Agent Based Models for Supply Networks
Information and Decision Sciences
University of Illinois at Chicago
May 24, 2010
Revolutionary Strategies and Tactics in Research Design
And Data Collection for E-Business Management Research
International Conference on Electronic Commerce 2003.
Advancements in information technology impact supply chain management in two ways:
electronic integration and electronic markets (Malone, Yates et al. 1987). Electronic
integration effect refers to strengthening existing relationships among partners of a
supply chain. Electronic market effect refers to a shift towards decentralization that
emphasizes dynamic and market-like relationships among partners of a supply chain.
Both effects have been noticed in the real world. For instance, Vendor Managed
Inventory and private B2B e-markets are examples of electronic integration effect. And
public B2B e-markets (exchanges) are examples of electronic market effect.
Malone et al. (1987) argued that market effect will dominate integration effect in the long
run. This argument is consistent with transaction cost theory (Williamson 1975), which
states that market structure carries higher transaction cost than hierarchical structure. As
advances in information technology lowers transaction costs, the disadvantages of a
market structure become less significant, and the structure will be more prevalent in
supply chains (Croom 2001).
The management challenge of supply chains (integrated) arises from various
uncertainties, such as demand fluctuation, information distortion, and capacity
constraints. The dynamic customer-vendor relationship in decentralized supply chain
adds another component to these uncertainties. In traditional and electronically
integrated supply chains, static long-term customer-vendor relationships are emphasized.
The stable relationships allow a chain leader to perform system-wide coordination so as
to control the uncertainties. In decentralized supply chains, the role of a chain leader
diminishes, thus supply chain dynamics (Forrester 1961) result from dynamic
interactions of participants. Little is known about the impact of this new type of
This study takes a step in this direction by examining impacts of marketization on several
aspects of supply chain dynamics, including bullwhip effect (Lee, Padmanabhan et al.
1997) and service level. The widely observed bullwhip effect refers to the phenomenon
that order variance increases up along a supply chain. The bullwhip effect has been
attributed to demand signal processing, rationing, order batching, price variation, demand
seasonality, and forecast error (Lee, Padmanabhan et al. 1997; Metters 1997). Service
level is a major performance indicator in supply chains (Beamon and Chen 2001). It
typically refers to the portion of customer demand that is fulfilled on time and measures
the effectiveness of a supply chain.
The impact of marketization was examined through comparisons of bullwhip effect and
service level between networked (marketized) and divergent (integrated) supply chains.
In divergent supply chains, each player has one and only one upstream partner, but can
have multiple downstream partners (Beamon and Chen 2001). In networked supply
chains, customers have choices on which vendor to use for each order they place. In
divergent supply chains, customers always place orders to a same vendor. Two
networked supply chain models are constructed, which differ in vendor selection
methods. In one model (network-random, NR) that is used as a baseline, customers select
vendors randomly. In the other model (network-inventory, NI), customers select vendors
who have the highest net inventory levels at the time of placing an order. Two models
are considered for the divergent structure too. One model (divergent-single, DS) contains
a single supply chain and the other (divergent-multiple, DM) contains multiple supply
chains. These two divergent models are in consideration of the two different levels at
which marketization may occur. At the industry sector level, marketization blurs lines
between different supply chains. In traditional and electronically integrated supply
chains, static long-term customer-vendor relationships are emphasized. Firms of a same
industry sector are divided into different supply “chains”. Although there are interactions
between different chains (Fransoo and Wouters 2000), the separation is so profound that
each chain is often managed and analyzed independently. At the supply chain level, a
single chain might break down into a network when the original chain leader is replaced
by multiple peer players (Croom 2001).
2 Agent Based Modeling
Agent-based modeling (ABM) is employed in this study. ABMs undertake a bottom-up
approach to modeling of individual agents and the way they act and interact; the overall
dynamics emerge from the collective interaction of heterogeneous agents. ABM is noted
to be useful for problems that can’t be mathematically modeled, or where analytical
solutions are not obtainable (Axtell 2000). Compared to equation-based modeling and
simulation, ABM is more suitable for complex problems that have high degree of
localization and distribution (Parunak, Savit et al. 1998). The Swarm1 agent based
modeling toolkit is used.
The supply network is modeled as a composite of a collection of retailers and vendors,
together with outside customers and suppliers. Each agent in the supply network is
defined by a number of attributes and actions that it takes, and the model incorporates
various delays, informational and physical, in its operation. So the supply chain itself is
defined. ABM can accommodate a much higher degree of detail and complexity than
other approaches. This advantage makes it an ideal tool for leveraging detailed real-world
data in studies of e-business phenomena. An agent-based model can be calibrated with
real-time data and provides an opportunity to experiment with "reality" in a way that is
difficult to do otherwise.
ABMs can be aligned with observed behavior and phenomena at varying levels. Models
can be ‘docked’ with analytical results by constraining the model to match assumptions
and constraints in the analytical model. Individual agent models can also be set up to
correspond to ‘rules’ followed by real-world supply network entities. Models can be
calibrated and validated using data at the agent level, or at aggregated-agent levels as in,
say, a vendor-group or at the level of the organization.
3 The Models
There are four types of agents used in this study. At the beginning of each period, a
customer agent generates demands and pass them to buyer agents (demands follow a
uniform distribution in the range of [10 20]). Buyer agents then perform three tasks in
the following order: accept inbound goods (if any), dispatch outbound goods (if any), and
place new orders (to vendor agents). Vendor agents then perform the same three tasks,
but with slightly different rules, in the same order. And finally, a supplier agent fulfills
vendor agents’ orders. Each model in the results reported here consists of one customer
agent, ten buyer agents, and one supplier agent. The number of vendor agents differ
among models. There are three vendor agents in model NR, NI and DM, but only one in
model DS. All buyer agents form a buyer stage, and similarly all vendor agents form a
vendor stage. Specific configurations of the models is shown in Figure 1.
In the current setup, both buyers and vendors adopt a modified order-up-to-inventory
replenishment policy. Order sizes are determined by the following two equations:
O = U – I – P + (D – S) (1)
U = (1 + IL + PL) * DMA + α * (1 + IL + PL) * DMV (2)
α: constant coefficient
D: demand of current period
DMA: moving average of demand
DMV: moving variance of demand
I: inventory at hand
IL: information lead-time
O: order size
P: orders in pipeline (orders placed but not yet received)
PL: physical lead-time
S: shipment of current period
U: order-up-to level
Figure 1: Configurations of Models
a: configuration of models NR and NI
Vendor 1 Buyer 2
Supplier Vendor 2 Buyer 5 Customer
4 Initial Results
For the results given here, each model was operated for 200 periods, and use zero values
for information delays (time for transmitting orders from originator to destination) (Chen
1999) (The models can take other values though). Orders are processed in a first-come-
first-serve basis together with a no-partial-shipment policy2. Shipping of a period stops
when all orders are fulfilled or inventory is insufficient to fulfill any order in queue.
Once an order is shipped, it is received by the originator after a physical delay (Chen
1999), which is modeled as a uniformly distributed random variable in a specifiable range
([0 3] for experiments presented here, unless otherwise noted).
Buyers and vendors handle inventory shortage differently. A buyer loses an order
permanently if he can’t immediately (in the same period that the order is received) fulfill
it. However, a vendor maintains orders that are not immediately fulfilled and tries to
fulfill them in following periods.
To alleviate effects of randomness, simulations for each model were replicated 30 times,
each time with a different set of random seeds. A separate random number generator was
used by the customer agent so that the demands remain identical across models. Initial
inventory levels are set for supply stages to increase comparability among models.
Prior to experimental runs, the coefficient α in equation (2) is fine tuned, for the buyer
and vendor stages, to minimization overall cost (Chen 1999). Buyers and vendors incur
costs in every period. Buyer costs include penalty cost, holding cost, and ordering cost.
Partial shipments can be an important factor, and are currently under study.
Vendor costs include holding cost and ordering cost. All costs are linear to the number of
units of products.
4.1 Bullwhip Effect
Bullwhip effect is been observed for all four models. Since there are multiple buyers and
vendors in our models, orders of agents that belong to a same stage are aggregated into a
stage order. Figure 2 shows that the degree of order variability increases up along the
supply chain in model NR. The two graphs in the figure shows that bullwhip effect
increases with physical lead-time.
Bullwhip effect can be quantified by ratio of order variance of adjacent stages (Metters
1997). Since our models have three stages, two such ratios are computed. Ratio 1 is
computed by dividing the variance of aggregated buyer stage orders by the variance of
aggregated customer demands. And ratio 2 is computed by dividing variance of
aggregated vendor stage orders by variance of aggregated buyer stage orders. To reduce
the effect of initial conditions, data from the first 50 periods is discarded.
Comparison between model NR and DS shows that marketization at supply chain level
reduces bullwhip effect. Model NR’s ratio 1 (5.53) is significantly smaller (p < 0.0001)
than that of model DS’ (6.47). Model NR’s ratio 2 (1.20) is marginally smaller
(p =0.0606) than that of model DS’ (1.2).
Comparison between model NR and DM shows that marketization at the industry level
has no significant impact on bullwhip effect. Neither ratio 1 nor ratio 2 is significantly
different between the two models. (See table 1 for all ratios)
Figure 2: Bullwhip Effect
A: Aggregated stage orders (model NR, physical delay [0 3], random seed =1):
0 50 100 150 200
B: Aggregated stage orders (model NR, physical delay [10 20], random seed =1)
0 50 100 150 200
Together, the comparisons between model NR, DS and DM shows that it is the change
from one vendor (as in model DS) to multiple vendors (as in model NR and DM), instead
of the change from static customer-vendor relationships to dynamic (as in model NR) that
reduces bullwhip effect.
This, however, is contingent on the vendor selection mechanism. Comparison between
model NI and DM shows that using inventory level as a vendor selection mechanism
marginally (p=0.1008) increases bullwhip effect between the buyer stage and customers,
but significantly (p<0.0001) reduces bullwhip effect between the vendor and buyer
Table 1: Ratio of stage order variances
Model Ratio 1 (stddev) Ratio 2
NR 5.53 (0.77) 1.20 (0.02)
NI 5.65 (0.60) 1.15 (0.03)
DS 6.47 (0.90) 1.22 (0.02)
DM 5.37 (0.65) 1.21 (0.02)
4.2 Service Level
Service level is measured by averaged (per period) buyer stage lost sales. Comparison
between model NR, DS and DM shows that that marketization at both supply chain and
industry level leads to lower service level (more lost sales, see table 2). Model NR’s lost
sales are significantly more than model DS’s (p<0.0001) and model DM’s (p=0.0217).
The vendor selection mechanism did not show a significant impact on service level.
Model NI’s lost sales are also significantly higher than that of model DS (p<0.0001) and
model DM (p=0.0219). Note that service level as measured by lost sales can be
dependent on the no-partial shipment policy used for the experiments here.
Table 2: Average lost sales per period
Model Lost Sales (stddev)
NR 54.4 (0.9)
NI 54.6 (1.6)
DS 51.9 (1.8)
DM 53.8 (1.0)
4.3 Inventory Level
Inventory level indicates efficiency of a supply chain. The more inventory a supply chain
carries, the less efficient it is. It was found that marketization at both supply chain and
industry level leads to lower vendor stage inventory levels (see figure 3a). Marketization
was not found to be of impact on buyer stage inventory levels (see figure 3b).
At individual agent level, the agent-based supply network tool developed in this study
can incorporate information lead-time, production lead-time, and physical
(transportation) lead-time. The tool can also model different production capacities,
inventory-replenishment rules, and vendor selection rules for upstream agents. Different
demand patterns can be modeled through the customer agent.
At the supply chain/industry level, the current tool can model a varying number of agents
and stages and with different configurations between stages. With model configurations
and parameters set in consultation with supply chain managers, face validation of models
and emergent effects can be examined. When aligned with real world data, the tool
allows supply chain managers to “experiment” with different business scenarios and
observe results. Models constructed can be aligned at individual, stage, and supply chain/
Figure 3a: Aggregated vendor stage inventory levels
0 10 20 30
Figure 3b: Aggregated buyer stage inventory levels
0 10 20 30
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