The Beer Game and the Toyota Supply Chain

January 26, 2010 - Tags:

The beer game was introduced as an exercise in industrial dynamics in 1960. And what has beer to do with automobiles? The beer game is used as a fun way to illustrate some of the pitfalls of operating a supply chain. Certainly, beer gets the attention of students. Even though the product used in the game is beer, the processes are similar to most supply chains, including those involving automobiles. This chapter will compare and contrast how the original beer game is played versus how Toyota’s managers would play the game, which will illustrate how Toyota’s processes can streamline the supply chain.

The Beer Game Rules

In the beer game, four players play the roles of managing a serial supply chain as a retailer, distributor, wholesaler, and factory. A schematic of the beer game is shown in Beer game information/order flow. The retailer is the only one who observes customer demand. Each player fills demands from the immediate customer: the retailer fills the customer orders, the wholesaler fills the retailer’s orders, the distributor fills the wholesaler’s, and the factory serves the distributor. Each player carries inventory, which is represented by large shaded squares in the figure. Orders can be filled only from inventory in these boxes. The factory produces beer.

The game is played one week at a time. Each player receives orders and tries to fill as much as he or she can. If orders are not filled, they are backlogged and have to be satisfied in the future. Each player then places orders for the next week. Players possess only local information about their inventory: the demand by their immediate customer and the orders placed to their immediate supplier.

The goal for each player is to minimize the cost of holding inventory and of backlogged orders. Holding inventory costs $1 per unit per week, whereas backlogged orders cost $2 per unit per week. The team with the smallest sum of the costs of the four players wins.

The time to receive orders from the immediate supplier is two weeks. So it takes two weeks for orders shipped by the distributor to reach the wholesaler. Similarly, the delay in shipping is two weeks between the wholesaler and the retailer and between the factory and the distributor. The factory receives orders two weeks after they are planned for production. The small square shaded boxes represent these delays. Beer game information/order flow shows that there are 8 units en route to each player, 4 being one week away (on truck) and 4 more being two weeks away (on train). The game is played one week at a time.

Order processing delays are two weeks between players—for example, the order placed by the retailer one week reaches the wholesaler two weeks later. These delays are designated in the illustration by the small square boxes with question marks in them. The question marks indicate that the data are revealed only to the player and only when they are needed. To reiterate, the information delays between stages are two weeks each, and the shipping delay between stages is two weeks each.

The instructions given to players are as follows:

  • The purpose of this game is to experience firsthand the flow of materials through a distribution system. Teams of four people will work to minimize the total cost (both carrying costs and stockout costs) of the distribution network. The four positions of the team members are retailers, wholesalers, distributors, and factory inventory managers. Each person fills one position. There will be no collusion (i.e., talking) among team members.
  • Players will be moving two things through the network: orders (on index cards, placed facedown) and cases of beer (poker chips). They will keep track of each event on the form supplied. The holding costs are $1 per case in current inventory. The stockout cost is $2 per case on backlog (basically, negative inventory). The players must pay attention to follow along with the group. The team that achieves the lowest total cost will win the pot of money.
  • Even though the game sounds complex, the play is relatively simple. Each player executes five steps every week in synchronization. The game is supposed to start in steady state—that is, each player begins with 8 units of inventory, 4 units arriving one week later and another 4 units arriving two weeks later. In the game, those units are called “units on the truck” and “units on the train,” respectively. Each player has incoming orders and outgoing orders written out for the first week and placed facedown. Those orders are 4 units each. The incoming orders for the retailer (i.e., customer demand) are written out in advance and placed facedown. Beer game information/order flow shows the state of the game.

The five steps are as follows (described for the retailer and factory). All other groups operate in a similar manner. Every week the following happens:

  1. The retailer receives delivery of the units on the truck. The retailer records the units that are just received and adds those to his inventory. The units on the train are then shifted to the truck (and so are now one week away from the retailer). Likewise, the factory gets shipments from a truck and takes those into inventory. The shipments on the train are moved to the truck.
  2. The retailer then reads the current week’s demand from the incoming orders. The demand slips for the retailer are made ready in advance and kept facedown. The retailer fills the demand by counting that number of units from his inventory and removing them from inventory. The factory reads the demand from the distributor (in the incoming orders) and fills that many units from inventory by placing them on the train going to the wholesaler. In such a case, demand cannot be satisfied from inventory. It is backlogged and must be filled eventually.
  3. The retailer moves the order that was placed facedown (as the outgoing order) to the incoming order of the wholesaler. The factory reads the outgoing order from the distributor and places that number of units on the train going to the distributor. The outgoing order for the factory represents the production planned by the factory.
  4. The retailer decides how much to order, writes down that number on a piece of paper, and places it facedown in the outgoing order. The factory likewise plans how much to produce and writes that amount on a piece of paper and places it facedown in the outgoing orders.
  5. Only the very last step, placing an order, requires a decision. The rest of the steps are meant to simulate movement of material and information in a supply chain: getting a shipment, taking it into inventory, filling demand during the week, and placing an order with the supplier. Those are routine tasks that every real-life retailer, wholesaler, distributor, or factory does week in and week out.

A key constraint in the game is that players are not allowed to speak to each other about their orders. They can see the supply chain and orders that are coming to them, but they cannot see the orders placed by other players. To some extent they are “forced” to work using local information, that is, information available only to each person. A version of the game is described later in the section Understanding the Results Using the Standard Inventory Management Method.

The Typical Outcome

Typically, the game is played for 20 to 40 weeks. The original aim of the game was to show that even a small change in customer demand from 4 units a week to 8 units a week could create exceedingly large variations in the orders placed by the players. The customer demand is predetermined and is 4 cases each week for the first four weeks. Thereafter, the demand jumps to 8 cases per week and stays at that level for the rest of the game. The retailer who watches the demand unfold week by week sees a level demand first. Typically, the retailer tries to work down the starting inventory by ordering less than the demand. For example, the retailer might order 2 or 3 units each week for the first four weeks. In the fifth week suddenly the demand increases to 8. The retailer reacts and orders 8 or more units. Possibly, the retailer has run short of inventory and orders, say, 12 units. The wholesaler views the small demand for 2s and 3s in the first four weeks, then the order jumps to 12 or more units. The wholesaler also has run down the inventory, probably even more than the retailer has because the orders receipts have been 2s and 3s (against the retailer demand of 4 units per week), and in turn reacts and orders more. Possibly, the wholesaler has only 4 units on hand and so orders 8 units that are backordered this week and 12 for the next, for a total of 20 units. Following a similar reasoning, the distributor in turn reacts and orders even more, and eventually the factory sees a spike of orders that can be as large as 40 units!

The factory might even produce as many as 60 units in response. Notice also that the reaction is not simultaneous because of the delay in orders reaching each player. That sequence of overreacting stuffs the supply chain with unwanted material. Eventually, the players realize that they have overreacted, but it is too late. It takes quite a while (maybe even a year) to work down the surplus inventory. The game is played for at least 20 weeks to demonstrate the buildup of inventory and its gradual builddown. This phenomenon, in which each stage in the supply chain overreacts to changes in customer demand, has been termed the “bullwhip effect.” This phenomenon has been widely documented and studied. See, for example, the article on this subject by Lee, Padmanabhan, and Whang (1997),1 which is one of the top 10 most cited papers in supply chain management.

A plot of orders placed at different stages of the game in a typical experiment is provided in Typical outcome of beer game. Notice the growth of spikes as orders are tracked from the customer to the retailer, then to the wholesaler, then to the distributor, and then to the factory.

The beer game has been played internationally in management schools with students drawn from different programs: undergraduate, graduate, executive education, and short programs. The results are always the same: The costs incurred by different players are very different from the “optimal” cost. The deviation in costs and the deviation in ordering and stocking pattern from the optimal are systematic, thus illustrating the bullwhip effect. John Sterman, in his 1989 article on the subject,3 analyzes the outcome as follows: he first suggests a heuristic (trial and error) to order cases in each week because the optimal rule can be quite complicated. The heuristic performs quite well for the parameters of the game discussed above. It essentially involves making a correction for the desired stocking level and a correction for the supply coming to the player. The player orders the expected demand, plus a correction for the deviation in the stock from its ideal value and a correction for the deviation from the actual to the ideal supply line (the supply coming to the player). In Sterman’s experiments, the optimal heuristic (the one with the best parameter values chosen by trial and error) has costs that are 10 times smaller than the costs reported by the players. The same can be said about games that were played under our supervision at different places and with different audiences.

How Would Toyota Play the Beer Game?

This section describes how the beer game might be played at Toyota. First, we provide a benchmark of how a “standard” inventory management method applies to the beer game; then we will provide the Toyota approach. The examples used in the following paragraphs are very complex and beyond the scope of Typical outcome of beer game. We will briefly highlight some key figures in each example to examine Toyota’s approach to the standard method; however, if you want to understand the logic behind the two approaches, you will need to analyze the logic of each example.

Understanding the Results Using the Standard Inventory Management Method

Which details the standard inventory management method, shows that each player operates individually. Because the positions are symmetric, only the actions of the retailer are described; keep in mind that the rest of the players act in a similar manner. The shaded line of the illustration shows the periods. The demand is seen two lines below. It starts out at 4 per period until period 10 and then jumps to 8 and stays at 8 for the rest of the game. The retailer uses an “order-up-to” policy. He assumes that the lead time (LT) is four periods (a delay of two for the information to propagate and two for the physical supply). He adds a safety stock (SS) of two weeks to that and computes that his pipeline inventory (on hand plus on order) should be (LT SS 1), or seven weeks of supply. Each week he revises his demand forecast using a simple exponential smoothing formula with a weight of (for example) 0.8:

The forecast for next week = 0.8 × the forecast made last week + 0.2 × this week’s demand

The retailer observes demand, adjusts next week’s forecast, uses the forecast value to compute the required pipeline inventory, and orders a quantity that raises the end stock to the required value. For example, in period 11, the demand forecast equals (0.8 4) (0.2 8) 4.8. The pipeline inventory desired equals 7 weeks of supply (7 4.8), which equals 33.6. The end stock equals 20. Therefore, the retailer orders 13.6 units. Observe that this order raises the pipeline inventory to 33.6. Reveals that this order reaches the wholesaler only in period 13 due to the communication delay. The wholesaler reacts with an order of 27.04. The distributor reacts in week 15 with an order of 59.30 and the factory reacts with an order of 114.59 in week 17!

Note that the result of using the standard inventory management method produces the outcomes observed when the game is played.

At this stage, you might want to try to determine whether the simple but powerful concept of learning through scientific experimentation can be replicated in a supply chain. Is it possible to learn Plan, Do, Check, and Act in a system? What might be some of the prerequisites? The next section explains briefly how a supply chain leader achieves learning. We shall also see how Toyota’s learning principles work when the beer game is played.

Toyota Method

If Toyota were to play the game, the game would be played from a top-down point of view. The following are some of the rules of the game played the Toyota Way:

  • Production is planned once every four weeks and kept stable for the next four weeks. At each four-week planning session the retailer and factory would collaborate to forecast demand. They would enter into a dialogue to consider recent trends, stock adjustments, and back-order condition. Retail demand changes between four-week planning cycles, adjustments to safety stock, and current back orders are all evaluated to determine new production level.
  • Dealers or retailers are provided some level of safety stock (inventory) to fulfill expected demand (usually about one month’s, or four weeks’ worth). Any additional spike in demand is placed on back order to be filled at the next planning cycle. Toyota wants to make sure that the demand change is going to be persistent so as to not to overreact to spikes that occur on a week-to-week basis.
  • The cycle starts at the factory, and production is based on the latest fourweek forecast.
  • The two intermediaries (i.e., the distributor and wholesaler) do not carry inventory but just pass shipments through from factory to retailer.

The retailer attempts to fulfill demand, and if any safety stock is used, the retailer sends a weekly adjustment order to recover the used up safety stock during the next production cycle. Orders that cannot be filled from safety stock are scheduled for production at the next four-week planning cycle.

Toyota’s approach would result in minimal inventory buildup at each level and provide a consistent four-week production and distribution plan. The tradeoff would be a delay in filling the back orders. In that situation, it is assumed that a certain fraction of the customers would wait while some others might walk away, which would result in loss sales.

The impact of these rules. The major assumptions are listed at the top of the table. Interestingly, the process begins with the factory plan instead of the retailer’s orders! That arrangement emphasizes the supply chain view when planning. The planning is done in four-week intervals. These are labeled 1st, 2nd, and so forth. The real demand increases to 8 in week 11 as before. Until then, it is constant at 4, thereafter it is 8. The factory produces at a level base rate that is established for each interval. Added to that are the stock adjustment and backlog recovery. They create some fluctuations, but those are known well in advance and controlled to minimize the spike at the factory, as we shall see below. Also interesting is the fact that Toyota treats the wholesaler and distributor as pass-through participants that account for six weeks of inventory. That arrangement is consistent with the way the game is set up, but it avoids the forecasting and overreaction at the two intermediate stages.

In the Toyota version of the game, the safety stock is decreased to 3.2 so that the starting inventory is 7.2 units. Safety stock that is used up is replenished by being smoothed out over four periods. In addition, an increase to accommodate the new demand levels is smoothed out over eight periods. Thus, there is a constant attempt to smooth out order changes when they are placed upstream. That effort automatically guarantees that the rest of the supply chain does not face violent demand swings.

For the retailer, observe that some complex calculations are involved. First, the retailer receives shipments after eight weeks from the factory. Second, if the retailer cannot fulfill the demand from available stock, then a back order is sent to the factory to be filled during the next planning cycle. The system manages the demand increase in week 11 with the following steps:

  1. The demand is for 8 units, but planned demand is 4. Retailer stock is 7.2.
  2. The retailer sells 7.2 units, and now the stock is 0. The dealer stock is exhausted, and 0.8 orders will be on back order.
  3. The extra 3.2 units sold from safety stock are reordered from the factory to be produced during the next production cycle in a weekly quantity of 0.8—that is, production is smoothed out over four weeks.
  4. For the next planning period beginning in week 12, adjustments are made for the recovery of the backlog smoothed out over four weeks (0.2 each for four weeks). Another adjustment is made for the new demand level of 8, which is communicated with a delay of two weeks. That takes effect for the fifth interval starting in week 14. A third adjustment is made so that the increase in production is smoothed out over eight weeks to avoid placing an unnecessary burden on the factory. All these adjustments are sent to the factory with a delay of two weeks. You can check that similar calculations are made at the end of each interval in order to propagate back orders or stock adjustments.

The results are evident. The system recovers by week 23 compared to the huge inventories in the same week in the benchmark case. The Toyota Way has smaller inventory. It is willing to backlog demand in a planned manner—an outcome that happens unplanned in the benchmark case if there is too little starting inventory. The Toyota system has not only lower inventory but also lower supply chain costs that are not accounted for in the game (e.g., less overtime, less costly transportation due to a level distribution activity, better quality and lower management cost due to sticking with an accepted bandwidth of operation, and fewer stockouts due to unavailable parts). The outcome is commendable because the Toyota Way, which was not designed to play the beer game, nevertheless intuitively aims to uncover the rules proposed by Sterman to play the beer game.

Interpreting the Outcome

One way to interpret the outcome of the game is to insist that there is a systematic flavor to the results. The results are due to the structure of the game, namely, the long lead times for supply, the delay in communicating orders, and the lack of communication between stages. But that is not the only way to interpret the outcome. There are many other ways of explaining the outcome of the beer game. We classify them as follows:

  • Drawback due to the system. During the debrief session, players often tend to blame the system. They point out that if they had known the real demand, the situation would not have happened; thus information availability is said to be a constraint. Similarly, it takes two weeks for an order to go from one stage to another; thus, information propagation delay is another problem. Players also say that it takes two weeks at least to get supplies—even longer if the immediate supplier is backlogged. Rush orders might solve the problem. Thus, supply lead time or delay is a problem. Finally, they say that it is difficult to visualize the supply line— that is, to see how many units are in the pipeline headed toward them to fulfill past orders.
  • Use of heuristics. Sterman suggests that players fall victim to “misperceptions of feedback”; for example, the players do not account for actions that they have already taken, such as the impact of placing a huge order, when viewing the response of the system. In other words, they fail to see that the system can handle regular-sized orders within the regular time but that large orders need more time. Sterman also finds that players assume that the initial stock level of 8 in stock and 8 in the pipeline is optimal. That assumption is probably due to the lack of time for optimizing these values. Similarly, players tend to underestimate the time to get deliveries.
  • Inability to learn. When asked how to improve the system, many players first say that they feel helpless. They mention their inability to control the system. Many attribute the cause of the dynamics (e.g., huge swings resulting in excess shortages followed by excess inventory) to external factors. As Sterman puts it: “These explanations reflect an ‘open loop’ conception of the origin of dynamics as opposed to a mode of explanation in which change is seen as arising from the endogenous interactions of decision makers with their environment.” Or, bluntly put, they have a collective inability to develop a policy to manage the system.

Here we can borrow from Peter Senge’s five disciplines of a learning organization—systems thinking, personal mastery, mental models, building shared vision, and team learning—to explain the inability to learn. Let us consider the five disciplines. Clearly, the beer game participants lack personal mastery because they are somewhat at the novice level, even if they are supply chain managers in real life. They have probably never been exposed to such rapid evolution in the systems they manage. Players have a mental model of how the supply chain functions. Whether right or wrong, these ideas are not shared with others due to the rules of the game. For example, players might expect immediate delivery of orders. They may not realize that information delays create a lag in the last player (i.e., the factory) recognizing that the demand has increased. The lack of synchronous flow of information and material is not obvious, and probably its effect is difficult to imagine!

The goal is to maximize supply chain profit, because the team with the lowest cost wins. In the game, the lack of principles and practices that are necessary to translate goals into action leads to the disorderly outcome.

Finally, by focusing on being a retailer or distributor, the players fail to see how playing their position can adversely affect others. In other words, by playing their position they fail to think of the supply chain as a system. They probably might not even learn that through repeated play, especially if the game were played over long distances. Players believe that the enemy is “out there” by simply blaming everything and everyone else but their own selves for the results. They say things like “the demand was random,” “we never got supply,” and “we were not allowed to talk.” The players additionally get trapped into the illusion of taking charge, preferring action to thought. In the beer game there is a lot of frantic calculation done with the focus on placing an order rather than trying to learn. Moreover, fixing attention on the ordering event prevents the players from taking a long-term view, such as contemplating the impact of placing a very large order on the entire supply chain.

Technology Helps Mitigate the Bullwhip Effect in the Supply Chain

Mitigating the bullwhip effect in the supply chain requires coordination, and manufacturing on JIT principles requires precise timing between the manufacturer and the supplier. Looking to increase its business with Toyota, Dana Corp. has relied on technology to help it manage timing and coordination in its plant in Owensboro, Kentucky, for manufacturing truck frames.

Using a sequencing system based on Internet FTP (File Transfer Protocol) communication, Dana receives orders hourly from Toyota and uploads them into a “production instruction system.” That information is fed to all the component cells, where it is displayed on bulletin boards to let the cell know which model is currently being produced. Instantaneous order delivery from Toyota means that lot sizes can be as small as one to five. The result is that the plant is extremely lean, yet flexible enough to produce 14 models for two unique platforms on a single assembly line.

As the plant completely relies on the order system to keep producing, multiple standbys have been built in. The communication relies on a cluster of servers with “hot failover” so that backup systems always track the state and can take over from the primary system at any time. If everything shuts down, the manual alternative is to print order sheets and use those instead. In another use of technology, the plant’s team modified a machine that was meant to apply model numbers to verify that the right type of frame had been assembled by scanning key parts of the frame.

Always an extremely lean plant, Dana has reaped benefits from this technology. In 2002, it reduced costs by US$1.8 million, while over a three-year period it reduced the in-plant defect rate by 29 percent, raw materials inventory by 65 percent, and finished goods inventory by 29.6 percent. As a tier 1 supplier, Dana also manages its own tier 2 suppliers who deliver parts just-in-time. A system of kanban cards and scheduled routes is used to deliver supplies to the floor, and drivers pick up cards for the next round as they drop off supplies. On the outbound side, a trigger board of 25 lights (the size of each shipment) tracks each frame rolling off the assembly line at Toyota’s plant. A driver knows that when 25 lights are on, it’s time for the next delivery.

Reflection Points

The manner in which the beer game is played can be related, at a somewhat deep level, to the two main themes in the book. We summarize these below. The following learning methods are systematically used in stages in every process and by every one of the participants in the Toyota version of the game:

  • Create awareness. In the game, limits are placed so that once demand fluctuates beyond the stock level, it becomes noticed.
  • Establish capability. Collaboration between the retailer and the factory to establish a new production plan empowers the team to take concerted action.
  • Make action protocols. The reaction is constrained so that gradual changes are made to accommodate demand, adjust safety stock, and recover backlog. The constraints are placed to help identify cause and effect. Clearly, the planner knows when the smoothed orders will arrive at the plant, when they will arrive at the distributor and wholesaler, and so on. Those events can be tracked and planned in advance. Notice too the similar way of reacting to changes, whether it be demand, safety stock, or back-order recovery.
  • Generate system-level awareness. The factory is placed at the forefront. The wholesaler’s and distributor’s roles are subsumed into a pass-through. The entire supply chain becomes visible, with cause and effect of actions at every stage becoming clearer as one moves up the chain. Notice that what occurs is exactly the reverse of what happens in many supply chains, where the sales group is often unaware of the rest of the roles in the supply chain. In the beer game scenario, the main burden of calculation of changes is placed on the retailer. A reader well versed in the theory of incentives might spot the necessity for centralizing the planning. That step would be made because of the need for complex calculations, which would require system-level considerations by the retailer.

Link to the v4L:

  • Variety is not explicitly considered in the beer game. But if an uncertainty related to the product mix were added to the game, the impact of Toyota’s approaches would be even more significant than in the typical game.
  • Velocity. Toyota’s approach to the game begins with the factory and its production rate adjustments as a mechanism to regulate product flow in response to demand data.
  • Variability. New adjustments related to the data about demand are smoothed over time to reduce the impact on order variability. That reduction in variability lowers inventory while lowering back-order levels in a period. In other words, the responses to new data are distributed throughout the system and over time.
  • Visibility (or lack of it) is a key component of the game. The lack of visibility of underlying demand and absence of collaborative planning create most of the problems in the standard game. Notice that the Toyota approach to the game provides room for collaboration—and thus a smoother response to new demand level information.