Based on the local decision perspective and the global decision perspective, considering the limitation of supply capacity and prohibiting returns, the system dynamics method is used to establish a nonlinear supply chain system model. We use the
Supply chain management has always been a concern of enterprises. To help enterprises better implement effective supply chains, Pittiglio, Rabin, Todd & McGrath (PRTM) and AMR Research (AMR) led the establishment of the Supply Chain Council (SCC) in 1996 and released supply chain operations reference (SCOR) model, realized the transformation from function-based management to process-based management, and improved the performance of the supply chain. With the emergence of cloud computing, Internet of things (IoT), artificial intelligence (AI), and other new information technologies (IT), supply chain management has a new background and requirements. New technologies can change the way of communication among the supply chain members. Before the 1960s and 1970s, due to technical limitations, the rapid flow and sharing of information cannot be achieved. In the early traditional SC model, each node enterprise is responsible for its inventory control, production, or distribution ordering activities, and each echelon only has its immediate customer information [
Gradually, some new supply chain models are formed and applied in practice. Among them, the more commonly used are the vendor-managed inventory (VMI) model and the third-party logistics management inventory (TMI) model [
The development of science and technology has promoted the vertical integration of the supply chain, and the management concept has also changed. More and more decision makers have magnified the decision perspective, and supply chain management presents the trend of vertical integration. More and more decisions are made based on local alliances and the whole supply chain. Also, there are many different types of uncertainties in the SC, such as changes in market demand, limited production capacity, the delay of transportation time, and so on [
The research on the dynamic behavior of supply chain systems started in the early 1960s. It first appeared in the classic work “Industrial Dynamics” by Forrester, which is the simplest manifestation of the dynamic complexity of supply chain systems [
In the early days of the concept of dynamic behavior emergence, many research studies were based on the inventory and order based production control system (IOBPCS) and analyzed as a linear system. Towill [
With the deepening of research, it is found that based on various assumptions, for example, orders at all levels of the supply chain are satisfied, regardless of inventory constraints, and the supply chain system is regarded as a simple linear system model. It leads to the inconsistency between the research results and the actual situation and fails to reveal the nonlinear phenomena except the bullwhip effect. Therefore, more and more research studies have been conducted to construct nonlinear system models to study the supply chain. Mosekilde and Laugesen [
In the existing research on the complex dynamic behavior of the supply chain, many scholars used hypotheses to simplify the research objects and used the linear model to analyze the bullwhip effect in the supply chain. At the same time, many scholars consider practical factors such as prohibiting returns and limited supply capacity, constructing nonlinear dynamic models, and studying the impact of different demand scenarios, production models, and decision parameters on the stability of the supply chain, which has achieved rich results.
The analysis found that most studies can be divided into the category of local decision-making perspectives. However, in the existing research, no research mentions the decision-making perspective, nor does it study and analyze the complex behavior of the supply chain under different decision-making perspectives. In this paper, the idea of a decision perspective is introduced. Based on the local decision perspective and the global decision perspective, the difference equations and simulation models of the system are established, respectively, and the simulation experiments are carried out to compare and analyze the complex dynamic behavior of the supply chain inventory system from different perspectives. At the same time, the effect of safety stock parameters on the complex dynamic behavior of the supply chain is analyzed.
The supply chain is based on a third-party logistics management inventory model (TMI) and includes a supplier, a retailer, and a third-party logistics service provider (3PLP). The operation process of the supply chain is shown in Figure
The TMI-SC operation flowchart.
To facilitate model description, the following relevant notations of model variables and parameters are introduced (Table
Model variables and parameters.
Notation | Description | |
---|---|---|
Variables | The actual demand of consumers in period | |
The forecast demand in period | ||
Retailer’s initial inventory in period | ||
Retailer’s end-of-cycle inventory in period | ||
Retailer’s arrivals in period | ||
Retailer’s sales in period | ||
Retailer’s order quantity in period | ||
Distribution center’s shipments in period | ||
Distribution center’s initial inventory in period | ||
Distribution center’s end-of-cycle inventory in period | ||
Distribution center arrivals in period | ||
The in-transit inventory of the distribution center in period | ||
The replenishment volume of the distribution center in period | ||
Warehouse shipments in period | ||
Warehouse’s initial inventory in period | ||
Warehouse’s end-of-cycle inventory in period | ||
Warehouse arrivals in period | ||
The initial inventory of system from the perspective of decision making in period | ||
The end-of-cycle inventory of system in period | ||
The replenishment of the system of system from the perspective of decision making in period | ||
Supplier’s WIP inventory in period | ||
Parameters | The expected WIP inventory level of the supplier | |
The adjustment coefficient of inventory | ||
The adjustment coefficient of WIP inventory | ||
Transport lead time | ||
Production lead time | ||
Safety inventory coefficient of the retailer | ||
Safety inventory coefficient of the distribution center | ||
Safety inventory coefficient of the system from the perspective of decision making. When | ||
Retailer’s expected inventory level | ||
Distribution center’s expected inventory level | ||
The expected inventory level of system from the perspective of decision making. When |
For the superior node of the supply chain, the demand forecast is based on the actual demand of terminal consumers. This forecasting method can reduce the amplification effect of orders in the supply chain, which is more reasonable than the demand forecasting based on the orders of subordinate nodes. The simple exponential smoothing method is often used in demand forecasting and has achieved good results. Therefore, this paper uses this method to forecast the demand. The prediction expression is shown in equation (
The study uses automated pipeline, inventory, and order based production control system (APIOBPCS), a commonly used method of production control. The specific meaning of APIOBPCS is that the order quantity (or production plan) is equal to the sum of the predicted demand quantity, the adjustment quantity to the actual inventory level, and the adjustment quantity to the inventory in transit (or work-in-process (WIP) inventory). Most of the existing literature on the complex behavior of the supply chain has adopted this strategy [
Based on the local decision perspective of the supply chain, the actual inventory of the warehouse-distribution system is considered as the supplier’s finished product inventory. The production strategy is expressed as follows:
Based on the global decision perspective of the supply chain, the actual inventory of the entire supply chain is considered as the supplier’s finished product inventory. The production strategy is expressed as follows:
The supplier, the retailer, and the distribution center adopt periodic inventory strategy. The strategy is to replenish at regular intervals, each time to the target inventory level.
From the local decision perspective, the initial inventory
From the global decision perspective, the inventory of the entire supply chain system is expressed as follows:
Due to the production delay, the following formula can be obtained:
The expression of the supplier’s WIP inventory is given by
The expression of the replenishment quantity of the distribution center is shown in the following equation:
The expression of the distribution center’s inventory is given by equations (
Among them, the distribution center’s shipments in period
Due to transportation delay, the following formula can be obtained:
The retailer is prohibited from returning goods, so the retailer’s order quantity is expressed as follows:
The expression of the retailer’s inventory is given by
The replenishment of the retailer can be quickly obtained from the distribution center. That is, the replenishment notice is issued at the end of the period, and the replenishment can be received at the beginning of the next period. So, the following expression can be obtained:
At the same time, the retailer’s sales and consumer demand satisfied the following formula:
Using the discrete system
For retailers, the information input of the inventory system is customer demand, and the information output is order quantity. For the distribution center, the information input of the inventory system is customer demand, retailer’s order quantity, and inventory in transit, and the output information is the replenishment quantity. The block diagrams of the retailer and the distribution center are shown in Figures
The block diagram of the retailer from the local decision perspective.
The block diagram of the distribution center from the local decision perspective.
Based on the perspective of local decision making, for the production-warehouse system, the production-warehouse system and the distribution center are regarded as a combined system, and retailer inventory is not taken into account. The block diagram of the production-warehouse system is shown in Figure
The block diagram of production and warehouse systems from the local decision perspective.
Based on the perspective of global decision-making, for retailers and distribution centers, the operation process, information input, and output of the inventory system are unchanged, so the block diagram is the same as that based on the local decision-making perspective. For the production-inventory system, the inventory of the entire supply chain including the retailer’s inventory is used as the basis for decision making, and the input information is customer demand, distribution center replenishment volume, distribution center inventory, and retailer inventory. The block diagram of production and warehouse systems from the global decision perspective is shown in Figure
The block diagram of production and warehouse systems from the global decision perspective.
According to the models established above based on the local perspective and the global perspective, combined with the unitary transformation theory, the block diagrams of the system under the two models are shown in Figures
The block diagrams of the system under the global decision perspective.
The block diagrams of the system under the local decision perspective.
The largest Lyapunov exponent (LLE) is a standard to measure the stability of the system. Many studies use it to judge the stability of the system. When LLE is less than or equal to 0, it indicates that the system is in a stable, periodic, or quasiperiodic state. It is an ideal state for ordering decisions. When LLE is greater than 0, the system is in a chaotic or quasichaotic state. In the paper, the Wolf reconstruction method is used to calculate the largest Lyapunov exponent (LLE) value of each node or combined system to judge the stability of the system. The calculation principle of this method is as follows.
Suppose the time series is
Based on the constructed model and block diagrams, we plan to further study the impact of different ordering strategies and inventory management strategies on the nonlinear supply chain system with restrictions on the prohibition of returns and limited inventory from different perspectives. Previous studies have shown that relevant order decision parameters such as inventory adjustment parameters have an important impact on the dynamic characteristics of the system.
We designed a simulation experiment under various order parameter combinations in the decision space
In general, the decision makers pay more attention to inventory adjustment, and the adjustment parameters are less than 1; this article assumes the value range of these two inventory adjustment coefficients is
According to the selection of the aforementioned decision parameter range, use Matlab to carry on the simulation experiment. Suppose that in this research supply chain, the production delay is 1, the transportation delay is 2, and the safety inventory coefficient of the retailer is 2. That is,
This article combines practical issues and considers two demand scenarios including the random demand that meets the normal distribution and the random demand that meets the uniform distribution. Both of these demand scenarios are more commonly used in real-world problems. The latter are more stringent and have higher requirements for supply chain response.
Firstly, based on a global perspective, under the scenario of random demand obeying normal distribution, we use the model shown in Figure
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from the global decision perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from the global perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from the global perspective when
By comparing and analyzing Figures
In addition, based on the global decision perspective, under the setting of different demand scenarios and the combination of safety stock parameters, the LLE of each node and combination system under 1275 adjustment parameter combinations was calculated separately. It is found that, based on the perspective of global decision making, there are 374 adjustment parameter combinations that can keep each node and combination system of the supply chain in a stable state in the case of positive distribution demand and
The number and optimal combination of reasonable adjustment parameter combinations under the scenario of random demand obeying normal distribution from the global decision perspective.
Combination of safety stock parameters | Number of reasonable adjustment parameter combinations | Optimal combination |
---|---|---|
[1, 4] | 374 | [0.38, 0.3] |
[2, 5] | 746 | [0.24, 0.14] |
[3, 6] | 1109 | [0.16, 0.14] |
Then, we change the demand scenario and perform simulation under the scenario of random demand obeying uniform distribution to obtain the contour map of each node under different combinations of safety stock coefficients, as shown in Figures
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from the global perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from the global perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from the global perspective when
As can be seen from Figures
In addition, among the 1,275 kinds of adjustment parameter combinations, for different safety stock parameters, the number of parameter combinations that can keep each node of the supply chain and the combined system in a stable state is 146, 334, and 532 in order. Among these parameters, when
The number and optimal combination of reasonable adjustment parameter combinations under the scenario of random demand obeying uniform distribution from the global perspective.
Combination of safety stock parameters | Number of reasonable adjustment parameter combinations | Optimal combination |
---|---|---|
[1, 4] | 146 | [0.18, 0.06] |
[2, 5] | 334 | [0.32, 0.26] |
[3, 6] | 532 | [0.24, 0.22] |
Based on the local perspective, under the scenario of random demand obeying normal distribution, using the model shown in Figure
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from local perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from local perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying normal distribution from local perspective when
It can be seen from Figures
In addition, based on the local decision perspective, under the scenario of random demand obeying normal distribution, for different safety stock parameters, there are different numbers of reasonable decision-making schemes in the entire decision-making area. When
The number and optimal combination of reasonable adjustment parameter combinations under the scenario of random demand obeying normal distribution from local perspective.
Combination of safety stock parameters | Number of reasonable adjustment parameter combinations | Optimal combination |
---|---|---|
[1, 4] | 380 | [0.38, 0.3] |
[2, 5] | 775 | [0.18, 0.06] |
[3, 6] | 1156 | [0.16, 0.14] |
Then, based on the local perspective, we change the demand scenario and perform simulation under the scenario of random demand obeying uniform distribution to obtain the contour map of each node under different combinations of safety stock coefficients, as shown in Figures
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from local perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from local perspective when
LLE diagram of supply chain nodes under the scenario of random demand obeying uniform distribution from local perspective when
As can be seen from Figures
In addition, for the three combinations of safety stock parameters considered, there are 174, 361, and 542 reasonable adjustment parameter combinations that can keep the supply chain nodes and combination system in a stable state. In these reasonable decisions, when
The number and optimal combination of reasonable adjustment parameter combinations under the scenario of random demand obeying uniform distribution from local perspective.
Combination of safety stock parameters | Number of reasonable adjustment parameter combinations | Optimal combination |
---|---|---|
[1, 4] | 174 | [0.2, 0.12] |
[2, 5] | 361 | [0.16, 0.14] |
[3, 6] | 542 | [0.24, 0.22] |
According to the above analysis, it can be found that, on the whole, regardless of the local decision perspective or the global decision perspective, as the safety stock factors increase, the stability of each node of the supply chain gradually increases, and the requirements for adjustment parameters gradually decrease, that is, more adjusting parameters can keep the supply chain inventory system in a stable state. Regardless of the safety stock factors and the decision perspective, in the entire supply chain, the distribution center has the highest requirements for adjustment parameters, that is, the decision area of adjustment parameter where the distribution center is unstable is the largest. At the same time, based on the perspective of global decision making, a lower overall inventory of the supply chain can also keep the nodes in the supply chain and the system under the perspective of a stable state. At the same time, an interesting phenomenon can be found. When only considering the quantity of goods, when the system composed of multiple nodes is in a stable state, the nodes in it may be in an unstable state. This is also a manifestation of the complexity of the system’s dynamic behavior.
In order to more intuitively analyze the changes in inventory and the impact of demand types, adjustment parameters, and safety stock factors on the ability of each node of the supply chain and the system from different decision perspectives, a reasonable combination of adjustment parameters is selected for simulation experiments under different demand types and safety stock factors. This adjustment parameter combination can make the supply chain node and system in a stable state, and its average value is minimum.
In order to analyze the influence of different decision-making perspectives on the complex behavior of the supply chain, the inventory change chart of the nodes in the supply chain and the system under the perspective from the local perspective and the global perspective is drawn, as shown in Figures
The initial inventory changes of the retailer in a stable state under the scenario of random demand obeying normal distribution from different perspectives.
The initial inventory changes of the retailer in a stable state under the scenario of random demand obeying uniform distribution from different perspectives.
The initial inventory changes of the distribution center in a stable state under the scenario of random demand obeying normal distribution from different perspectives.
The initial inventory changes of the distribution center in a stable state under the scenario of random demand obeying uniform distribution from different perspectives.
The initial inventory changes of the system from the perspective of decision under the scenario of random demand obeying normal distribution from different perspectives.
The initial inventory changes of the system from the perspective of decision under the scenario of random demand obeying uniform distribution from different perspectives.
It can be seen from Figure
It can be seen from Figures
For the combined system under the decision perspective, regardless of the state of the goods, as can be seen from Figures
Under the scenario of random demand obeying uniform distribution, when the supply chain system is in a stable state, Figure
In the supply chain, the stability of production has a great influence on the cost, and the production system produces according to the order quantity of the warehouse. In order to analyze the fluctuation of production in a stable state more intuitively, we draw the production fluctuation chart, as shown in Figures
The production fluctuation under the scenario of random demand obeying normal distribution from different perspectives.
The production fluctuation under the scenario of random demand obeying uniform distribution from different perspectives.
As can be seen from Figures
Based on the needs of practical problems, this paper introduces the global decision-making thoughts in order to adapt to the trend of supply chain integration and puts forward different decision-making perspectives of supply chain inventory system management. Based on the proposed local decision perspective and global decision perspective, the complex dynamic behavior of the supply chain inventory system is studied. At the same time, the influence of the safety inventory setting on the dynamic behavior of the supply chain inventory system is studied.
The study found that, based on the perspective of global decision making, choosing a reasonable adjustment parameter scheme can reduce the overall inventory level of the supply chain. The overall inventory volatility has increased slightly, but it does not affect the stability of the overall inventory. When the safety stock parameter combination is [1, 4], based on the global decision perspective, the overall stock level is about 425. Based on the local decision-making perspective, the combined system inventory level under the perspective is 446. Based on a global decision perspective, the overall inventory can be reduced by about 180. When the safety stock parameter combination is [2, 5], the overall stock can be reduced by about 118. When the safety stock parameter combination is [3, 6], the overall stock can be reduced by about 159. At the same time, based on different decision-making perspectives, the status distribution maps of each node or combination system under different demand scenarios and the most reasonable parameter settings are obtained.
On the whole, regardless of the local decision perspective or the global decision perspective, as the safety stock parameters increase, the stability of each node of the supply chain gradually increases, and the requirements for adjustment parameters gradually decrease. The analysis also found that each node has a different sensitivity to the adjustment parameters. Changes in adjustment parameters have little effect on the retailer. Under different scenarios and decision parameters, the retailer is in a stable state in almost the entire decision area. However, changes in adjustment parameters have a significant impact on the distribution center. In addition, the study also found that, whether based on a local decision perspective or a global decision perspective, the overall inventory level is in a stable state and maybe in an unstable state for internal nodes. This has important guiding significance for actual operation.
Although this paper selects three safety stock parameter combinations for research and obtains some effective conclusions, it does not study the entire safety stock parameter decision area. In the follow-up, we hope that interested scholars will conduct further research on the impact mechanism of safety stock parameters on the complex dynamic behavior of the supply chain.
The data used are the data obtained by simulation.
The authors declare that they have no conflicts of interest.
This study was supported by the National Key Research and Development Program of China (grant no. 2019YFB1706101) and Chongqing Technology Innovation and Application Demonstration Project (grant no. cstc2018jszx-cyzdX0143).