Operations Management

1. Tradeoffs in a Waiting Line Model (25 points)

You are a workforce management specialist at a large call center, and you are trying to determine how many agents to schedule to answer inbound calls. You have used historical data to forecast the following rates:

• The arrival rate between 9:00 and 10:00 am is 5 5 calls
• The average phone call takes 11 minutes

You know that the longer customers have to wait, the less likely they are to be loyal to your company in the future . Specifically, you believe that for every minute a customer has to wait you r company will lose $1 0 of business from that customer.

You also know that it costs you $15 per hour for each agent that is staffed to answer customer phone calls .

Throughout this problem, you may assume that the M/M/s model is appropriate, and therefore that you can use the Excel worksheet for this model that is provided with your textbook (and on iLearn if your book came without a CD).

For parts (a) and (b) below, suppose that you have decided to staff 11 agents from 9:00 am to 10:00 am .

1. (8 points) Based on the parameters given above, determine the Utilization Rate () and the mean customer Waiting Time (W _q ).
2. (5 points) What is the probability that a customer calling in to this center has to wait before receiving service? Briefly explain what you think the implications of this are for customer satisfaction.
3. (8 points) Suppose that your goal is to minimize costs, where you are considering both the cost of waiting and the labor costs of the agents. Would you prefer to staff 12 agents rather than 11? Explain why or why not.
4. (4 points) Would you prefer to staff 13 or 14 agents rather than 12? Explain why or why not.

2. Using Linear Programming for Planning (25 points)

The Party Nut Company (PNC) has 550 0 pounds of peanuts, 150 0 pounds of cashews, 90 0 pounds of almonds, and 70 0 pounds of hazelnuts on hand. PNC’s goal is to use these available nuts to maximize profit.

PNC sells four different nut mixes in ½ pound cans, with each mix requiring a different combination of nuts, as shown in the table below. The table also includes the profit per can for each of the different mixes.

In addition, based on PNC’s experience with its retailers, the company ’s operations team knows that it must produce at least 500 cans of each mix from the nuts that it currently has.

1. (10 points) Formulate a Linear Program that accurately captures the problem that PNC is faced with. Be sure to clearly indicate the Decision Variables, the Objective Function, and the Constraints [this can be hand-written or typed – it is up to you].
2. (10 points) Based on the prices and parameters above, use Excel and Solver to determine the optimal solution to this problem. Be sure to clearly indicate the optimal value for each of the Decision Variables as well as the optimal value for the Objective Function [feel free to include printouts from Excel, but be sure that your answers are clearly marked].
3. (5 points) Suppose that suddenly you find out that eating Party Mix is a new craze for college students, and that you can raise your price per can of Party Mix (Mix #2) so that your profir per can is now $ 0.75.

Use Excel and Solver to determine the optimal solution to this problem. Be sure to clearly indicate the optimal value for each of the Decision Variables as well as the optimal value for the Objective Function [once again, feel free to include printouts from Excel, but be sure that your answers are clearly marked].

Price: $19.49

Solution: The downloadable solution consists of 10 pages, 949 words.
Deliverable: Word Document