As previously stated, our main contribution is the methodology that applies game theory to analyze multi-agent simulations. This methodology is interesting for the two fields adressed in this disseratation; our contributions for supply chain management are presented first, followed by our contributions for multi-agent systems.
1.4.1
Contributions to Supply Chain Management
Contributions to supply chain management are obvious, because the studied problem belongs to this field. In fact, the three main contributions of this thesis for supply chain management are:
1. the explanation of why delays are themselves a cause of the bullwhip effect, while such delays are only seen in the literature as an aggravating factor of another cause of the bullwhip effect;
2. the proposition of two principles for minimizing this cause of the bullwhip effect, and two schemes illustrating these two principles;
3. the study of companies’ incentive for collaboration, i.e., the use of our methodol- ogy that applies game theory to verify the incentive for applying our two principles; 4. a broad, critical review of literature about the bullwhip effect, that presents this
effect as a special case of stream fluctuations in distributed systems;
5. the study of the dynamics in an entire supply chain. In particular, we verify that collaboration is not only the best strategy for the whole supply chain, but also, that no companies have incentives to stop collaborating.
The two first contributions are closely related. On the one hand, our explanation of why delays are themselves a cause of the bullwhip effect permits us to propose our two principles, and on the other hand, these two principles aim at reducing the bullwhip effect generated by delays. Two ordering schemes are then proposed based on these two principles. In the first scheme, companies only have O to know the market consumption. Therefore, Θ are proportional to the variation of O to respect the second principle. This first version is called “Ordering scheme B” in this document. In the second ordering scheme, information centralization is used, that is, retailers multi-cast the market consumption to the whole supply chain. Like (O, Θ) orders, information centralization also transmits the market consumption information, except that information centralization is much quicker because it is instantaneous and in real- time. To profit from this acceleration of information sharing, our second ordering scheme is made more efficient by setting Θ proportional to the variation of the market consumption: as soon as the market consumption changes, non-zero Θ are sent by all companies. Moreover, companies set O equal to the market consumption transmitted by retailers instead of on incoming O, again in order to react quicker to the market consumption change.
These two ordering schemes are then compared with simulations under different scenarios. Precisely, we compare our two ordering schemes with five other schemes under nineteen different market demand patterns to study the efficiency of our schemes at the supply chain and individual levels, that is, we check if our schemes are efficient for the entire supply chain in the QWSG, and if every company agrees to use them.
In order to address the third main contribution listed above, i.e., companies’ incen- tive for collaboration, we carry out additional simulations. In these simulations, we use a cost function adapted from the Québec forest industry, and we apply ordering pa- rameters that are optimized so that the overall supply chain cost is minimum. In fact, our two ordering schemes assume companies collaborate, because they share demand information, but we have to check if they agree to share this information. Here, we consider not only the efficiency of collaboration by information sharing for the whole supply chain, but also the efficiency for each company. That is, we study selfish com- panies’ behaviours versus the minimization of the overall cost with game theory. The analysis of simulation outcomes with game theory shows that collaborating is a Nash equilibrium, while non-collaborating is not a Nash equilibrium. Therefore, every com- pany prefers collaboration, because its logistics cost increases when it ceases unilaterally to collaborate.
Finally, our last contribution to supply chain management is a broad, critical review of literature about the bullwhip effect. In particular, we introduce the bullwhip effect as a particular case of stream fluctuations in distributed systems, and we present some studies of the bullwhip effect in several fields, such as inventory management, economics, traffic flow theory, control theory. . . We now present contributions of this dissertation for the multi-agent field.
1.4.2
Contributions to Multi-Agent Systems
Multi-Agent Systems allow us to design, simulate and analyze our collaboration strate- gies, but we also contribute to this field by doing our research. In particular:
1. We have proposed a decentralized coordination mechanism based on communica- tion to stabilize linked streams in a distributed system;
2. We have taken into account both the global efficiency of the system and individual agents’ incentives to evaluate our coordination mechanism by applying concepts from game theory. This point was addressed with a methodology involving game theory to analyze simulation outcomes;
3. We have used game theory and multi-agent systems in a complex realistic study of a problem from supply chain management, and to our knowledge, this is the first time that these three fields have been applied in a common approach. 4. We have written a broad, critical review of literature about the use of multi-agent
systems in supply chain management.
5. We have compared coordination in supply chain management and coordination in multi-agent systems.
Before we see these three main contributions for multi-agent systems, we recall that the bullwhip effect is a distortion of demand information when this information is trans- mitted as orders along the supply chain up to the most upstream suppliers. Therefore, we can note that this deformation of information not only interests supply chain man- agement, but also Computer Science, because Computer Science studies information processing, and thus, information distortion.
From a less general point of view, this thesis studies the dynamics in a complex distributed system that can be viewed as a multi-agent system. In particular, the performance of many systems is reduced by fluctuations in their internal streams, e.g., traffic density during computerized network and road congestions. As a distributed system, a multi-agent system may face this problem too. For this reason, reducing the bullwhip effect in supply chains may give some hints for fluctuation reduction in other kinds of distributed systems, in particular when these systems are modelled as multi-agent systems. Therefore, the two above principles may be adapted by replacing some words, e.g., the bullwhip effect can be replaced by system instability, e.g., traffic congestions, market consumption by system input, company by agent, ordering scheme by agents’ behaviour. . . With these replacements, the first principle ‘Lot-for-lot orders eliminate the bullwhip effect’ can be translated into ‘If agents do exactly what they are asked to, according to the system output, the system fluctuations will be eliminated’ and the second principle ‘Companies should react only once to each market consumption change’ into ‘Agents should react only once to each change in the system input’.
Of course, like in supply chain management, these two principles only hold for fluctuations incurred by delays in the system, and these principles have to be adapted if other causes of fluctuations also occur. But these principles are general, because delays may also cause fluctuations in many other types of distributed systems than supply chains or multi-agent systems. For example, if all cars on a highway were decelerating and accelerating at the same rate and as soon as the first car, the road stream would be smoother, which would reduce the number of traffic jams.
Next, the agents’ behaviour based on these two principles can be seen as a decen- tralized coordination mechanism based on communication. The problem lies in the fact that agents are selfish, and have therefore the choice of obeying or not to this coordina- tion mechanism. This is the reason why the second contribution of this thesis is to take into account both individual and common interests. This is achieved through our third contribution consisting in the use of game theory to analyze inter-agent interactions. This methodology can easily be applied to analyze other kinds of multi-agent systems. The advantage of game theory is to give a high point of view on local interactions in a multi-agent system. Precisely, this high point of view allows researchers to immediately identify bad and good agents’ behaviours before they implement a multi-agent system. In our case, we do not know how companies choose their ordering scheme, but we know which one they may eventually choose, because they correspond to a Nash equilibrium. Moreover, game theory allows understanding why local optimizations do not lead to a global optimum, and how to add social rules constraining agents such as to reach this optimum. In this thesis, game theory is used to analyze a huge quantity of simulation outputs. Each simulation computes company’s costs in the supply chain when each company decides to use a specific ordering scheme. Next, the application of some game-theoretic concepts such as dominations, Nash equilibria or Pareto-dominations causes relevant simulation outputs to appear, and therefore, the inter-agent dynamics in the multi-agent system is made clearer.
Finally, our approach is supported by a broad review of literature about the use of multi-agent systems in supply chain management. In particular, this review allows us to compare our work with some others, and also, to compare coordination in supply chain management with coordination in multi-agent systems. Some of the possible comparisons of our work with others are described in the next section.