骰子遊戲：於擲間學經營之道

骰子遊戲：於擲間學經營之道

嘗否怪乎，工坊運作，百事難順，凡事皆有前後相依之故？ 此有一高德拉特骰子戲，簡而明之，揭示商賈所臨之挑，皆繫於此等依存關係，及營運間自然起伏。 本文將解其戲法、示人意表之果、剖其蘊藏之理，並論其於商海之實用。

骰子戲之弄法

設想一微型生產線，由數個工位組成，以列坐之玩家擬之。 基本之戲需五人，然可酌情增減。 其法如下：

1. 每人執骰一具： 每位玩家得一標準六面骰。 此骰擬作其工位一段時日（一“輪”）之潛在產出。 所擲之數，即其可處置之單元數。
2. 始以“庫存”（首位除外）： 除首位玩家，餘者皆備一碗。 此碗象徵在製品庫存——待處置之物。 首位玩家（姑且稱之安迪）有物無限供之（如原戲中之火柴）。
3. 分輪而戲： 戲分輪次進行，玩家依次而動。
   • 安迪始： 安迪擲骰，並將相應數量之物移入次位玩家（班）之碗中。
   • 後續玩家： 班隨之擲骰。 其視所擲之數及其碗中之物數。 班僅可將二者之較小數移交下位玩家（查克）。 譬如，班擲五，而碗中僅有三物，則其僅能處置並移交三物。 其產出五之潛力，受限於工之不足。
   • 餘者皆仿此： 諸位玩家依次擲骰，並將其所擲之數與碗中物數之較小者，移入下位玩家之碗中。
   • 末位玩家： 末位玩家（伊萬）亦擲骰。 隨後，其將所擲之數與碗中物數之較小者，移出系統。
4. 計量“產出”： 每輪自末站（伊萬）移出之物件數，即為該輪整個生產線之產出。 其代表已完成產品之數量。
5. 多輪而戲： 欲真見其效，此戲需經多輪。 需記錄每輪之產出，以計其長期平均值。

意料之果與意外之果

或以為，若每位玩家每輪平均可產出 3.5 單位（六面骰之平均值），則整線每輪亦當產出約 3.5 單位。 然事實往往不然。

• 產出之“退化”： 或可察之，系統之實際產出，常低於理論潛力。 此“退化”乃由二因合致所致：
  • 事件相依： 每位工位皆賴其前位以供工。 若一站之輪次緩慢，則次站或將無事可為。
  • 統計漲落： 擲骰之隨機性，意味每站之產出逐輪各異。 時而產多，時而甚少，致使流動失衡。
• 產能愈大未必愈佳： 奇哉，徒予玩家更大之骰（象徵更高之潛在產能），並不能自致最佳之果。 蓋大骰雖可意味更多產出，然亦引入更大之變異性（更廣之可能結果範圍）。 此增之方差，實可惡化退化，並致更低之總產出及利潤——若大產能之成本逾越其實際產出之增益。
• 減小變異性之效： 奇趣者，具較小方差之產能方案（即便平均潛力相同），反可致更高之產出。 譬如，用擲幣之法，恆得產出三或四，或優於用六面骰——均值雖為 3.5，然結果更難預料。

骰子戲之啟示

此骰子戲，為營運管理之道，供數要義：

• 相依性放大問題： 此戲明示，流程中各步驟之相互關聯，意味一點之問題或滯緩，可於整個系統中產生漣漪效應。
• 變異性乃流動之敵： 骰子之隨機性凸顯，流程中任何部分之不可預測性，皆可擾亂工作之順暢流動，並降低總產出。
• 庫存為緩衝： 庫存之碗，充當工位間之緩衝。 有些許待工之物，可助工位持續運作，即便前站之輪次緩慢。 然此戲亦示，增添過多庫存，徒增成本，且效益終將遞減。
• 瓶頸定節奏： 於任何時點，有效產能最低之站，即為瓶頸，其限制整個系統之產出。 改善瓶頸，乃提升總產出之最有效途徑。
• 瓶頸之位至關重要： 此戲提示，若有瓶頸，置於生產線之始端，通常更優。 此可使後續各站，於初始瓶頸確有產出時，盡可能以其全產能運作，且庫存可於其後堆積。 末端之瓶頸，則易使整個系統於其前受阻。

予商賈之實用教訓

此看似簡單之骰子戲，為經營企業或管理流程者，供有力之教訓：

• 理解汝之相依性： 識別汝營運中各部分如何相互依存。 薄弱之環或不可靠之步驟，可顯著影響整體績效。
• 管控變異性： 於汝之流程中，尋找變異性之源（如不可靠之供應商、機器停工、需求不穩）。 施行措施以減小此變異性，可致更可預測且高效之營運。
• 策略性地運用緩衝： 考量於何處持有一定之“庫存”（可為實物、信息，甚或可用之員工時長），可助汝之流程免受變異性及相依性之負面影響。 然亦需注意持有過多緩衝所涉之成本。
• 識別並專注於汝之瓶頸： 判定限制汝總產出之約束。 致力於改善此瓶頸，將對汝系統之績效產生最大之影響。
• 勿僅逐更高產能： 若變異性未得管控，則投資更多資源或更高之潛在產出，未必為最佳之解。 有時，專注於一致性並減少擾動，反可收效更佳。
• 模擬與測試： 於對汝之流程作重大更動前，可考慮運用模擬之法（如基於 Excel 之骰子戲版本），以於安全且具成本效益之方式，理解汝擬議改善之潛在影響。

總而言之，高德拉特骰子戲，不僅僅是擲骰之樂。 其為理解支配任何系統中工作流動之基本原則之有力工具。 藉由親身體驗相依性及統計漲落之影響，玩家可獲得關於如何更有效地管理現實世界之商業運營之寶貴見解，專注於流動、管控變異性，並策略性地應對約束。

The Dice Game: Learning About Business with a Simple Roll

 

The Dice Game: Learning About Business with a Simple Roll

Have you ever wondered why things don't always go smoothly in a factory or any process where one step depends on another? A simple game using dice, known as Goldratt's Dice Game, brilliantly shows the challenges that businesses face due to these dependencies and the natural ups and downs of any operation. This article explains how to play, what surprising results you might see, the valuable lessons it teaches, and how these lessons apply to the real world of business.

How to Play the Dice Game

Imagine a small production line with several workstations, represented by players sitting in a row. The basic game involves five players, but you can have more or fewer. Here's how to play:

1. Each player gets a die: Each person receives a standard six-sided die. This die represents the potential output of their workstation in a given time period (a 'round'). The number rolled is how many units they could process.
2. Start with 'inventory' (for everyone except the first): Everyone except the first player should have a bowl. These bowls represent the work-in-process inventory – items waiting to be worked on. The first player (let's call them Andy) has an unlimited supply of items (like matches in the original game).
3. Play in rounds: The game proceeds in rounds, and players take turns in order.
   • Andy starts: Andy rolls their die and moves that many items into the bowl of the next player (Ben).
   • Subsequent players: Ben then rolls their die. They look at the number they rolled and the number of items in their bowl. Ben can only move on to the next player (Chuck) the smaller of these two numbers. For example, if Ben rolls a 5 but only has 3 items in their bowl, they can only process and pass on 3 items. Their potential to produce 5 was limited by the lack of work.
   • This continues down the line: Each player in turn rolls their die and moves the minimum of their die roll and the items in their bowl to the next player's bowl.
   • The last player: The final player (Evan) also rolls their die. They then move the smaller of their roll and the items in their bowl out of the system.
4. Measure the 'throughput': The number of items that leave the final station (Evan) in a round is the throughput of the entire production line for that round. It represents the number of completed products.
5. Play multiple rounds: To really see the effects, the game needs to be played over many rounds. You keep track of the throughput in each round to calculate the average over time.

Expected vs. Unexpected Results

You might expect that if each player can potentially produce an average of 3.5 units per round (the average of a six-sided die), then the whole line should also produce around 3.5 units per round. However, this is often not the case.

• The 'degradation' of throughput: What you'll likely observe is that the actual throughput of the system is often lower than the theoretical potential. This 'degradation' happens because of the combination of two things:
  • Dependent events: Each workstation relies on the one before it to provide work. If one station has a slow round, the next might run out of things to do.
  • Statistical fluctuations: The random nature of the dice rolls means that output at each station varies from round to round. Sometimes a station produces a lot, sometimes very little, creating imbalances in the flow.
• Larger capacity isn't always better: Surprisingly, just giving players bigger dice (representing higher potential capacity) doesn't automatically lead to the best results. While a larger die could mean more output, it also introduces more variability (a wider range of possible outcomes). This increased variance can actually worsen the degradation and lead to lower overall throughput and profit if the costs of the larger capacity outweigh the actual throughput increase.
• The power of reduced variability: Interestingly, a capacity option with lower variance (even if the average potential is the same) can lead to higher throughput. For example, using a coin flip that results in an output of 3 or 4 consistently can be better than a six-sided die with an average of 3.5 but more erratic results.

Learning from the Dice Game

Playing the Dice Game provides several key insights relevant to managing any process:

• Dependencies amplify problems: The game clearly shows how the interconnectedness of steps in a process means that problems or slowdowns at one point can have a ripple effect throughout the entire system.
• Variability is the enemy of flow: The random nature of the dice highlights how unpredictability in any part of a process can disrupt the smooth flow of work and reduce overall output.
• Inventory as a buffer: The bowls of inventory act as buffers between workstations. Having some work waiting can help a station keep working even if the previous station has a slow round. However, the game also shows that adding too much inventory comes with costs and the benefits eventually diminish.
• The bottleneck dictates the pace: The station with the lowest effective capacity at any given time acts as the bottleneck, limiting the output of the entire system. Improving the bottleneck is the most effective way to increase overall throughput.
• Location of the bottleneck matters: The game suggests that if you have a bottleneck, it's generally better to have it at the beginning of the line. This allows subsequent stations to potentially work at their full capacity when the initial bottleneck does produce, and inventory can build up after it. A bottleneck at the end can easily starve the entire system before it.

Practical Lessons for Businessmen

The seemingly simple Dice Game offers powerful lessons for anyone running a business or managing a process:

• Understand your dependencies: Identify how different parts of your operation rely on each other. Weak links or unreliable steps can significantly impact overall performance.
• Manage variability: Look for sources of variability in your processes (e.g., unreliable suppliers, machine downtime, inconsistent demand). Implementing measures to reduce this variability can lead to more predictable and efficient operations.
• Strategic use of buffers: Consider where holding some 'inventory' (which could be physical goods, information, or even available staff time) can help insulate your process from the negative effects of variability and dependencies. However, be mindful of the costs associated with holding too much buffer.
• Identify and focus on your bottlenecks: Determine the constraint that is limiting your overall output. Efforts to improve this bottleneck will have the biggest impact on your system's performance.
• Don't just chase higher capacity: Investing in more resources or higher potential output might not be the best solution if variability isn't managed. Sometimes, focusing on consistency and reducing disruptions can yield better results.
• Simulate and test: Before making significant changes to your processes, consider using simulation techniques (like the Excel-based version of the Dice Game) to understand the potential impact of your proposed improvements in a safe and cost-effective way.

In conclusion, Goldratt's Dice Game is more than just a bit of fun with dice. It's a powerful tool for understanding the fundamental principles that govern the flow of work in any system. By experiencing the impact of dependencies and statistical fluctuations firsthand, players gain valuable insights into how to manage real-world business operations more effectively, focusing on flow, managing variability, and strategically addressing constraints.