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日期：2024-03-16 10:53

SIMULATION OF BUSINESS SYSTEMS

R. YOOGALINGAM

  INSTRUCTIONS:

ASSIGNMENT 2

DUE: SEE BRIGHTSPACE

• Assignments should be done individually

• Submit your Arena model(s) & analysis in Brightspace

➢ Click ‘Assignments’

➢ Click on the action link for Assignment 2

➢ Click ‘Add Attachment’ and upload the *.doe file(s) containing your models and all Word/Excel

files with your answers

➢ Click ‘Submit’

➢ Please keep a backup copy of your work

PROBLEM:

Consider a popular coffee chain that has decided to introduce warm sandwiches and pastries to its menu. The current system can be described as follows. Customers join a FCFS queue to place their order and then proceed to the next counter to collect their completed order. Coffee customers can be divided into two types:

1) Those that order a Regular coffee. These customers have an arrival pattern that follows an exponential distribution with a mean of 2 minutes and the processing time for their order follows a uniform distribution with parameter values equal to 0.5 and 1 minute.

2) Those that order a Specialty coffee. Their arrival pattern follows an exponential distribution with a mean of 4 minutes and the processing time for their order follows a triangular distribution with parameter values equal to 2, 3, and 4 minutes.

3) The proposed system would allow customers to also purchase a sandwich/pastry with their coffee. The process involves the employee selecting the item the customer wants then placing it in the oven to heat it up. Management estimates that the additional time to process a sandwich/pastry order follows a triangular distribution with parameter values equal to 3, 5, and 9 minutes. They expect the arrival pattern of customers wanting a sandwich/pastry will follow a lognormal distribution with mean 5 minutes and a standard deviation of 3. Since this is one of the best coffee places in the world, management expects that every customer who purchases a food item will also purchase a regular or specialty coffee.

A few additional issues that management would like you to consider are:

1) In the fashion typical of these types of establishments, management feels that one employee at the

ordering station and two for preparing food/coffee is sufficient. In this setup, each food preparation employee has their own workstation: Order Prep WS1 and Order Prep WS2. The café has a sophisticated computer system that directs each order (and customer) to the employee with the shortest queue. If the two queues are the same, the computer will direct the order/customer to Order Prep WS1.

2) Management has done some research and studied past data and feels that customers will decide to forgo their coffee or grande double soy mocha lattes and/or foccacia smoked ham with aioli sandwiches if their waiting time exceeds three minutes (which is typical for this type of industry). They feel this translates into a customer balking when the sum of the order preparation queues for WS1 and WS2 exceeds 12 people.

SIMULATION OF BUSINESS SYSTEMS R. YOOGALINGAM

  3) They expect that many of the customers will already be familiar with their drinks menu so the ordering time for drinks only will follow a uniform distribution with parameter values [1,1.5]. This includes payment. On the other hand, with their sandwiches/pastries, they expect the same type of customer behavior they experienced when they first opened their establishment many years ago (i.e., a somewhat catatonic-like state while perusing the many options on the menu). In any case, they expect the coffee and food ordering process to follow a lognormal distribution with a mean of 2 minutes and standard deviation equal to 0.5.

4) It has been several decades since some of the executives have taken a simulation course or any course for that matter, so it would help if you animate the model (entities, resources) for their benefit.

5) Many coffee establishments are now including a self-serve kiosk for customers who drop by for a regular coffee. These customers would select their coffee from several choices of blends, dispense it themselves (assume this process follows a uniform distribution between 1.5 and 2.5 minutes), then proceed to their own order counter to pay (which takes half a minute). Suppose approximately 80% of regular coffee customers can be diverted to this option and these customers will balk if the queue at the kiosk exceeds 5 people (they really do not see why it should take so long to get their coffee!).

For the following, include your first initial and last name in the file name.

Part (a): *.doe

Develop a simulation model and simulate the proposed coffee and sandwich system for a 4 hour period from 11:00pm to 3:00pm (30 replications). Animate the model (entities, resources). What are the main problems the café is facing? Identify the bottleneck process and values for the following performance measures for this system in a table, and discuss the results.

• Number of each type of customer served

• Number of each type of customer who balks

• Waiting time and queue length • Utilization

Part (b): *.pan

Suppose management has provided you with additional funds of $100,000 per year to improve the process

in part (b). The annual cost of each option you are considering is as follows.

a) An additional self-serve kiosk costs $50,000

b) An additional order taker costs $35,000

c) An additional coffee/food preparation employee costs $40,000

What are the possible scenarios for allocating the additional funds (e.g., one kiosk only, one kiosk and one order taker)? Use Arena’s Process Analyzer with 10 replications per scenario and select/discuss the best option in terms of the number of customers who balk and waiting times. Copy and paste a snapshot of your PAN file in your analysis.