The Production Dice Game

Handling Variability in a Production Environment

Robert Boute

By Robert Boute

Professor of Operations Management

22 December 2012

The Production Dice Game is a powerful learning exercise that demonstrates the impact of variability and dependency on throughput and work-in-process inventory. The insights obtained by playing the game can also be extended to a service or supply chain context. The game can be played online, and the software can be downloaded for free.


Robert Boute, Associate Professor Vlerick’s Operations & Technology Management Center, and colleagues – Marc Lambrecht, Stefan Creemers and Roel Leus of the Research Center for Operations Management at K.U.Leuven – have written a technical paper to present an overview of the dice game and the four extensions they’ve made to the game to reflect real-life characteristics more accurately.

The Production Dice Game

The Production Dice Game deals with flow-shop layouts: i.e. layouts in which equipment or work stations are arranged progressively, according to the steps in which a product is made. A good example is an assembly line, in which the manufacturing path of a product is a straight line.

Unfortunately, all sorts of outages (e.g. machine failures, repairs, minor stoppages, changeovers) can make the rate of production highly variable. And because variability is inherent in almost every production environment, work stations are usually buffered with inventory (i.e. work-in-process is stored in front of each station).

These buffers can serve to absorb (part of) the variability in the production line, but the buffer space between two stations is usually limited. Therefore, stations along the line can be dependent on each other: i.e. certain operations cannot begin until other operations have been completed.

Variability and dependency between work stations can cause starvation or blocking – which ultimately impact the flow-shop’s throughput and level of work-in-process.

For example: consider two consecutive machines. If the upstream machine fails to produce, the downstream machine may become ‘starved’ because its input buffer is empty, and so the machine is forced to be idle. If the downstream machine fails, the upstream machine may become ‘blocked’: i.e. the buffer between the two machines fills up, and so the upstream machine is forced to be idle.

The frequency of starvation and blocking (and consequently, the amount of idle time and lost throughput) depends on the size of the buffers. Buffers defer idleness and thus increase throughput, but of course at the cost of greater inventory.

The Production Dice Game can be used to illustrate these concepts – and the insights obtained from the game can be transferred immediately to real-life situations.

Extensions to the Game

The authors present 4 extensions they have made to the game:

  1. Operations are allowed to take place concurrently as opposed to sequentially, which is the more traditional way of playing the game.
  2. Both starvation and blocking of the line are allowed (usually only starvation is considered).
  3. Different sets of dice are used to represent a wide range of production rate variation coefficients.
  4. The game works with balanced lines (i.e. the expected production output is the same for every work station), but the work stations under consideration can have different levels of variability.

Thanks to these 4 extensions, the dice game reflects real-life characteristics more accurately.

The Game Fosters 5 Major Insights

The insights obtained from the game can help optimise the design of production lines.

  • Insight 1: The output ratio/buffer size curve is sharply concave: the more variability, the greater loss of throughput.
  • Insight 2: To achieve a given output ratio, the buffer capacity should be proportional to the squared variation coefficient of the processing rate.
  • Insight 3: A small amount of work-in-process is very helpful, but its usefulness gradually decreases. The rate at which it decreases depends on the level of variability.
  • Insight 4: In designing production lines, it is crucial to accurately assess the in-process inventory space that is required. Making the buffer space too small may result in a dramatic output shortfall.
  • Insight 5: Work stations with large variability impact the whole line’s output performance. This means that a high-variability work station has to be protected by extra buffer capacity. Because of the knock-on effect of variability, the other work stations need extra protection as well. A bell-shaped allocation is therefore advisable.

Applying the Game To Real Life

The game’s key lesson is understanding the relationship between variability and throughput in an environment with dependent work stations and limited buffers.

The dice game can also be used in a broader supply chain context in which each work station represents a unique organisation (customer, distributor, production plant, …) characterised by various sources of variability such as machine breakdowns, material shortages, quality errors, bottlenecks, demand variability and replenishment rules. Inventory is maintained throughout the supply chain to buffer against this variability.

The game can even be used in non-manufacturing or service operations environments. For example: healthcare operations are very much characterised by variability and flow constraints. The authors take a product-based view in this paper, but the flow units can easily be interpreted as ‘customers’ or ‘patients’.

Management and engineering students should pay attention to the size of the in-process inventory space. The availability of buffers prevents blocking or starvation of other work stations caused by the variability of each machine’s production. All this indicates that reducing variability is a key focal issue for management. Although this does not come as a surprise for most students, the authors’ experience indicates that students – as well as managers – usually underestimate the impact of variability.

The Production Dice Game can be played as a computer-based simulation or as a hands-on manual game. The game can be played at:

Related article

"Extending the Production Dice Game” by Marc Lambrecht, Stefan Creemers, Robert Boute and Roel Leus

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