2.4: Summary

Simulation model construction approaches have been presented. System components: arrivals, operations, routing, batching, and inventory management have been identified. How each component is commonly represented in simulation models has been discussed and illustrated.

Problems

1. Discuss why it is important to be able to employ previously developed models of system components in addition to the more basic modeling constructs provided by a simulation language in model building.
2. Discuss the importance of allowing multiple, parallel processes in a model.

   (For each of the modeling problems that follow, use the pseudo-English code that has been presented in this chapter.)

3. Develop a model of a single workstation whose processing time is a constant 8 minutes. The station processes two part types, each with an exponentially distributed interarrival time with mean 20 minutes.
4. Embellish the model developed in 3 to include breakdowns. The time between breakdowns in exponentially distributed with mean 2 days. Repair time is uniformly distributed between 1 and 3 hours.
5. Build a model of a two-station assembly line serving three types of parts. The sequence of part types is random. The part types are distributed as follows: part type 1, 30%; part type 2; 50%, and part 3, 20%. Inter-arrival time is a constant 5 minutes. The first station requires a setup task of 1.5 minutes duration whenever the current part type is different from the preceding one. The operation times are the same regardless of part type: station 1, 3 minutes and station 2, 4 minutes.
6. Embellish the model in problem 5 for the case where there are two stations that perform the second operation. The part goes to the station with the fewer number of waiting parts.
7. Embellish the model in problem 5 for the case where a robot loads and unloads the second station. Loading and unloading each take 15 seconds.
8. Combine problems 5, 6, and 7 in one model.
9. Consider Bob’s Burger Barn. Bob has a simple menu: burgers made Bob’s way, french fries (one size), and soft drinks (one size). Customers place orders with one cashier who enters the order and collects the payment. They then wait near the counter until the order is filled. The time between customer arrivals during the lunch hour from 11:30 to 1:00 P.M. is exponentially distributed with mean 30 seconds. It takes a uniformly distributed time between 10 seconds and 40 seconds for order placement and payment at the cashier. The time to fill an order after the payment is completed is normally distributed with mean 20 seconds and standard deviation 5 seconds.
   1. Build a model of Bob’s Burger Barn.
   2. Embellish the model for the case where a customer will leave upon arrival if there are more than 7 customers waiting for the cashier.
10. Consider the inside tellers at a bank. There is one line for 3 tellers. Customers arrive with an exponentially distributed time between arrivals with mean 1 minute. There are three customer types: 1, 10%; 2, 20%; and 3, 70%. The time to serve a customer depends on the type as follows: 1, 3 minutes; 2, 2 minutes; and 3; 30 seconds. Build a model of the bank.
11. Modify the model in problem 10 for the case where there is one line for each teller. Arriving customers choose the line with the fewest customers.
12. Develop a process model of the following situation. Two types of parts are processed by a station. A setup time of one minute is required if the next part processed is of a different type that the preceding part. Processing time at the station is the same for both part types: 10 minutes. Type 1 parts arrive according to an exponential distribution with mean 20 minutes. Type 2 parts arrive at the constant rate of 2 per hour.
13. Develop a process model of the following situation. A train car is washed and dried in a rail yard between each use. The same equipment provides for washing and drying one car at a time. Washing takes 30 minutes and drying one hour. Cars arrive at the constant rate of one each hour and three-quarters.
14. Develop a model of a service station with 10 self-service pumps. Each pump dispenses each of three grades of gasoline. Customer service at the pump time is uniformly distributed between 30 seconds and two minutes. One-third of the customers pay at the pump using a credit card. The remainder must pay a single inside cashier which takes an additional 1 minute to 2 minutes, uniformly distributed. The time between arrivals of cars is exponentially distributed with mean 1 minute.
15. Mike’s Market has three check out lanes each with its own waiting line. One check out lane is for customers with 10 items or fewer. The check out time is 10 seconds plus 2 seconds per item. The number of items purchased is triangularly distributed with minimum 1, mode 10, and maximum 100. The time between arrivals to the check-out lanes is exponentially distributed with mean 1 minute.
16. Develop a more detailed model of Bob’s Burger Barn (discussed in problem 9). Add an inventory for completed burgers and another inventory for completed bags of fries. Filling an order is an assembly process that requires removing a burger from its inventory and a bag of fries from its inventory. The burgers are completed at a constant rate of 2 per minute. It takes three minutes to deep fry six bags of fries.
17. Develop a model of the following inventory management situation. A part completes processing on one production line every 2 minutes, exponentially distributed and is placed in an inventory. A second production line removes a part from this inventory every two minutes.
18. Visit a fast food restaurant in the university student union and note how it serves customers. Specify a model of the customer service aspect of the restaurant using the component models in this chapter.