the supplier in making a decision about setup and delivery policy: If the supplier’s capacity is greater than the threshold level (
4.1. Modified MSMD model (I): Unequal number of setups and deliveries
In this section, we develop a modified multiple setup multiple delivery model (modified MSMD Model (I)), which retains the assumption that the setup reduction through learning is confined to each lot alone and does not continue across lots. However, the modified MSMD model (I) proposed in this section allows the number of setups to be unequal to the number of deliveries in each lot. This model may provide greater flexibility to the supplier in determining the production and delivery policy compared to the MSMD model. For certain parameter values, this modified MSMD model (I) will result in lower total cost compared to the MSMD model. In our modified MSMD model (I) with unequal setups and deliveries, the total cost function takes the following form:
In this modified MSMD model (I),
Minimize:
Subject to:
Q, m, N > 0,
Q ≤ D,
4.2. Modified MSMD model (II): Cumulative learning on setups over production cycles
In this section, we propose another extension of the MSMD model, which allows the learning of setup reduction achieved through earlier operations to accumulate across production cycles throughout the entire planning period. When this is imposed on the modified MSMD model (I), the model becomes modified MSMD model (II), which has the dual properties of both the SSMD and the MSMD models. This model can be applied to the situation where the time interval between consecutive orders is short enough for the supplier not to lose the learning gained from earlier setup operations. The model is thus built along the lines of single setup multiple deliveries with learning on setups over the multiple cycles. The benefits of this model over the MSMD model may be twofold: First, the overall setup cost and, in turn, the total cost is lower compared to the MSMD model. Second, the opportunity cost component incurred owing to additional setups in the MSMD model can be eliminated since the setup times are reduced as the production cycle is repeated. This, in turn, increases the scope for further reduction in the total cost for the same parameter values compared to the MSMD model. The total cost function takes the following form:
In this model, the total cost is comprised, as shown above, of the ordering cost, the setup cost that reduces through learning for subsequent setups during the entire finite planning period, the inventory cost of the buyer and the supplier, and the transportation cost, which is comprised of the fixed and the variable transportation cost components. The model is built along the lines of the single setup multiple delivery models with the addition of the variable N, the number of shipments from the supplier to the buyer in each setup. Owing to multiple shipments during each production lot, the supplier’s inventory cost function is similar to the one obtained by Kim and Ha (2003).
The modified MSMD model (II) can be formulated as a mixed integer nonlinear programming problem with the objective to minimize the total cost as shown below:
Minimize:
Subject to:
The variables to be determined are the production batch quantity Q and the number of shipments N in order to determine the supplier’s production and delivery policy at the minimal total cost for the supply chain.
5. Numerical illustration
Suppose a buyer, who is currently using an
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4,800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
D = 4800 units/year | HS = $4 per unit per year |
A = $25 per order |
|
HB = $5 per unit per year | a = 0.003 |
F = $50 per shipment |
|
V = $1 per unit |
|
C = $100 per hour | K = 100 |
S = 6 hours per setup | α = 0.5 |
We coded the models as mixed integer nonlinear programming problems in AMPL language and solved them using the MINLP solver on the Neos solver website (
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,535.00 | $9,816.00 | $11,107.00 | $9,678.57 | $9,678.57 |
Q* | 962 | 1770.34 | 853.33 | 1569.76 | 1569.76 |
N* | N/A | 6 | 1 | 5 | 5 |
D/Q* | 5 | 2.71 | 5.62 | 3.06 | 3.06 |
m* | N/A | N/A | N/A | 5 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,535.00 | $9,816.00 | $10,633.14 | $9,525.09 | $9,525.09 |
Q* | 962 | 1770.34 | 737.3 | 1460.36 | 1460.36 |
N* | N/A | 6 | 1 | 5 | 5 |
D/Q* | 5 | 2.71 | 6.51 | 3.29 | 3.29 |
m* | N/A | N/A | N/A | 5 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,535.00 | $9,816.00 | $10,115.00 | $9,333.90 | $9,333.90 |
Q* | 962 | 1770.34 | 618.08 | 1221.23 | 1221.23 |
N* | N/A | 6 | 1 | 4 | 4 |
D/Q* | 5 | 2.71 | 7.76 | 3.93 | 3.93 |
m* | N/A | N/A | N/A | 4 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,035.38 | $10,249.77 | $10,662.91 | $10,036.27 | $10,036.27 |
Q* | 1039.23 | 1453.27 | 926.21 | 1254.36 | 1254.36 |
N* | N/A | 4 | 1 | 3 | 3 |
D/Q* | 4.62 | 3.30 | 5.18 | 3.83 | 3.83 |
m* | N/A | N/A | N/A | 3 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,035.38 | $10,249.77 | $10,248.29 | $9,796.28 | $9,796.28 |
Q* | 1039.23 | 1453.27 | 804.82 | 1138.27 | 1138.27 |
N* | N/A | 4 | 1 | 3 | 3 |
D/Q* | 4.62 | 3.30 | 5.96 | 4.22 | 4.22 |
m* | N/A | N/A | N/A | 3 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $11,035.38 | $10,249.77 | $9,791.52 | $9,521.93 | $9,521.93 |
Q* | 1039.23 | 1453.27 | 678.657 | 883.795 | 883.795 |
N* | N/A | 4 | 1 | 2 | 2 |
D/Q* | 4.62 | 3.30 | 7.07 | 5.43 | 5.43 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,859.7 | $10,330.52 | $10,506.20 | $10,105.46 | $10,105.46 |
Q* | 1069.36 | 1345.26 | 954.78 | 1236.42 | 1236.42 |
N* | N/A | 3 | 1 | 3 | 3 |
D/Q* | 4.49 | 3.57 | 5.03 | 3.88 | 3.88 |
m* | N/A | N/A | N/A | 3 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,859.70 | $10,330.52 | $10,111.98 | $9,840.35 | $9,840.35 |
Q* | 1069.36 | 1345.26 | 831.4 | 1009.21 | 1009.21 |
N* | N/A | 3 | 1 | 2 | 2 |
D/Q* | 4.49 | 3.57 | 5.77 | 4.76 | 4.76 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,859.70 | $10,330.52 | $9,676.44 | $9,521.93 | $9,521.93 |
Q* | 1069.36 | 1345.26 | 702.62 | 883.795 | 883.795 |
N* | N/A | 3 | 1 | 2 | 2 |
D/Q* | 4.49 | 3.57 | 6.83 | 5.43 | 5.43 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,771.34 | $10,367.18 | $10,427.27 | $10,132.32 | $10,132.32 |
Q* | 1085.18 | 1336.4 | 969.8 | 1130.33 | 1130.33 |
N* | N/A | 3 | 1 | 2 | 2 |
D/Q* | 4.42 | 3.59 | 4.95 | 4.25 | 4.25 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,771.34 | $10,367.18 | $10,043.21 | $9,840.35 | $9,840.35 |
Q* | 1085.18 | 1336.4 | 845.39 | 1009.21 | 1009.21 |
N* | N/A | 3 | 1 | 2 | 2 |
D/Q* | 4.42 | 3.59 | 5.68 | 4.76 | 4.76 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,771.34 | $10,367.18 | $9,618.30 | $9,521.93 | $9,521.93 |
Q* | 1085.18 | 1336.4 | 715.27 | 883.795 | 883.795 |
N* | N/A | 3 | 1 | 2 | 2 |
D/Q* | 4.42 | 3.59 | 6.71 | 5.43 | 5.43 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,715.40 | $10,396.43 | $10,377.26 | $10,132.32 | $10,132.32 |
Q* | 1095.45 | 1243.65 | 979.55 | 1130.33 | 1130.33 |
N* | N/A | 2 | 1 | 2 | 2 |
D/Q* | 4.38 | 3.86 | 4.9 | 4.25 | 4.25 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,715.40 | $10,396.43 | $9,999.60 | $9,840.35 | $9,840.35 |
Q* | 1095.45 | 1243.65 | 854.49 | 1009.21 | 1009.21 |
N* | N/A | 2 | 1 | 2 | 2 |
D/Q* | 4.38 | 3.86 | 5.62 | 4.76 | 4.76 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
Lot for Lot | SSMD | MSMD | Modified MSMD (I) | Modified MSMD (II) | |
TC(Aggregate) $ per year | $10,715.40 | $10,396.43 | $9,581.39 | $9,521.93 | $9,521.93 |
Q* | 1095.45 | 1243.65 | 723.49 | 883.795 | 883.795 |
N* | N/A | 2 | 1 | 2 | 2 |
D/Q* | 4.38 | 3.86 | 6.63 | 5.43 | 5.43 |
m* | N/A | N/A | N/A | 2 | N/A |
N*/m* | N/A | N/A | N/A | 1 | N/A |
We compare the results for the 5 models in the context of annual TCAggregate in Table 1 based on the data obtained from Tables 17 through 31 for the 15 different sets of parameter constants.
|
|
|
|
|
|
1. 9600, 90% | $11,535.00 | $9,816.00 | $11,107.00 | $9,678.57 | $9,678.57 |
2. 9600, 80% | 11,535.00 | 9,816.00 | 10,633.14 | 9,525.09 | 9,525.09 |
3. 9600, 70% | 11,535.00 | 9,816.00 | 10,115.00 | 9,333.90 | 9,333.90 |
4. 19200, 90% | 11,035.38 | 10,249.77 | 10,662.91 | 10,036.27 | 10,036.27 |
5. 19200, 80% | 11,035.38 | 10,249.77 | 10,248.29 | 9,796.28 | 9,796.28 |
6. 19200, 70% | 11,035.38 | 10,249.77 | 9,791.52 | 9,521.93 | 9,521.93 |
7. 28800, 90% | 10,859.70 | 10,330.52 | 10,506.20 | 10,105.46 | 10,105.46 |
8. 28800, 80% | 10,859.70 | 10,330.52 | 10,111.98 | 9,840.35 | 9,840.35 |
9. 28800, 70% | 10,859.70 | 10,330.52 | 9,676.44 | 9,521.93 | 9,521.93 |
10. 38400, 90% | 10,771.34 | 10,367.18 | 10,427.27 | 10,132.32 | 10,132.32 |
11. 38400, 80% | 10,771.34 | 10,367.18 | 10,043.21 | 9,840.35 | 9,840.35 |
12. 38400, 70% | 10,771.34 | 10,367.18 | 9,618.30 | 9,521.93 | 9,521.93 |
13. 48000, 90% | 10,715.40 | 10,396.43 | 10,377.26 | 10,132.32 | 10,132.32 |
14. 48000, 80% | 10,715.40 | 10,396.43 | 9,999.60 | 9,840.35 | 9,840.35 |
15, 48000, 70% | 10,715.40 | 10,396.43 | 9,581.39 | 9,521.93 | 9,521.93 |
It is observed that in all 15 cases, the SSMD model yields better (lower) TC compared to the Lot-for-Lot model. It is apparent that, as the supplier’s production capacity and learning rate increase, the MSMD policy becomes more and more efficient. For a given production capacity level, the performance of the MSMD policy improves as the system retains more learning on setup operations. In other words, the smaller the supplier’s production capacity, the more beneficial the SSMD becomes. Throughout all the 15 cases, both the modified MSMD (I) model and modified MSMD (II) consistently outperform the other three models. Due to the specific parameter values, the ratio of
6. Conclusion
An effective linkage between the stages (or parties) that form the supply chain, based on a cooperative strategy that strengthens buyer-supplier relationships, improves the competitive position of the entire chain. Through such integration, both buyer and supplier can obtain benefits in terms of quality, flexibility, costs, and reliability of supply, etc. A key goal of supply chain management is therefore the coordination of all the activities from the material suppliers through manufacturer and distributors to the final customers.
In an effort to improve the supply chain coordination, this study compares the single-setup-multiple-delivery (SSMD) and the multiple-setup-multiple-delivery (MSMD) policies, where frequent setups give rise to learning in the supplier's setup operation. The consistency of our results obtained from the SSMD is also observed in a more complex environment, i.e., multiple setups and multiple deliveries. The learning effects in MSMD policy tend to decrease the capacity loss and opportunity cost that may result from more frequent setups. As the learning rate on setup operation increases, the rate at which MSMD becomes more efficient accelerates. This paper extends the MSMD model in two directions:
Modified MSMD Model (I): multiple setup multiple delivery with allowance for unequal number of setups and deliveries, and
Modified MSMD Model (II): multiple setup multiple delivery with allowance for cumulative learning on setups over the subsequent production cycles.
The modified MSMD models showed improved performance in aggregate total costs over the MSMD model throughout the entire finite planning horizon. Overall, the supply chain coordination strategy facilitating multiple setups and multiple deliveries in small lot sizes show a strong and consistent cost-reducing effect, in comparison with the Lot-for-Lot approach, on both the buyer and the supplier. It is suggested that the surplus benefits are shared by both parties according to the contribution (or sacrifice) each party made to the integration efforts.
As a guideline for the supplier in selecting the policy, this study claims that it is more beneficial for the supplier to implement the multiple setups and multiple deliveries (MSMD) policy if the supplier’s capacity is greater than the threshold level (
For future research purposes, the proposed model may be further embellished to address cases involving multiple buyers, suppliers, and products. Finally, the development of stochastic models in this area is likely to result in a more meaningful, albeit more complex, analysis under real world conditions.
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