Consequences for any Multi-Agent Systems

More generally, the cause of the bullwhip effect presented in this chapter may also incur stream fluctuations in any multi-agent system. To see this link between supply chains and multi-agent systems, Table5.1presents a translation dictionary. Indeed, the defini- tion of multi-agent systems in Subsection 2.1.1is sufficiently wide to encompass supply chains, because this definition does not assume that agents are softwares, but they can also be people. As a result, the following dictionnary only reflects the specificities (and not the differences) of supply chains.

1. Of course, the word “company” refers to “agent”. . .

2. . . . and “bullwhip effect” comes from “stream fluctation” or “system instability”.

In this context, the proposed cause of fluctations, i.e., delays, have the following equivalents in multi-agent systems:

3. “Ordering delays” in supply chains correspond to delays on the network that links agents, when these agents run on different computers. Such delays are referred as “network latency” in Table 5.1. We can feel this latency, when we browse on the Internet.

But even without this latency, delays are also incurred by agents’ message buffers. In fact, agents cannot always process incoming messages as soon as they are

Supply chain Multi-agent system

1. Company Agent

2. Bullwhip effect Stream fluctuation/instability

3. Ordering delay Network latency

4. Shipping delay Request execution time

5. Market consumption Requirement of the multi-agent system

6. Inventory Resource storage

7. Ordering scheme Agent’s behaviour

8. Lot-for-lot ordering policy Behaviour in which the considered agent acts exactly as another agent Table 5.1: Instantiation of multi-agent vocabulary into supply chain vocabulary.

received, and thus, incoming messages first arrive in a buffer, i.e., a mail box, in which they wait until the agent picks them up. This delay is not presented in Table 5.1, because in this dissertation we do not consider its equivalent in the world of supply chains, in which they are orders waiting by the company before their processing, e.g., in a mail box. In addition to ordering delays and waiting in mail box, we consider another delay:

4. “Shipping delays” in supply chains are similar to the execution time of the requests addressed to agents. That is, when an agent S (supplier) is requested to perform an action by an agent C (client), if agent S agrees to achieve this action, a certain time has to be spent by C until the action has been completely performed. It is similar to the shipping delay that a client C has indure to receive its products. 5. The “market consumption” resembles the “requirement of the multi-agent system”,

because both are the output, that sets the point at which the supply chain/system has to be.

6. The “inventory” of a company has an equivalent in agents, which depends on the application of this agent. We give the general term of “resource storage” to this equivalent. Of course, when this agent models a company, the stored ressource may be products, and we will see another example soon.

7. The “ordering scheme” rules our company-agent’s behaviour, and thus, such a scheme implements the “agent’s behaviour”.

8. The “lot-for-lot ordering policy” is one particular ordering scheme in which a company orders exactly its incoming demand. More generally, it means that the company-agent performs exactly the same action as another agent, like a young child repeating what his elder brother says to bother him.

Obviously, the way that delays incur fluctuations in a multi-agent system depends on the considered application. We can only note the similarity between the product stream in a supply chain and the flow of tasks in a multi-agent system, and between the ordering stream in a supply chain and the flow of requests in a multi-agent system. With these two similarities, we can infer that the flow of tasks in the multi-agent system may fluctuate, when there are changes in the requested output of the multi-agent system. More precisely, when this requested output changes, fluctuations appear in the flow of tasks carried out by agents, when these agents act so that the multi-agent system output is correct. As previously stated, such fluctuations reduce the efficiency of the multi-agent system in carrying out its functions.

To illustrate both this point and what can be a “resource storage”, let us consider the case of intelligent highway systems outlined in Subsection 2.2.6 in which some researchers [Hallé et al., 2003] are working on how to design platoons of cars. Each vehicle is modelled as an agent, and therefore, the platoon corresponds to a coalition or to a team of agents travelling toward a common destination. Except the front vehicle of a platoon, every other vehicle has to follow the preceding vehicle. The question is how to design agents’ behaviour in order to carry out this functionality. In this scenario, inter- vehicle distance is one of the possible stored resources. When we give each vehicle-agent the equivalent of the Lot-for-Lot policy, i.e., when we make each vehicle have the same speed as its preceding car, curves in Figure5.1(a) explain why the stored resource, i.e., the inter-vehicle distance, increases when the platoon accelerates, and decreases when the platoon decelerates. In other words, the inter-vehicle distance may fluctuate, leading to a “slinky effect” in the platoon [Ioannou and Chien, 1993;Chien and Ioannou,1992;

Sheikholeslam and Desoer, 1990]. This effect corresponds to variations in the resource

storage.

If we want the inter-vehicle distance to be constant, each vehicle-agent must be given another behaviour. But this behaviour has to be designed carefully to avoid distance fluctuations, and in particular a translation of(O, Θ) orders to this problem of platoons. In this case, the front vehicle, which imposes the speed of the whole platoon, would transmit its velocity to the rest of the platoon. Other vehicles would accelerate or decelerate more or less than the first vehicles in order to keep a steady inter-vehicle distance9.

Of course, this platoon problem is more complex in real-life than what has just been described, for example, because of the lack of accuracy in speed measurement 9_{Similarly to supply chains, in which we aim at having eventually a steady inventory in this disser-}

tation, we can also object when we say that inter-vehicle distance should be kept steady, because the security distance should increase with speed.

by each vehicle, and because vehicle-agents’ behaviour is more complex than a simple transpostion of (O, Θ) orders. Similarly, we have neglected a part of the supply chain complexity to propose(O, Θ) orders, in particular, because we do not consider all known causes of the bullwhip effect presented in Table3.2, such as demand forecast updating, order batching, price fluctuation. . ..

5.7

Conclusion

This section has proposed to consider ordering and shipping delays as a new cause of the bullwhip effect. Up to now, delays were only seen as a factor aggravating another cause of the bullwhip effect, called the demand signal processing [Simchi-Levi et al.,

2000; Chen et al., 2000; Lee et al., 1997a,b; Ryan, 1997]. Notice that demand signal

processing can also cause the bullwhip effect, because forecasts made by all companies, during information processing, induce errors that add up in the supply chain, and the longer forecasts are, the greater these errors are. Therefore, the longer delays are, the bigger the bullwhip effect incurred by this cause is, because companies forecast on a longer time horizon.

In order to address the bullwhip effect, we have proposed two principles to design ordering schemes, in which this effect induced by delays would be minimized. These two principles are that the lot-for-lot ordering policy eliminates the bullwhip effect, but does not manage inventories, and companies should react only once to each market consumption change. This second principle makes that companies should collaborate, because sharing the market consumption information requires collaboration.

Then, two ordering schemes were proposed according to these two principles. The supply chain behaviour under such schemes was also outlined, and an illustration was proposed for a multi-item scenario.

Finally, we outlined the implication of this chapter for multi-agent systems. Of course, the information sharing that we propose has consequences for information sys- tems in supply chains that are modelled as multi-agent systems, because agents have to manage this additional information. But a further implication concerns multi-agent systems in general. To see this point, we proposed a short dictionary to translate vocab- ulary in supply chains into vocabulary in multi-agent systems. This dictionary shows that the bullwhip effect is referred to as stream fluctuations in multi-agent systems, and that such fluctuations can also be induced by delays in multi-agent systems. In this context, our two principles can also be translated to any multi-agent system to reduce

these fluctuations, and thus, to increase the efficiency of the considered system.

The next chapter presents the simulation model used to validate the efficiency of our two principles in reducing the bullwhip effect.

Multi-Agent Simulation of a Québec

Forest Supply Chain

The previous chapter has presented how delays in distributed systems induce stream fluctuations from a conceptual viewpoint. To this end, two principles to reduce the fluctuations induced by this cause have been presented. In the remainder of this disser- tation, we study the efficiency of the two proposed principles on supply chains modelled as multi-agent systems. In this context, we verify whether our two principles reduce stream fluctuations (called bullwhip effect, since we consider supply chains) in an agent- based simulation of a supply chain.

In other words, we verify in the following chapters, whether our solution to stream fluctuations coordinates the way that company-agents place orders, so that the bullwhip effect is reduced. We now need a simulator to validate these principles, by verifying if our two ordering schemes actually reduce the bullwhip effect. The goal of this chapter is to introduce this simulator.

Since, in this entire dissertation, we use company and supply chain models that are based on the Québec Wood Supply Game (QWSG), we introduce this game in detail first. To this end, we show that it is an adaptation of the Beer Game to the Québec wood industry. Notice that the Beer Game has been designed to teach the dynamics in supply chains, and specifically, the bullwhip effect. These two games are first introduced in Section 6.1.

We have implemented the QWSG in a spreadsheet program. This implementa- tion closely simulates the QWSG, and is described with time-dependent equations in Section 6.2.

Products stream Orders stream 1 week order delay 1 week shipping delay

Customer

Wholesaler

Player 1 Player 2 Player 3 Player 4

Distributor Factory Retailer

Supplier

Beer Beer Beer

Beer

Figure 6.1: Supply chain in the Beer Game [Sterman, 1989].

Finally, we have designed and implemented a more realistic simulator with the agent-oriented language JACKTM_{. JACK}TM _{and our second simulator is presented in}

Section 6.3.