Question

Production Line Simulation

Random variation is an important part of most processes in operations and supply chain management. For example, customer demand, supplier lead time, answering a customer inquiry, or processing a batch of material at a machining center all vary from customer to customer, delivery to delivery, and batch to batch. As the chapter notes, simulation allows us to model randomness. Although most large-scale simulations are done on computers using random numbers, there are other ways to generate random distributions and thus simulate random variations. Two examples are rolling a die, which produces a uniform distribution ranging from on to six, and flipping a coin, which produces a binomial distribution. Let’s simulate a production system consisting of two work centers using two dice. The simulation proceeds in daily increments. Production at each work center is equal to the number on the corresponding die. Threes and fours are “average” days, whereas a one (or two) represents a bad day (perhaps one with a lot of machine breakdowns) and a five or a six is an above-average day. To do the simulation, take two pieces of paper and draw a line down the middle of each piece. Put the pieces side by side. Each piece of paper represents a work center. The right side is the machine at each work center. The left side is space for the queue (units waiting to be processed) by the machine. Material flows from left to right, first through work center 1, then through work center 2. After units are processed at work center 2, assume they go to a distribution center. Put about 100 pennies (or toothpicks or poker chips) in the queue of work center 1. This represents raw material, which we assume our plant has unlimited access to. Put four units in the queue of work center 2 (so that when the simulation begins, work center 2 has something to work on).

Work Center 1 Work Center 2
Queue Machine Queue Machine Machine

To simulate the first day, roll the die for work center 1 and the die for work center 2. This is the number of pennies the work center can process in the first day. For example, if work center 1’s roll is 2, then take 2 pennies from its queue and move them over the machine and into work center 2’s queue. Similarly, if work center 2’s roll is a 3, take 3 pennies from its queue and move them over the machine and then put them aside (they are in the distribution center). Now, at the end of day one, there are 3 pennies in work center 2’s queue. To simulate the second day, roll both dice again and, for each work center and for work center 1, move the corresponding number of pennies downstream (from work center 1’s queue into work center 2’s queue and from work center 2’s queue into the distribution center). Note that during a particular week, a work center can only process units that were in its queue at the beginning of the week. In our example above, if work center 2 had rolled a 6 on day one, it could only process 4 units because it began the day with only 4 units.(This simulates a situation in which work on all units must begin at the beginning of the day).

1. How many pennies could this production line process in 25 days? Note that the average roll is 3.5 (the midpoint between 1 and 6).

2. Simulate the line for 25 days. Keep track of each work center’s role for each day and the number or pennies each work center processes each day.

3. How many pennies did your line process in 25 days (this is the sum of pennies processed by work center 2)?

4. For each work center, what was the average roll? What was the average number of pieces processed?

5. How does the average roll for work center 1 compare to the average roll for work center 2? How would you expect the averages to compare if you continued the simulation for another 25 weeks? How do the pennies processed for work center 1 compare to the Distribution Center pennies processed for work center 2? How would you expect the pennies processed to compare if you continued the simulation for another 25 weeks? 6. Is the simulation in this exercise a continuous or discrete event simulation?

Answer 1

1. How many pennies could this production line process in 25 days? Note that the average roll is 3.5 (the midpoint between 1 and 6). If both work centers had sufficient raw material, then it would be expected to be able to process 3.5 + 25 = 87.5 pennies in 25 days 6 6 2 2. Simulate the line for 25 days. Keep track of each work center's role for each day and the number or pennies each work center processes each day. The simulation data was recorded in the following table PWI IQW2 Dice2 PW2 FQW2 Distributed Day 0 Day 1 2 Day 2 1 2 3 2 1 Day 3 1 3 2 Day 4 2 9 Day 5 5 1 13 Day 6 1 3 1 2 14 Day 7 5 2 3 2 1 16 Day 8 1 6 1 5 Day 9 22 Day 10 0 5 0 5 19 Day 11 5 Day 12 3 2 Day 13 3 Day 14 0 Day 15 5 0 3 Day 16 3 3 3 0 Day 17 0 Day 18 0 Day 19 1 Day 20 3 2 Day 21 2 2 2 Day 22 2 2 41 Day 23 3 2 1 1 42 Day 24 1 0 1 0 1 42 Day 25 4 1 3 1 2 43 Mean 3.04 2 3.64 1.72 3 2 2 Where: • PW1: the number of pennies processed in the work center 1. In this case it coincides with the number of the die since it has infinite raw material

• IQW2: queue from work center 2 at the beginning of the day, which is equal to the queue at the end of the previous day • Dice 2: result of the die 2 PW2: the number of pennies processed in the work center 2. In this case it is the minimum between IWQ2 and Dice2 • IQW2: queue from work center 2 at the final of the day. This is equals to the queue at the beginning of the day plus those processed by work center 1 minus those processed by work center 2 Distributed: the amount of pennies processed to date. This is equal to those processed by work center 2 plus those processed from the previous day 3. How many pennies did your line process in 25 days (this is the sum of pennies processed by work center 2)? 43 pennies 4. For each work center, what was the average roll? What was the average number of pieces processed? • Average roll for work center 1 is 3.04 • Average roll for work center 1 is 3.64 • Average number of pieces processed is 1.72 5. How does the average roll for work center 1 compare to the average roll for work center 2? How would you expect the averages to compare if you continued the simulation for another 25 weeks? How do the pennies processed for work center 1 compare to the Distribution Center pennies processed for work center 2? How would you expect the pennies processed to compare if you continued the simulation for another 25 weeks? The average rolls for work center 1 and 2 are very similar and both are around the expected 3.5 average. I would expect that within 25 days more these two values will come closer to 3.5. The pennies processed by work center 2 are less than those processed by work center 1. This is because the amount of pennies in the queue of center 2, at the beginning of the day, tends to be low and stops producing, while work center 1 always has raw material (pennies) available. For this reason, the amount of cents processed in work center 2 will always be less than that processed in work center 1, particularly if we extend production for another 25 days. 6. Is the simulation in this exercise a continuous or discrete event simulation? It is a discrete simulation.