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Operations Research Models and Methods
Computation Section
Subunit P & G Game
 - Play the Game

Clicking the OK button on the Initial Conditions dialog opens the PNG worksheet where the game is played. The figure below shows the worksheet as it first appears. The dialog at the upper left holds the step or week number, the current cost and the production change field labeled "Prod. Chg.". The Step is the current week. The Total Cost is the sum of all costs expended from week 1 to the current week.

The simulation starts at the beginning of week 2. The data for week 1 is shown in the row labeled 1. The beginning inventory of week 1 is set as an initial condition. The demand for week 1 is randomly generated from a normal distribution with mean 100 and standard deviation 30. The first week's demand is 97 for the example. The production in week 1 is set as an initial condition and is 70 for the example. The ending inventory is the beginning inventory plus the production minus the demand. Shortages are backordered and a shortage condition is indicated by a negative value for inventory.

Only the production change field is controlled by the user. In the example, we choose 0 as the production change. If a nonzero value with magnitude greater than 5 is entered, the production change occurs two weeks later. A number greater than 10 may be entered, but the production change is limited to 10.

The Next button leads to the next week. The Quit button closes the dialog.


The example continues for step 3 in the figure below. Here we see step 2 added to the table of results. In step 3 we choose to increase the production by 5.


For the example, we add another 5 units to the production in week 4. For weeks 5 through 16 we choose not to change the production. The resultant table for the first sixteen weeks is shown below. The high costs in weeks 3 and 4 include the costs of changing production. The production changes specified in weeks 3 and 4 are reflected after a two week lag in the production quantities for weeks 5 and 6. Production remains at 80 for weeks 6 through 16. Since the mean demand is 100, we should not be surprised to see the inventory decline until the ending inventory at week 16 is negative. This indicates that 76 units are backordered in week 16. The corresponding cost for that week is 76*100 or $7600.


We continue the example by increasing production by 10 units in weeks 17, 18 and 19. The production level reaches 110 at week 21 and remains at 110 through week 25. As shown below, the inventory begins to recover until the plant shuts down in week 26 and 27. Since demand continues, the backorder position becomes considerably worse. Production resumes at 110 in week 28 and the inventory improves until it is finally positive in week 45. For week 46 we begin to reduce production because the end of the year is drawing near.


When week 52 is complete, the dialog shown below presents the options to stop or to play again. Clicking Yes repeats the game with the same demand sequence.

Clicking No leaves the history of the game on the worksheet. The example game is shown below. (Note that the total cost is not exactly equal to the cost on the dialog. We will correct this in a later version.)


Our example was created to illustrate the use of the game, but it certainly was not very successful in minimizing the cost of operating the system. Download the game and try it yourself. After a little practice you should do better.

The example was run on a Macintosh computer. The program also runs using Microsoft Excel for Windows. It is not clear whether the same seed will give the same demand sequence when the program is run with Windows.

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

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