“Bowl and Stick” Game Description
The bowl and stick game highlights the importance of statistical fluctuations in a process with dependent events and its impact on throughput of the process. Mr. Alex Rogo, the protagonist of the book “Goal” invents a game wherein there are five bowls on a table and some match sticks.
Each bowl is given to a kid who has to manage it. Now every child has to move several matchsticks through each of the bowls in succession. The number of sticks each child can move will be determined by the number that turns up on dice that the child has to throw before moving the sticks. For example, if a child gets a three upon throwing the dice, he can move at most three sticks ahead. Hence each bowl will move sticks which will fluctuate between one and six based on the number that turns up on the die. Depending on the average number of sticks passed through by each bowl, the average output of the entire process varies.
During the course of the game:
Matches represent the inventory or work in the process.
Bowls represent the different workstations.
Dice are used to determining the Statistical fluctuations.
Alex reserved a standard quota of 3. 5 which he arrived at by calculating the average of those six numbers on the dice. To measure statistical fluctuations, Alex recorded the number appearing on the dice each time the boys threw dice and recorded deviation from the 3. 5 quotas. Every player of the game started from zero. If the roll of the die is 4, 5, or 6, then respective gains of 0. 5, 1. 5, or 2. 5 are recorded.
If the outcome from the throw of die comes out to be 1, 2, 3 respective gains of -2. 5, -1. 5 or -0. 5 are recorded. The deviations were taken to be cumulative wherein if somebody recorded a gain of say 2. 5, his starting point on the next turn will be 2. 5 and not zero. According to a mathematical principle, the fluctuations of the variable down the line will fluctuate around the maximum deviation established in the preceding operation.
Analogy With a Production Set-Up
The Bowl and stick game models a simple production process where the material is processed sequentially through several workstations.
In a typical manufacturing setup, several independent production lines with several workstations exist. An operator usually runs one workstation. A similar setup with six workstations is illustrated in the figure below. Except for the first workstation, each workstation maintains work-in-process inventory. The first workstation takes material from raw material stores, processes the material, and passes it to the work-in-process inventory storage area for station two. Workshop station two eventually processes and moves the material to station three, etc.
When a unit of material has been processed by the last workstation, it becomes the system output. Raw materials
Station 3 – Finished Goods
In the game, the roll of dice is used to simulate the actual production capacity of each workstation. The potential cycle capacity of the process varies from one to six units, with an average of 3. 5 units. Each child is allowed to process (move) the number of match sticks determined by the roll of the dice, subject to the availability of work-in-process inventory at that station at the beginning of the cycle.
No child is permitted to use sticks that were not available at the station at the beginning of the day – those units become part of the next cycle’s work queue. Thus, it often happened that an individual workstation (Bowl in this case) was not able to produce to its capacity due to a lack of available materials. The bowls here represent work stations of a manufacturing unit or an organization and the matches represent production output as well as work in process inventory. Rolling of a die helps to simulate the statistical fluctuations (variation) in performance at each work station or operation.
The bowls are set up as a production line representing dependent events where each operation has the same capacity, i. e. , six products per day with a range of variation from one to six. Rolling of the die and determining how many matches to move from one bowl to the next represents one cycle of the production run. Each operation is dependent on the upstream operation for input. For e. g. if a scout rolls a five, he can only move four from his bowl if there are only four available to him from the previous bowl (upstream operation) in the process.
The previous operation hence becomes the bottleneck operation. If another player downstream rolls are less than a four, then he becomes the bottleneck. Rolling the die several times in sequence represents several cycles of production runs and each time the bottleneck nearly always appears at a different operation or scout. Demonstration through the “Bowl and Stick” game is to show that where each operation in a sequence of dependent events has the same amount of capacity (a balanced plant), the variation and dependent events will cause the bottleneck to moving from operation to operation, i. , floating bottlenecks occur. Hence it is difficult for the Manager to determine where the bottleneck will show up next and manage the system.
Defining Dependency and Variability
Dependency is said to exist when certain operations or activities cannot begin until certain other operations or activities have been completed, whereas variability is manifested in the form of random events and statistical fluctuations. Random events are those events that occur at irregular intervals and have a disruptive effect on the process.
Statistical fluctuation refers to the idea that all processes are characterized by some degree of inherent variability. Dependency is manifested in the dice game by the requirement that units of sticks cannot be moved by a workstation until first being passed by all previous workstations. Variability is manifested by the different numbers that may occur when the dice are rolled.
Statistical fluctuations occur when one is unable to precisely predict events and quantities and can only be specified within a certain range.
The book gives very good illustrations to explain this principle – Alex and Jonah were sitting in a restaurant and Jonah says that they can precisely predict the capacity of the restaurant by counting the available seats. While on the other hand, they are unable to predict how long the waiter will need to fulfill their order. This uncertainty is referred to as statistical fluctuations. Even if one gets fairly accurate estimates for each stage in the development project, it is still possible, and quite probable, that a project will come in later than expected due to the effects of statistical variation.
Statistical Fluctuation in the Bowl & Stick Game
In stick and bowl game Every time the dice is rolled, a random number is generated that is predictable only within a certain range, specifically numbers one to six on each die. This is an example of statistical fluctuations.
Relation Between Dependent Events and Statistical Fluctuations
Dependent events are processes that must first take place before other ones can begin, For example, a product has to be assembled before it can be transported.
The relation between the statistical fluctuations and the dependent events is expressed as “Maximum deviation of a preceding operation becomes the starting point of a subsequent operation. ”
Effect of statistical fluctuations on Inventory levels
The Author predicted that on an average in each round the throughput (No. of matches coming out of the final bowl) should be 3. 5, which is the average of all the possibilities that is, 1 to 6. But after he experimented 10 times he found that the throughput was significantly lower (21) instead of 35 as predicted.
As the process goes on it can be seen that the forecasted throughput is never reached. This happened as the six-sided die was causing the variance (statistical fluctuations) by changing the production capacity of each of the stages. Thus, due to the relation between dependent events and Statistical fluctuation, each time some step in the process was working as a bottleneck for the capacity of the whole process meaning many sticks were stuck in the intermediate bowls. Hence, statistical fluctuations increase the inventory (stock) of the system.
Implications of Statistical Fluctuations for Organizations
This in organization setup means:
The system wastes money by stocking excess inventory that is not immediately converted to throughput, yet raises operational expense in the form of carrying cost.
Some areas have lower capacity than others and in turn work as a bottleneck for the whole system.
In General, Running areas of the factory that have higher capacities will not increase the overall throughput of the system. The measure that the increase is inventory, as the factory produces parts that cannot be assembled into finished goods that will ultimately result in sales until the area of the lowest capacity produces enough parts.
Inventory is an investment of money and thus subtracts from the bottom-line. Keeping large amounts of inventory is not desirable, because warehouse space is costly.
Challenges That Statistical Fluctuations Present in Front of Organizations
How to Make More Reliable Predictions About Projects?
This is one of the major challenges an organization faces. Statistical fluctuations hinder the management to accurately predict the output they can produce as they are unable to gauge the maximum potential of each station.
Due to the fluctuations, they end up getting lower throughput than predicted which ultimately leads in the late delivery of the orders.
How to Improve the Development Process Itself?
Due to statistical fluctuations, and unregulated development process will be slower than the slowest of the process steps. Therefore, it is impossible to accurately estimate the time required by adding together the time estimates for individual process steps and thus it is difficult to improve the development process.
Perils of High Statistical Fluctuations
One of the outcomes of high statistical fluctuations is excess inventory. The major disadvantages of the same are:
Companies typically want to produce or maintain only enough inventories to meet immediate demands and to avoid stock-outs. When companies have excessive amounts of inventory, they are generally not selling enough to prevent inventory build-up. This is not a good situation as businesses need to turn over inventory efficiently to maintain reasonably high-profit margins and to avoid the costs and other disadvantages that come with high levels of inventory.
Carrying excess inventory has significant costs. One of the highest costs for many companies is financing the purchase and holding of inventory. Also, the more inventories you hold, the more you have to spend on labor to manage it, space to hold it, and in some cases, insurance to protect against its loss or damage. Physically counting and monitoring the levels of inventory you hold also takes time and has costs.
Low inventory turnover can result in higher carrying costs. Inventory needs to be stored, handled, and insured, all of which represent costs to the business.
Stored inventory is also susceptible to shrinkage, which is lost due to occurrences like damage and theft. As with obsolete merchandise, carrying a large volume of slow-moving products also results in lost opportunities due to not being having the storage space for more rapidly turning items.
Loss or Damage
Related to the high costs of high inventory, some inventory can also go bad after a certain amount of time and go to waste. When retailers buy excess inventory of perishable food items, for instance, they may have to throw out inventory that spoils or becomes rotten.
When you carry high inventory, you also have greater exposure to the lost or damaged products. Thieves have more products to choose from and you have greater potential for the product to turn up missing or broken when you count inventory.
Shifts in Demand
Another disadvantage of keeping a large amount of inventory on hand is that certain goods might not sell due to shifts in market demand. For example, a clothing store that stocks too many tank tops during the summer may find itself unable to get rid of the tank tops before fall. During the fall, consumers might demand different types of clothing, like T-shirts or sweatshirts, leaving the company with a large number of goods on hand that simply take up space.
Strategic Planning Time
Company leaders typically have to spend more time in strategic planning meetings when the company has high inventory levels. Management must figure out how to communicate with suppliers, how to improve ordering processes, or how to increase market demand to reduce the high levels of inventory.
This problem takes away from the ability of these managers to focus on other proactive or more important strategic decisions to move the company forward. Dealing with inventory problems is a more reactive strategy to resolve the issue at hand. On the other end of spectrum is the problem that arises due to inventory levels getting too low are:
If inventory turns over too quickly, it could negatively affect sales. Merchants may elect to limit the variety of products they carry to prevent a backlog of inventory and keep goods moving through the operation.
While merchants might quickly sell the stock they have on hand, they may have difficulty keeping shelves full or may not offer a broad enough selection to meet customer needs. Customers who cannot find what they’re looking for or are not impressed with the product mix will look elsewhere and may not return to the establishment.
Merchants who purchase in small quantities to keep inventory turnover high typically incur greater costs. They may not be eligible for volume discounts or special deals available to those who buy in bulk.
Transportation costs may also be higher, as manufacturers and distributors often charge higher shipping prices for small orders. In some cases, merchants may have to resort to expensive express delivery methods to prevent out-of-stock situations. Merchants may need to place orders more frequently, resulting in greater processing expenses.
In operations where inventory turnover is low, merchants run the risk of being stuck with merchandise that becomes unsalable due to obsolescence. This can be a major problem in industries where consumer tastes constantly change or technology rapidly evolves.
Carrying obsolete merchandise means the merchant may not have adequate storage space to carry items currently in demand, resulting in lost sales. The merchant may have to resort to selling the merchandise at greatly reduced prices, which reduces its profits.
When allocating time for each activity project managers and planners often introduce buffer times. These buffer times might be small numbers for each activity that might be added to guard against statistical fluctuations that normally occur in each activity.
While these numbers are small they add up over the entire project activities to a significant time frame. When the workers realize that they have the necessary time built in as buffers they are more likely to push out the start of the job and concentrate their efforts on other task at hand.
Concept of Balanced Plant
One of the learnings from the bowl and stick game is that dependency and variability will combine to degrade overall plant performance. Several balanced plant models have been proposed to test the hypothesis that increasing (decreasing) levels of dependency and variability will increasingly degrade (improve) plant performance.
A balanced plant requires that every workstation have identical capacity. In the context of the game, every workstation will have an average capacity of 3. 5 units of matchsticks.
Impact of Dependency and Variability on Balanced Plants
After understanding the basic dice game setup, the key learning is that in the long run the average number of units of output a plant should be able to produce in every cycle is the mean of the range of outputs that each station can produce which is 3. 5 units in the game.
But the plant may not actually achieve the theoretically expected results because of the variations that occur in the output of each workstation which may disturb the balance of the plant.
In virtually all processes, the capacities of the various workstations are unbalanced. Goldratt initially developed the production dice game to illustrate the combined effects of dependency and variability on flow processes. Moreover, he combines insights derived from the basic production dice game to provide the foundation for understanding the dynamics in unbalanced plants.
Statistical fluctuations disturb the balance of plant which in turn leads to an increase in work in process inventory.
In The Goal, Goldratt describes three general unbalanced models which are described as follows:
Fastest to Slowest
This occurs when the workstations are arranged according to the fastest producing to the slowest producing. In this model, the first worker transfers the highest output, the second worker lesser, and so on.
The average cycle capacities for all the workstations are in order.
Result: High output and high inventory
Slowest to Fastest
In this model, the workstations are distributed in order of increasing capacity. That is, the first worker receives transfers the smallest output, the second worker transfers a higher output, and so on.
Result: low inventory
Randomly Distributed Capacity
In this model, different workstations producing at different capacities are randomly distributed in the process line.
Result: High output and high
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