In a recently published article, my co-author and I investigate supply network topology and robustness against disruptions. In this post I provide details of the study that couldn't be published due to the word limit constraints in the journal.
Research Motivation
Supply disruptions have been an important managerial consideration for several years. Considerable attention is now being given to this issue, especially after recent high profile events such as the terror attack on the World Trade Center on September 11, 2001 and the disruption caused by hurricane Katrina. Supply chain implication of the terrorist attack on September 11, 2001 by giving the examples of adverse effect on Ford’s and Toyota’s operations. In the case of Ford, several assembly lines were stopped due to delayed deliveries from Canada and Mexico, resulting in a 13% decrease in Ford’s outputs during the fourth quarter of 2001 as compared to its production plan. Meanwhile, Toyota also had to halt its production as the supplies from one of its key supplier could not be delivered due to the supplier’s inability to receive a key component (steering sensors) that were expected to arrive from Germany.
Firms constantly face supply disruptions that adversely affect their performance. The delayed deliveries of microprocessor chips to Ericsson and the consequential $400 million losses incurred by the company due to a fire that affected the semiconductor plant of its key supplier is an often cited example of the costly implications of supply chain disruptions. In their recent news brief, Cadbury Schweppes reported that their market share of candy is expected to be adversely affected due to the disruption of production at one of their main candy facility in Sheffield, U.K. caused by floods in June. In July 2007, 70% of Japan's auto production was temporarily paralyzed for a week due to the disruptions in the supply of piston ring costing $1.50 a piece. The disruption was caused by a 6.8-magnitude earthquake that hit central Japan thereby damaging Riken Corp.’s production plant, the supplier that makes custom piston rings for most of the car makers in Japan. Toyota Motor Corp. had to halt production for about one and a half days at all 12 of its domestic plants, causing a loss of output of at least 25,000 vehicles, with 60% of these earmarked for exports. Honda Motor closed a plant that produces the popular Civic and Fit models for a day, resulting in the loss of 2,000 vehicles. Nissan Motor Co. halted operations on several production lines at all four of its plants for almost two days. Mitsubishi Motors Corp., Mazda Motor Corp., Suzuki Motors Corp. and Fuji Heavy Industries Ltd., all had to stop or slow down their production for a day or two.
Several supply networks exhibit incredible robustness in the presence of disruptions while others fail to survive random failures or targeted attacks. Supply chain practices such as redundancy and flexibility play an important role in determining the resilience and robustness of a supply network against disruption. Yet, the growing understanding of the importance of network characteristics in determining the error tolerance of the world wide web , Internet, and metabolic networks raises the question: Are resilience and robustness of supply networks encoded in their topologies? Firms such as American Airlines, McDonald’s Corp, Limited Brands and Ace Harware Corp., have characteristically different supply networks, which make their levels of resilience and robustness to random failures and targeted attacks to be considerably different. While the resilience of a supply network is its ability to come back to normalcy after disruption, the robustness of a supply network focuses on the ability of the network to withstand disruptions and continue normal mode of operations as much as possible. It can be argued that the inherent robustness of the supply network lends a significant contribution to the resilience of a supply network. In this study we focus on the robustness of a supply network and examine whether the topology of a supply network explain its robustness in the presence of random failures and targeted attacks.
Research Design
We study this system by building a multi-agent simulation model. The use of multi-agent simulation fits within the complex adaptive systems (CAS) perspective of analyzing organizational issues. CAS are characterized by macro-level emergent and adaptive properties that are not exhibited by the individual agents at the micro-level. Several tenets underpin supply networks as complex adaptive systems. The foremost is the adaptive nature of supply networks, since they continually evolve in dynamic environments. Secondly, as CAS, supply networks exhibit self-reinforcing positive and negative feedbacks that invoke path dependencies. Emerging phenomena originating in one part of the network, in effect, propagate forward and backwards throughout the network driving strategic decisions. Multi-agent simulation provides an ideal approach to examine various issues underlying the research objectives of this study. Using this approach we are able to capture the complexities and dynamics associated with network topologies and examine the evolutionary nature of choices made by firms within these supply networks. The multi-agent simulation method enables an examination of patterns emerging at the network level due to the micro level decisions made by individual supply chain agents. It also allows an investigation of the impact of failure of a node (representing a supply chain entity) on the overall behavior of the supply network. We adopt the agent-based modeling framework and generate networks by using the underlying principles of random networks and scale-free networks. Some domain constraints related to supply networks are considered in the agent-based model to eliminate networks that are impractical and lack conceptual validity. We use the NetLogo modeling platform for developing the agent-based model. The details regarding the agent-based model and the experimental design are presented in the following sub-sections.
Agent-Based Model
Our model extends the basic Beer game pby allowing for more complex network topologies. The Beer game has four players - factory, distributor, wholesaler and retailer – linked in the form of a serial supply chain. Using the agent based model framework, we model the stock and flow structure of the system and the decision rule used by managers. Once the validity of the results for the basic beer game structure was established we extended it by supporting the existence of any number of distributors, retailers, and customers. The model allows the network to evolve until a specified number of nodes (i.e. factories, distributors, warehouses and retailers) are created. During the evolution, we can specify the logic by which the nodes attach to other nodes. We subject the network formation process with certain conditions to ensure that the resulting network represents a supply network. In particular, we consider a single factory who can supply to warehouse, distributors or retailers depending upon the specific network topology that is under consideration. The supplies to the factory are modeled with a lead time without explicitly modeling the raw materials and component suppliers. In our network considerations, the end customer demand is always satisfied from a retail location. This condition is included in the model, since otherwise in scale-free network it will make several nodes redundant as the customer demand would link with those nodes that are already highly connected.
Since our factory, distributors, warehouses, and retailers can have more than one player buying from them we had to add some extra rules that are not present in the basic beer game. The players satisfy the orders they receive on a first-come first-serve basis, regardless of the amount in the order. If an order cannot be completely filled then the player fills as much of the order as it can and fills the rest when it receives new inventory (in the case of factory when it completes the manufacturing process). The quantity that a factory, distributor or wholesaler is unable to fulfill is treated as backorder. The shortages at the retail location are lost orders. Another difference from the basic Beer game is in the initial conditions. In the original Beer game all players start with the same inventory since each one only has one customer. In our model the initial inventory of each player is proportional to how many other players buy from it, so a player with 2 customers will start with an inventory that is twice as large as that of a player who only has 1 other player that buys from him.
Two players that are connected directly to each other, where one of them buys from the other one, are said to be at a distance of 1. More generally, the distance between any pair of players is the smallest number of edges which one would need to traverse in the graph to go from one node to the other. The calculation of these values is the classic max-flow problem in graph theory that can be solved using Dijkstra’s algorithm. Our model implements Dijkstra to find the shortest path between all pairs of nodes and then uses these values to determine the average path length and the largest connected component.
Using this framework, we generate supply network topologies. It has been observed that complex networks are characterized by large degree of clustering. The complexity inherent in supply networks suggest that these networks too would be characterized in terms of higher clustering coefficients than random networks. While studies have begun to consider the scale-free nature of supply networks, rigorous empirical validation of the topological nature of supply networks is yet to be done. Therefore, for the purpose of generalizability and in concert with other studies that examine topological issues, we consider two types of network topologies: (i) scale-free topology (in line with the complex nature of supply networks) and (ii) random networks (these most widely studied network topology are considered for comparison). With the overall framework and constraints presented earlier, scale-free networks were generated by using the preferential attachment logic and the random networks are generated by following a random attachment of nodes. Within each topological type, we randomly generate 10 network topologies for in-depth examination.
To generate a new network we start with one node, the factory, and then create new nodes one at a time connecting them to existing nodes. In the random topology each new node is connected to one randomly chosen existing node where all existing nodes have equal probability of being chosen. In the preferential attachment topology we follow the standard algorithm and connect each new node to one existing node but now each node's probability of being chosen is directly proportional to the number of edges that it has. For example, if there are three nodes and they have 1, 2, 3 edges respectively then each will chosen with probability 1/2, 2/6, 3/6, respectively. We measure the network characteristics, i.e. average path length, clustering coefficient, size of the largest connected component and maximum distance between nodes in the largest connected component by using the standard conceptual and mathematical definitions.The conceptual definitions are as follows:
Average path length: The average path length presents an approach to characterize the spread of a network by calculating the average distance between any pair of nodes.
Clustering Coefficient: The clustering coefficient presents an approach to evaluate the probability that two nodes are nearest neighbors of each other.
Size of the largest connect component: A connected, isolated subgraph or cluster of a network is defined as its component. We measure the size of the largest component in a network. We also measure the maximum distance between nodes in the largest connected component.
In an agent based model all the facilities as well as the customers (modeled as a random demand function that sets the value of demand at every time step as a number between 0 and 8) are treated as agents. We set the number of agents to 30. To ensure comparability of these topologies we ensure that each topology consists of 18 facilities comprising of one factory, twelve retail locations that are directly facing the customer demand and five intermediaries acting as distributors or warehouse. The choice of the scale (i.e. one factory, five intermediaries and twelve retailers) is arbitrary and the model can be scaled to higher and lower number of nodes. The specific network topologies considered in the study are presented below.
Note: Square represents manufacturing plant, circle represent distribution center/ warehouse and pentagon represents retail outlets that are in direct contact with the customers
*The following ten network topologies were generated by using the algorithm for preferential attachment:
**The following ten network topologies represent random networks:
In the event when a facility fails due to random failure of targeted attack, the purchase orders and deliveries arriving to the facilities accumulate until the facility becomes functional. Once the facility is operational, the purchase orders and deliveries are attended to on a first-come first-serve basis.
The timing in our model is the same as in the original Beer game. The unit of analysis is in weeks and all facilities take decisions on a weekly basis. Both orders and deliveries have to spend one week in transit and the total replenishment cycle (from order to receipt) is 4 weeks.
Experimental Design
The development of the simulation model and the analysis of the data gathered from simulation runs follow the systematic approach suggested in literature. To ensure a close correspondence to theory, we choose the parameter values to be identical to the original beer game. The overall experimental design and parameters used for the study are reported in table 1. We ran the agent based simulation model for 105 time ticks. These 105 time ticks correspond to 105 weeks, constituting 2 years of data of decision making and performance in a supply network context. Twenty replications of simulation runs are used and we average the weekly data obtained from these 20 replications. In total 25 experiments (with 20 replications of each experiment) were conducted for each topology (i.e. a total of 500 experiments for the 20 network topologies considered in the study) using 3 instances of probability of random failures (0, 5%, 10%), 3 instances of probability of targeted attacks (0, 5%, 10%) and 3 instances of severity of disruptions measured in terms of the downtime of the affected facility (1 week, 2 weeks, 3 weeks).
We examine the robustness of individual topologies by undertaking paired sample t-test for each network topology considered in the study. The performance of a network in the absence of both random failures and targeted attacks is used as the base case. The performance of all twenty network topologies considered in this study in the presence of varying degrees of random and targeted disruptions are compared with the base case. In total 24 paired sample t-tests (for each disruption scenario explained in the experimental design) were conducted for each topology. Robustness of a network topology against disruptions is gauged by a non significant difference in the mean for the performance measures as reported by the paired sample t-test (i.e. p-value > 0.05). The topologies that exhibit significant difference of performance (i.e. p-value ≤ 0.05) are considered as vulnerable.
As a next step, we utilize the information from the paired t-test and categorize the topologies as robust (coded as 1) or vulnerable (coded as 0). We use binomial logistics regression analysis to examine the relationship between network characteristics, i.e. average path length, clustering coefficient, size of the largest connected component within the network and the maximum distance between nodes in the largest connected component, and the robustness of supply network against disruptions. First, we undertake the binomial logistics regression analysis for the entire sample of network topologies considered in this study. We use the topology type (categorical variable denoting scale-free or random network) as a control variable. Subsequently, we split the sample into scale-free and random-networks and investigate the hypothesized relationships in these network topologies separately. For each topology, we use the data collected from the 24 disruption scenarios based on the probability of random failures, probability of targeted attacks and severity of the facility shutdown.
Results
The results for the overall sample present a compelling evidence of the association between network characteristics and robustness of supply networks. We find that a unit increase in average path length and clustering coefficient substantially increase the odds of making the supply network vulnerable from the point of view of inventory levels, backorders and total costs. For every unit increase in the size of the largest connected component the odds of having a robust supply network from the perspectives of inventory levels, backorders and total costs increase by about 1.6 times, 3 times and 2.6 times respectively. A unit increase in the maximum distance between nodes in the largest connected component increases the odds of a robust supply network from backorders and total cost perspective by a factor of 8.7 and 10.2, respectively. The significant association of the categorical control variable (1: Scale-free network; 2: Random network) also deserves some discussion. The results show that a scale-free network is relatively more robust from the inventory perspective, however, when viewed from the backorders and total cost perspectives, the odds of a random network being robust than scale-free networks are as high as 5.6 times and 2.9 times respectively.
We also conducted separate analyses for the data representing scale-free and random networks.
For scale-free networks we find that the average path length, clustering coefficient and size of the largest connected component are significantly associated with deterioration of inventory levels in the presence of disruptions. We do not find support for the association of maximum distance between nodes in the largest connected component with deterioration in inventory levels in the presence of disruptions. All network characteristics considered in this study are significantly associated with robustness of supply networks evaluated from the perspective of deterioration in backorders in the presence of disruptions. We do not find evidence for the association of average path length and maximum distance between nodes in the largest connected component with deterioration of total costs in the supply network in the presence of disruptions. However, clustering coefficient and the size of the largest connected component were significantly associated with robustness from total cost perspective.
The results suggest that a unit increase in clustering coefficient substantially increase the odds of making the supply network vulnerable. A unit increase in average path length also substantially increase the odds of making the supply network vulnerable from the point of view of inventory levels and backorders. As the size of the largest connected component of scale-free networks increase by one unit the robustness of the network from inventories, backorders and total costs perspectives increase by almost 2, 2.7 and 5 times, respectively. While the maximum distance between nodes in the largest connected component is not significantly associated with inventory and total cost based robustness measures, a unit increase in this variable increases robustness from backorders perspective by almost 5 times.
For random networks the results indicate weak association of clustering coefficient and maximum distance between nodes in the largest connected component with robustness of supply networks in terms of inventory levels. The results do not support an association of average path length and size of the largest connected component with robustness in terms of inventory levels. Relationships for robustness, measured in terms of backorders and total costs, were supported. We find that similar to scale-free networks, a unit increase in clustering coefficient substantially increases the odds of vulnerability of random networks against random failures and targeted attacks. A unit increase in average path length substantially increases the odds of vulnerability from backorders and total cost perspectives. A unit increase in the size of the largest connected component increases supply network robustness, viewed from backorders and total cost perspectives, by a factor of 3.2 and 2.1 times, respectively. A unit increase in the maximum distance between nodes in the largest connected component was found to increase the odds of a robust supply network by 3.7 times, 14.1 times and 16.9 times when the robustness is evaluated from inventory, backorders and total cost perspectives respectively.
Managerial Implications
The results of this study present important managerial guidelines to build a robust supply network. Along with redundancy and flexibility, we highlight the role played by supply network topology in characterizing its robustness. The findings motivate a reassessment of supply chain structure from a topological perspective with an explicit consideration of network characteristics. Instead of relying on security professionals, business continuity planners and insurance professionals, risk management and business continuity should be a part of the strategic initiatives of a firm. From a supply chain context, network design forms an important strategic consideration. Our study sheds light on the salient aspects of network design that play an important role in building a robust supply network.
Based on the findings from this study we emphasize that long average path lengths between nodes in a supply network are detrimental for its robustness against disruptions. Shorter average distances between nodes in the network allow faster propagation of products and information and thus aid in enhancing the responsiveness of supply network in the event of disruption. A clustered form of supply network has been widely adopted by several firms due to its advantages in terms of consolidation, efficiency and quick response. The significant association of the size of the largest connected component with robustness of supply networks provides motivation for formation of large sub-structures in the supply network. However, the results also suggest careful examination of the nature of connection between nodes in these clusters as well as in the overall supply network. Specifically, a negative association between clustering coefficient and robustness of supply networks suggest a caution against forming cliquish structures. Managers ought to give due cognizance to this issue and carefully balance the advantages of a clustered configuration of facilities in the supply network with the potential disadvantages in the presence of disruptions. Finally, the reach of a facility in the largest sub-structure plays a positive role in enhancing the robustness of a supply network.
For firms that are in the process of creating a supply network, it is useful to take these factors into account. At the same time for supply networks that are evolving in a complex fashion it is important to constantly keep track of the overall network in light of its basic characteristics. A topological perspective when combined with the aspects of flexibility and redundancy can greatly enhance the robustness of supply networks. By presenting the association of individual network characteristics with robustness of supply networks, we present an approach towards a carefully nuanced supply network design.
The study’s findings motivate the need for an evaluation of supply network robustness from multiple outcome metrics. It is evident from the results that even though a topology is robust when viewed from the inventory perspective it could be vulnerable when examined from the perspectives of backorders and/or total cost. Likewise, a network that is robust from the perspectives of backorders could be vulnerable when evaluated from the perspectives of inventory and total costs. It is therefore important to give consideration to various performance metrics to get a better understanding of the robustness of the supply network.
Source: Nair, A. and Vidal, J. M. (2011). Supply Network Topology and Robustness against Disruptions: An investigation using Multiagent Model. International Journal of Production Research, Special Issue: “Multi‐agent and Holonic Techniques for Manufacturing Systems: Technologies and Applications,” 49(5), 1391-1404.