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Operations Research Models and Methods
Models Section

Excel Simulation

Simulation Tour
Excel Simulation

This is a story adapted from The Goal by Goldratt. We use it to describe a sequential production process. Further, this process is used to explain the idea of simulation.This simulation is accomplished using Excel with the Simulation add-in.

We start with a big pile of matches to the left of the first boy. Boy 1 throws a single die. The number showing is his production, so in this case the first boy produces 4 matches. These matches are the raw materials for the second boy.

The second boy throws the die. His production capability is the amount shown on the die, but he can only produce as much as available from the first boy. His production is the minimum of his capability or the number remaining from the first boy. There are 4 matches available, but the capacity of the second boy is only 2. He passes these to the third boy, leaving 2 matches remaining with the first boy. These two are called work in progress (WIP).

The raw materials for the third boy are the matches provided by the second boy. Again, he produces the minimum on his die or the matches available. His production is the system output. For this case the capacity of the third boy is 5, but only 2 matches are available as raw material. The remaining 3 units of capacity are wasted. At this first iteration, the system produces 2 matches. Two matches remain in the system as the first boy's WIP. The WIP is available to processed in the next iteration.

The boys continue to play the game. Each play consists of three rolls of the die that define the capacities of the boys. The production of each boy is limited by his capacity and the amount of material available. Ten plays of the game are shown below. Averages over the ten plays are shown at the top of the table. The play illustrated above is shown on row 1. The WIP produced in the first play is shown in the WIP 1 column of row 2.

We see from these ten plays, that the average system output is 3 units. The WIP that gathers after the first and second boys varies over the play of the game. We would like to estimate the long term properties of this game.

  • What is the average production of this system per play of this game?
  • How do you expect the piles of matches between the boys (the WIP) to vary as the game progresses?
  • Using this example, explain the effects of the variability in capacity on system output and in-process inventory (WIP).


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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved

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