different among the five players, and do those averages change with different simulation runs (i.e. every time that is pressed)? Why do you think that these observations are occurring? Hint: You have a mistake in your spreadsheet if it contains negative numbers or if any of your throughput columns contain a number greater than 6. Note, however, that some of the entries in your bowl columns will likely exceed 6. 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 uctuations" together. We now explore what happens when these effects are diminished. 1. One use of buffer inventory stock is to decouple operations and eliminate dependencies among stations. Save your spreadsheet under a new name. Put 100 matches in the four "bowl" cells for round 0. Run the simulation 10 times (i.e. press the key 10 times). Write on a sheet of paper (either typed or handwritten) 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 approach? 2. Open your base case (Part A) spreadsheet again, and save it under a new name. This time, reduce the variability (i.e., the "statistical uctuations") of your process (your die rolls). To do that, pretend that you ip a coin. Heads means a potential throughput of 3 and tails means a potential throughput of 4. Specifically, change all of your roll columns from "=RANDBETWEEN(1,6)" to "=RANDBETWEEN(3,4)" . Notice that the expected value of each roll is the same (3.5), but the variance has decreased. Run the simulation 10 times (i.e. press the key ten times). Write on a sheet of paper (either typed or handwritten) 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 Alex's ideas about how the placement of the bottleneck affects the total inventory in the system. Open your base case (Part A) spreadsheet again, and save it under a new name. To calculate total inventory, we need to add the matches in all four of the bowls. Use the SUM command in Excel to add up all 125 rows in the matches in all four total bowl amounts together. This represents the total inventory in the system over the course of the game. (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, i.e., changing "=RANDBE'I'WEEN(1,6)" to "=RANDBE'IWEEN(1,4)\" 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 these amounts in one table.) Compare your three scenarios. Where should the bottleneck be placed? Scenario 1: Andy is the bottleneck