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Delays

Dynamical systems often show considerable delays in behavior, causing unexpected and counter-intuitive effects. One famous example of such delays is the bullwhip effect as characteristic feature of forecast-driven supply chains. It stems from changes in customer demand and causes feedback-driven and at times self-augmenting oscillations in the stock of factories and firms.

The Beer Distribution Game

The bullwhip effect is often demonstrated on the example of the so called MIT Beer Distribution Game originally invented in the 1960s by Jay Forrester. This game simulates a (traditional) supply chain without information sharing or collaboration. Usually, it is enacted as a four stage supply chain with the task of producing and delivering units of beer. The chain consists of a beer brewing factory, a distributor, a wholesaler and a retailer, all of them responding blindly, that is, without global knowledge of available beer, to orders coming in from their chain neighbors and originally issued by customers (which are not part of the game, but are simulated with some kind of random generator). Locally, the task is simple: each link in the chain has to fulfill the incoming orders for beer. The global aim however, is tricky: to maintain a regular supply of beer for customers, without running dry or overloading inventories. 

Beer game

Usually the game is played with several players taking turn in representing the links in the supply chain. the rules can be found here. The problem to solve is the supply of beer in respect to customer orders, with the supply facing delays caused by the time it takes for orders issued to reach the factory (order flow) and then again caused by the time the newly brewed beer needs to be delivered to the retailer (product flow). The following applet offers a simplified version of the beer game which abstracts from the order flow (and from expressing the delays in terms of costs). The task however is the same: to match the beer shipped to customers with the orders for beer issued by customers. 

The rules of the game

The slider below lets you adjust the factory production. Each click on the <submit>-button transfers beer to the next link in the supply chain. The goal is to lastingly match shipment and total customer orders (the shipment indicator turns green in the case of a match). You have 25 steps to try.

(The game is beta. If you like you can report bugs or suggestions to manfred.fuellsack at uni-graz.at)

SubmitRestart beginnerRestart advanced

The Hog Cycle (aka the Cobweb model)

Another example for the consequence of delays in system dynamics is the so called hog cycle concerning an often heard simplification in economics about supply and demand eventually adapting to each other and finding a balance when exposed undisturbed to free market forces. The hog cycle, as first discussed by the economist Mordecai Ezekiel, demonstrates that delays in the supply of goods can impair any such balance even without governmental interference.

Rising demand for pigs on the market will cause pig farmers to raise production and breed pigs. The assumption is that sensible farmers will stop their production when supply reaches the level of market saturation. Piglets however, need a couple of years to grow up and thus to respond to demand for pork meat on the market. In this time, demand lingers on and farmers will not sense any saturation. Once pigs have grown up however, farmers will offer their products concurrently on the market, encountering a large over-supply of pork meat.

Stopping production in consequence might cause another imbalance, since farmers again face delays in the possibility to react to market demand. Once there are delays in the game hence, the system will hardly find balance. Delays cause suboptimal allocations with free interplay of supply and demand.