SimRisk: An Integrated Open-Source Tool for Agent-Based ...

3 Background
3.1 Related Works
Existing stochastic analysis techniques for supply chains include stochastic simulation, deductive
proof, and stochastic programming. Stochastic simulation works by simulating operations of a supply
chain under different sceneries and then applying statistic methods to the simulation results.
Stochastic simulation is widely used for a variety of applications such as risk analysis and performance
evaluation (cf. [Kleijnen, 2005]). Although stochastic simulation generally scales well, it is
also prone to statistic errors; in deductive proof, one can prove stochastic properties of a supply
chain using an array of methods, such as Bayesian networks, Fuzzy logics, and Hybrid networks
(cf. [Pai et al., 2003]). Deductive proof requires a strong theoretical background. Since deductive
proof is often done by hand, it is not suitable for large-scale supply chains; stochastic programming
approach models the design of a supply chain with uncertainty as an optimization problem. For
example, MirHassani et al. [2000] considered an integer stochastic programming (ISP) representation
and solution for a two-stage design of a supply chain. The first stage concerned decisions on
opening/close of facilities and their capacity levels before future demands were realized. The second
stage involved production and distribution plans during supply-chain operation. The authors
used Benders decomposition to solve stochastic programming programs for supply chain networks
involving up to 8 manufacturing sites, 15 distribution centers, 30 retailers, and with 100 scenarios.
Alonso-Ayuso et al. [2003] also studied two-stage stochastic supply chain using stochastic programming
and proposed an algorithm based branch-and-fix heuristic. They tested their algorithm on
networks up to 6 manufacturing sites, 12 products, 24 market regions, and with 23 scenarios. Santoso
et al. [2005] noticed the limitation of these techniques in terms of scalability. They proposed a
solution technique that leveraged the strength of statistic simulation. They developed a sample average
approximation schema (SAA) to approximate expectations in the objective function and then
applied an accelerated Benders decomposition problem to solve the rest of stochastic programming
problem. Although their approach could handle much bigger supply chain design problems, it also
suffered from the similar drawback of stochastic simulation: the accuracy of its result was prone
to statistic errors. Additionally the application of stochastic programming was limited to design
optimization, whereas requests for stochastic analysis may come from many other applications, for
instance, analyzing an existing design of a supply chain under “what-if” scenarios.
In this project we will develop an agent-based modeling framework as the front-end of the
analysis tool. Swaminathan et al. [1998] studied a multi-agent approach for modeling supply-chain
dynamics. As with us, they believed a multi-agent modeling framework is “a natural choice”
for modeling supply chains because “supply-chain management is fundamentally concerned with
coherence among multiple decision makers”. They modeled structural elements as agents, which
interacted with each others using control elements. Our agent-based research follows the same
line but we will extend it with stochastic modeling using Markov decision processes. Additionally
we will provide formal syntax and semantics to remove ambiguity in model interpretation and to
facilitate rigorous formal analysis.
Our formal analysis technique will be based on probabilistic model checking [Bianco and de Alfaro,
1995]. In recent years the scalability and efficiency of probabilistic model checking was drastically
improved with the development of symbolic techniques such as Multi-Terminal Binary Decision
Diagrams (MTBDD) [Wang and Kwiatkowska, 2005]. Probabilistic model checkers such as PRISM
[Hinton et al., 2006] have been successfully applied to large-scale complex systems in biological
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