MGT 309 Operations Management

Term Project

Dice Game1

Play the following game assuming there are five players and you have the supplies of matches (or pennies) and a die. The game places five players in a row. The first player has an unlimited supply of raw materials (use matches or pennies here). During each round, player 1 rolls one die and moves that number of products into the raw materials bowl of player 2. Then player 2 rolls the die and moves the minimum of the roll and the number of products in the bowl into the raw materials bowl of player 3.

This continues down the line. Player 5’s throughput (minimum of his/her raw materials and die roll) represents the system throughput for that round.

Part A: Use an Excel spreadsheet to simulate the match game. Use random numbers (dice rolls) to run the 5-person game for 125 rounds and observe the average throughput at each station (for each person).

At the bottom of your spreadsheet, calculate the average throughput for each of the five players. Run the simulation 10 times and record the average throughput for each player for all 10 simulations.

Specifically, are the average throughput amounts different among the five players, and do those averages change with different simulation runs? Why do you think that these observations are occurring?

Part B: Next let’s play with the rules of the game a bit. In particular, the match game effectively illustrates the effects of “dependent events” and “statistical fluctuations” together. We now explore what happens when these effects are diminished.

- i) Save your spreadsheet under a new name. Put 100 matches in the four “bowl” cells for round 0. Run the simulation 10 times (each one has 125 rounds). Write on a sheet of paper the average throughput amounts for each of your 10 simulations for each player. How do the results differ from your simulations in Part A? What’s the obvious disadvantage of this implementing this approach?
- ii) Open your base case (Part A) spreadsheet again, and save it under a new name. This time, reduce the variability (i.e., the “statistical fluctuations”) of your processes (your die rolls).

To do that, pretend that you flip a coin. Heads means a potential throughput of 3 and tails means a potential throughput of 4. Notice that the expected value of each roll is the same

(3.5), but the variance has decreased. Run the simulation 10 times. Write on a sheet of paper the average throughput amounts for each of your 10 simulations for each player. How do the results differ from your simulations in Part A?

Part C: Let’s introduce a bottleneck into the system and test how the placement of the bottleneck affects the total inventory in the system. To calculate total inventory, we need to add the matches in all four of the bowls. (In real plants, companies pay holding cost for every period (round) that they hold inventory.)

We will introduce a bottleneck by rolling a 4-sided die instead of a 6-sided one for one of the players.

For each bottleneck placement (scenario) below, run the simulation 10 times and record the total inventory each time. Then calculate the average inventory for that scenario (averaged over the 10 simulations). (Show all of these amounts in one table.) Compare your three scenarios. Where the bottleneck should be placed?

Scenario 1: A is the bottleneck

Scenario 2: C is the bottleneck

Scenario 3: E is the bottleneck

Part D: Finally, let’s explore the effects of introducing excess capacity into the system. Suppose that one of the players gets to roll two dice instead of one (and the other four players roll one die as in the base case). First give player A the extra die. Run the simulation 10 times and record the total inventory, as well as player E’s throughput, each time. Compute the average inventory and average throughput for

- Now repeat by giving player E the extra die instead of player A. Compare your two scenarios. Who should get the extra die?

Write a brief report of what you have learnt from changing the rules of the game in parts A to D. Make tables of the simulations of parts A through D and use them in your report.