# A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative.

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1. A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 (n = 6) customer calls are measured for time. Results from the last eight samples are shown in the following table.
 Observation (seconds) Sample 1 2 3 4 5 6 1 425 408 422 380 410 401 2 440 450 431 447 422 430 3 402 428 419 434 433 425 4 375 406 395 400 380 390 5 408 407 407 435 411 405 6 398 417 450 418 402 425 7 413 445 390 402 407 410 8 395 402 397 408 400 415

a)      Management is willing to use three-sigma limits. Using the factors in Table 5.1, determine upper and lower limits for mean and range charts.

b)      Plot sample means and ranges on their respective control charts. Is the process in control? Clearly explain what each chart shows.

1. The seven-person maintenance function at a hospital performs both preventive and corrective maintenance on hundreds of items each month. All the workers are scheduled for 40 hours per week and there are four weeks in a month. It is the goal of the maintenance department to achieve 90% utilization with a mix of three-fifths preventive maintenance and two-fifths corrective maintenance.

a)      How many hours each month are spent performing corrective maintenance if they achieve their 90% utilization and corrective/preventive mix targets?

b)      How many hours each month are spent performing preventive maintenance if they achieve their 90% utilization and corrective/preventive mix targets?

1. The figure below shows the call routing process for a customer service call center. Incoming calls are routed to work center B or C depending on the caller’s request. The numbers in parentheses are the times in minutes for each step of the process.

a)      What is the capacity per hour for the A-B-D-E process route? Explain your answer.

b)      What is the capacity per hour for the A-C-D-E process route? Explain your answer.

c)      If 60% of the calls are routed to work center B and 40% are routed to work center C, what is the average capacity per hour for the process?

1. A company is setting up an assembly line to produce 120 units per hour. The table below identifies the work elements, times, and immediate predecessors.
 Work Element Time (Sec.) Immediate Predecessor(s) A 21 — B 20 A C 25 A D 20 B E 10 B F 15 C G 10 C H 12 D,E I 12 F,G J 20 H,I

a)      What cycle time is required to satisfy the required output?

b)      What is the theoretical minimum number of stations?

c)      Use one of the heuristic decision rules to balance the assembly line so that it will produce 120 units per hour.

d)      What is the efficiency of the line you found in part c?

1. Observed monthly sales of a popular brand tennis shoe at a medium-sized sports store at the town’s mall over the first six months of the year are given in the following table.
 Month Jan Feb Mar Apr May June July Aug Demand 26 30 33 45 36 40 38 42

a)      Use a three-month moving average method to forecast the sales for the months April through September. Also compute the mean squared error (MSE) based on the sales and forecasts for months April through August.

b)      If the forecast for January was 25, determine the forecast for sales for the months February through September using an exponential smoothing method with a = 0.60. Also compute the mean squared error (MSE) based on the sales and forecasts for months April through August.

c)      Which method would you recommend based on MSE? Why?

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