This paper establishes VMI-APIOBPCS II model by extending VMI-APIOBPCS model from serial supply chain to distribution supply chain. Then TPL is introduced to this VMI distribution supply chain, and operational framework and process of VMI&TPL integrated supply chain are analyzed deeply. On this basis VMI-APIOBPCS II model is then changed to VMI&TPL-APIOBPCS model and VMI&TPL integrated operation mode is simulated. Finally, compared with VMI-APIOBPCS model, the TPL’s important role of goods consolidation and risk sharing in VMI&TPL integrated supply chain is analyzed in detail from the aspects of bullwhip effect, inventory level, service level, and so on.
Under vendor-managed inventory (VMI) operation mode, many suppliers outsource their logistics to third-party logistics (TPL) due to their poor logistics capabilities. So far, that TPL participates in VMI has been widely used in many industries. For example, Dell and Lenovo both chose Burlington Company to help them operate VMI service, and Wuhan Shenlong Automobile Company in China allows GEFCO to provide VMI service with components supply. On the one hand, this integrated operational model combining VMI with TPL ensures that the supply chain information is shared fully on one central platform. On the other hand, it can take full advantage of TPL and reduce the total operational cost of the supply chain.
As to the research of VMI&TPL integrated replenishment and delivery, Çetinkaya et al. [
Besides, some scholars consider replenishment strategies of TPL in VMI mode under different conditions, such as Çetinkaya et al. [
As to logistics optimization based on system dynamics, Towill [
In the other field, through STELLA/iThink software platform, Chen et al. [
After that Darya and Martin [
Our work differs from these studies in important aspects. First of all, these models are mainly constructed based on two echelon supply chains, that is, Disney and Towill [
Table
Definitions of parameters and variables.
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CON: demand rate | ACON: demand rate after forecast |
ORT: production rate | CRT: production fulfillment rate |
TINV: target inventory level | INV: actual inventory level |
EINV: inventory deviation | WIP: work-in-process |
TWIP: target work-in- |
EWIP: work-in-process deviation |
As shown in Figure
IOBPCS model of production and inventory system.
Figure
IOBPCS model causal relationship.
The productivity in IOBPCS model is decided by the demand forecasting mechanism and the inventory deviation adjustment mechanism, while the inventory deviation adjustment mechanism is decided by the inventory adjustment time and the target inventory level, and the demand forecasting mechanism is decided by the demand smooth time. Therefore, IOBPCS system optimization includes the definition of two basal parameters, such as demand smooth time and inventory deviation adjustment time. When designing the best production control strategy, cost from two sides should be balanced, including production cost due to production fluctuation and the inventory cost (or shortage cost) as the inventory level changes.
After many scholars amending and improving the model based on IOBPCS model, now it has been turned into an IOBPCS model family consisting of five parts as Figure
The main parts of expanded IOBPCS model.
The lead time of production delays can be regarded as production rhythm smooth time, which describes the speed of adjusting production rhythm to production order changes (ORATE). The production delay is one of the system characteristics, which cannot be controlled at random by the system’s designers, but designing different delay models will have an important effect on the entire system’s performance. Formula (
where
In IOBPCS model, target inventory level is a fixed value or the integer multiple of the demand forecasting number (ACON) after smoothing. Target inventory level is variable in VIOBPCS. Compared with IOPBPCS, the width of ORATE is larger, but the inventory adjustment response time is shorter. The only difference between APIOBPCS model and APVIOBPCS model lies in the setting of target inventory. In APIOBPCS model, target inventory level
Demand forecasting mechanism is an important part of the feed-forward loop. Demand forecasting mechanism is measured by exponential smoothing method in most literatures, because exponential smoothing method comprehensively includes all the historical information and is easy to use and to formulate a model. Exponential forecasting method (e.g., single exponential smoothing method, double exponential smoothing method, and triple exponential smoothing method) makes the steady-state error of system inventory in phase step and slope demand zero, but the steady-state error of system inventory becomes larger and larger when the demand function is a parabola.
Single exponential smoothing transfer function in
Double exponential smoothing transfer function in
Triple times exponential smoothing transfer function in
Inventory deviation adjustment mechanism is an inventory feedback loop which controls inventory deviation by controlling productivity. Inventory adjustment mechanism needs to consider production delay effect which means that only after a regular period of time can the controlling decision about productivity adjust the inventory level. The purpose of inventory adjustment is to reach target inventory level in a period of time (
WIP inventory deviation is caused by actual work-in-process inventory in contradiction with target work-in-process inventory when demand changes. WIP adjustment mechanism adjusts inventory deviation by controlling productivity so that it can reach the target value in a period of time (
Figure
Block diagram of APIOBPCS model.
In general, inventory dynamic fluctuation is measured by inventory rising time and adjustment time and overshoot, and productivity dynamic change is analyzed by frequency response method.
Here is the main control mechanism of APIOBPCS model in phase-step demand. Forecasting mechanism. Formula ( Target inventory setting. TINV = 0. Production process. Formula (
As a result, two important transfer functions about productivity and changes in inventory level can be obtained as follows:
Table
Definitions of parameters and variables.
Parameters and variables of suppliers | |
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VCON: demand rate of suppliers | AVCON: demand factor of suppliers after smoothing |
VINV: inventory level of suppliers | TINV: system target inventory level |
WIP: work-in-process inventory level | TWIP: target work-in-process inventory level |
EINV: inventory deviation | EWIP: deviation of work-in-process inventory |
ORT: productivity of suppliers | CRT: production fulfillment rate of suppliers |
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AEWIP: work-in-process inventory deviation regulation factor | |
AEINV: deviation adjustment rate of system inventory | |
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Parameters and variables of retailers | |
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CON: demand rate of retailers | ACON: demand rate of retailers after forecasting |
RINP: inventory level of retailers (including inventory on the way) | SS: safety inventory level |
G: safety inventory factor of retailers | ROP: reorder-point of distributors |
SRT: delivering rate to retailers | |
DSS: reorder-point of retailers variation | |
GIT: inventory of distributors on the way | |
RINV: actual inventory level of retailers | |
L: transportation time from suppliers to retailers | |
ETQ: economic order quantity |
In VMI operation mode, retailers share inventory information and sales information with suppliers dynamically and determine the customer service level together with suppliers. According to the fixed customer service level, suppliers choose quantity-based delivering model, which means that vehicle shipped way is chosen in order to guarantee economical efficiency of transportation when the total inventory level is lower than the reorder-point. Figure
VMI-APIOBPCS system dynamics model.
Here are the relational formulas in VMI-APIOBPCS model. They are as follows.
Demand forecasting mechanism:
Target work-in-process inventory level:
Work-in-process inventory level:
Finished goods inventory level:
Target inventory level:
System inventory level:
Finished goods fulfillment rate:
Productivity:
Inventory deviation adjustment rate:
Work-in-process inventory deviation adjustment rate:
Reorder-point of retailers:
Inventory levels of retailers:
Order arrival rate:
Safety inventory setting of retailers:
Suppliers can get customers’ demand in time and obtain the actual total customer demand downstream through terminal customer information, including the terminal customer demand and changes of reorder-points of downstream retailers:
Suppliers can check the inventory level of downstream retailers so that they can get the total supply chain inventory level which can optimize the total supply chain inventory decision:
In the actual operational process, suppliers can adopt VMI model on multiple downstream retailers. According to the aforementioned VMI serial supply chain when suppliers provide multiple retailers downstream with VMI service, they can get VMI distribution supply chain, as Figure
Operation mode of VMI distribution supply chain.
VMI-APIOBPCS II model as shown in Figure
VMI-APIOBPCS II system dynamics model.
To decrease the logistics cost and avoid the delivery risks in VMI system, in practice an upstream enterprise normally prefers to outsource its purchasing business to the third-party logistics (TPL) and requires his supplier to keep the inventory in the warehouse operated by TPL. For example, BAX Global is responsible for Apple, Dell, IBM, and other IT companies with their supplies in Southeast Asia, and United Parcel Service manages goods and materials procurement for Fender overseas and achieves its integration of process in distribution. Besides, Shanghai Volkswagen and Wuhan Shenlong Automobile adopt VMI&TPL integrated operation mode to effectively support the mixed flow job shop manufacturing with JIT delivering components to the work station directly.
After TPL is introduced into VMI, we consider the supply chain including one supplier (
Figure
VMI&TPL-APIOBPCS integrated operating model.
After carrying out TPL and VMI integrated operation, suppliers are not responsible for concrete logistics activities but give rights of inventory operation and decision to TPL through a contract. Therefore, TPL does not only undertake physical distribution business but is also responsible for orders generated in integrated logistics operation. The operational process of the whole system is illustrated in Figure TPL updates retailers’ inventory information everyday according to inventory information provided by retailers. TPL makes recommended orders according to retailers’ inventory level and service level and replenishment point confirmed in advance. TPL sends orders to retailers and chooses the proper distribution route according to self-inventory level and retailers’ demand after retailers confirm their orders. It is necessary to send requests for replenishment to suppliers and ask them to replenish inventory in time if self-inventory reaches replenishment level. Suppliers know well about the logistics operational situation by information sharing, then replenish inventory according to TPL’s demand, and settle accounts in time according to the orders confirmed by retailers.
VMI&TPL integrated operation process.
The definitions of parameters and variables in VMI&TPL-APIOBPCS model are given in Table
Definitions of parameters and variables.
ORT: productivity | CRT: production fulfillment rate |
RPT: replenishment rate | SRT: delivery rate |
W-ROP: TPL replenishment point | D-ROP: TPL redelivery point |
GIT: TPL transportation inventory | RINV: retailers’ temporary inventory level |
According to the operational structure in Figure
As shown in Figure
Causality diagram of suppliers’ production subsystem.
Difference equations of suppliers’ production operational process can be obtained according to the causality in Figure Work-in-process:
Work-in-process deviation:
Productivity:
Productivity fulfillment rate:
System inventory deviation:
Target system inventory:
TPL is responsible for replenishment and delivery decisions between suppliers and retailers. On the one hand, TPL sends requests for replenishment to suppliers in order to ensure proper inventory of the TPL warehouse (TPL-W). On the other hand, TPL needs to deliver products to the TPL distribution center (TPL-DC) near retailers in order to meet retailers’ demand. Figure
TPL replenishment and delivery subsystem causality diagram.
Formulas ( TPL total inventory level:
TPL-W replenishment point:
TPL replenishment capacity:
TPL-DC redelivery point:
TPL-DC inventory level:
TPL transportation inventory level:
( (
Retailers’ sales subsystem is relatively simple. Though TPL can adopt JIT delivery to retailers, as service level should be improved, retailers still need to keep a small quantity of safety inventory and this inventory level is related to the demand fluctuation level. Figure
Retailers’ sales subsystem causality diagram.
According to the retailer’s sales system causal diagram, the difference equations for retailers can be obtained as follows:
According to the aforementioned analysis, VMI&TPL-APIOBPCS system dynamics model is constructed as shown in Figure
VMI&TPL-APIOBPCS model causality diagram.
According to the aforementioned VMI&TPL-APIOBPC system dynamics model, the two different conditions with phase-step and random demands are investigated, respectively, and parameter settings are as follows. Production subsystem parameters settings. Referring to that of Disney and Towill [ Parameters settings of replenishment and delivery subsystem, Parameters settings of sales subsystem,
Then simulate the two models, VMI-APIOBPCS II and VMI&TPL-APIOBPCS, using Vensim, and run the test for 100 units of time (month).
The demand test functions CONS1 and CONS2 are both phase-step functions,
As shown in Figure
Comparison of production fluctuations in suppliers’ production orders.
System inventory levels. As shown in Figure Suppliers’ inventory level. Figure Comparison of downstream overall inventory level. In VMI-APIOBPCS model, the downstream inventory mainly includes retailers’ inventories. However, in the VMI&TPL-APIOBPCS model, the downstream inventory includes not only the retailers’ safety stock but also the inventory in TPL warehouse and distribution center. Figure
The comparison of system inventory level fluctuation.
The comparison of supplier inventory level fluctuation.
The comparison of replenishment batch fluctuation.
The comparison of downstream inventory level fluctuation.
From the aforementioned inventory analysis, we can know that after introducing TPL into VMI supply chain, although supply chains add an echelon, the downstream inventory level increases slightly, but the replenishment batch becomes smoother after TPL’s participation, thus effectively smoothing suppliers’ productivity and reducing supplier inventory levels.
What defines service level of retailers is the ratio between the retailers’ inventory level and customers’ demand. Figures
Service levels in the VMI operation mode.
Service levels in the VMI&TPL integrated operation mode.
With the deterministic demand, service level of the first retailer falls slightly, but the second retailer's service level increases substantially, and the overall average service level of retailers improves after introducing TPL. However, the response time of the system increases, because the system service level will not be enhanced till a long period of shortage.
The demand test functions, such as CONS1 and CONS2, are both phase-step functions.
Similar to the phase-step demand situation, supplier’s productivity is steadier apparently in VMI&TPL-APIOBPCS mode.
System inventory level. As Figure Suppliers’ inventory levels. As Figure Downstream inventory level: As Figure
Under the random demand and in the operation mode of VMI the first retailer’s average service level is 78.6% and the second retailer’s average service level is 40.4%.
In the VMI&TPL integrated operation mode, the overall service levels of the two retailers are 94.8%. It is clear that after introducing TPL the two service levels of retailers are improved under random demand; this benefits from the risk-sharing effect in centralized inventory after the introduction of TPL.
The complex simulations under phase-step demand and random demand show the following results as this study summarized from the follow-up interviews in practice.
First, VMI&TPL integrated operation mode can smoothen suppliers’ productivity under both phase-step demand and random demand as TPL introduced into VMI makes the whole system inventory levels smoother (see Figure
Fluctuation diagram of suppliers’ productivity.
Fluctuation diagram of system inventory level.
Fluctuation diagram of suppliers’ inventory level.
Fluctuation diagram of lower inventory level.
Second, VMI&TPL integrated operation mode can reduce the system inventory level significantly. Similarly, the response time of system inventory level reaching the steady-state in VMI&TPL-APIOBPCS model is relatively longer. Compared with under phase-step demand, system inventory level can be lower under random demand. This illustrates that the TPL centralized replenishment has a scale of economics and much risk pooling effects which can decrease the whole system inventory level [
Third, VMI&TPL integrated operation mode can improve average service level. Under phase-step demand, service level of the first retailer falls slightly, but the second retailer's service level increases substantially. As a contrast, service level of two retailers increases under random demand. On the whole, the service level under random demand is improved significantly than under phase-step demand (see Figures
The service level of VMI operational model under random demand.
The service level of VMI&TPL integrated operational model under random demand.
This paper constructs the VMI&TPL-APIOBPCS model after introducing TPL into VMI distribution based on VMI-APIOBPCS system dynamics model. The system performance of VMI&TPL integrated supply chain under phase-step and random demand is considered. The simulation analysis shows that though the supply chain is turned into a three-echelon structure from a two-echelon one TPL can effectively smooth the replenishment and delivery quantity between suppliers and retailers by goods collection, thus dramatically reducing the inventory level of the suppliers and the whole system, effectively smoothing the production rhythm of suppliers and improving the service level of customers.
Although system dynamics method can describe and simulate VMI&TPL integrated operational model, it lacks the optimization of TPL replenishment and delivery policy in this operation mode. As a result, it is necessary to optimize the TPL replenishment and delivery policy under various demands using mathematical programming and optimization theories, so as to enhance the study of VMI&TPL integrated operational model further.
This work was supported by the National Natural Science Foundation of China (no. 71102174, 71372019), Beijing Natural Science Foundation of China (no. 9123028, 9102016), Specialized Research Fund for Doctoral Program of Higher Education of China (no. 20111101120019), Beijing Philosophy & Social Science Foundation of China (no. 11JGC106), Program for New Century Excellent Talents in University of China (no. NCET-10-0048, NCET-10-0043), and Excellent Young Teacher in Beijing Institute of Technology of China (no. 2010YC1307).