Mark Lawrence€”the man with two first names€”has been pursuing a vision for more than two years. This pursuit began when he became frustrated in his role as director of human resources at Cutting Edge, a large company manufacturing computers and computer peripherals. At that time, the human resources department under his direction provided records and benefits administration to the 60,000 Cutting Edge employees throughout the United States, and 35 separate records and benefits administration centers existed across the country. Employees contacted these records and benefits centers to obtain information about dental plans and stock options, to change tax forms and personal information, and to process leaves of absence and retirements. The decentralization of these administration centers caused numerous headaches for Mark. He had to deal with employee complaints often since each center interpreted company policies differently€”communicating inconsistent and sometimes inaccurate answers to employees. His department also suffered high operating costs, since operating 35 separate centers created inefficiency.

(a) Mark first asks you to forecast daily demand for the next week using the data from the past 13 weeks. You should make the forecasts for all the days of the next week now (at the end of Week 5), but you should provide a different forecast for each day of the week by treating the forecast for a single day as being the actual call volume on that day.

(1) From working at the records and benefits administration center, you know that demand follows €œseasonal€ patterns within the week. For example, more employees call at the beginning of the week when they are fresh and productive than at the end of the week when they are planning for the weekend. You therefore realize that you must account for the seasonal patterns and adjust the data that Mark gave you accordingly. What is the seasonally adjusted call volume for the past 13 weeks?

(2) Using the seasonally adjusted call volume, forecast the daily demand for the next week using the last-value forecasting method.

(3) Using the seasonally adjusted call volume, forecast the daily demand for the next week using the averaging forecasting method.

(4) Using the seasonally adjusted call volume, forecast the daily demand for the next week using the moving-average forecasting method. You decide to use the five most recent days in this analysis.

(5) Using the seasonally adjusted call volume, forecast the daily demand for the next week using the exponential smoothing forecasting method. You decide to use a smoothing constant of 0.1 because you believe that demand without seasonal effects remains relatively stable. Use the daily call volume average over the past 13 weeks for the initial estimate.

(b) After 1 week, the period you have forecasted passes. You realize that you are able to determine the accuracy of your forecasts because you now have the actual call volumes from the week you had forecasted. The actual call volumes are shown next.

For each of the forecasting methods, calculate the mean absolute deviation for the method and evaluate the performance of the method. When calculating the mean absolute deviation, you should use the actual forecasts you found in part (a) above. You should not recalculate the forecasts based on the actual values. In your evaluation, provide an explanation for the effectiveness or ineffectiveness of the method.

(c) You realize that the forecasting methods that you have investigated do not provide a great degree of accuracy, and you decide to use a creative approach to forecasting that combines the statistical and judgmental approaches. You know that Mark had used data from one of the 35 decentralized records and benefits administration centers to perform his original forecasting. You therefore suspect that call volume data exist for this decentralized center. Because the decentralized centers performed the same functions as the new centralized center currently performs, you decide that the call volumes from the decentralized center will help you forecast the call volumes for the new centralized center. You simply need to understand how the decentralized volumes relate to the new centralized volumes. Once you understand this relationship, you can use the call volumes from the decentralized center to forecast the call volumes for the centralized center.

You approach Mark and ask him whether call center data exist for the decentralized center. He tells you that data exist, but they do not exist in the format that you need. Case volume data€”not call volume data€”exist. You do not understand the distinction, so Mark continues his explanation. There are two types of demand data€”case volume data and call volume data. Case volume data count the actions taken by the representatives at the call center. Call volume data count the number of calls answered by the representatives at the call center. A case may require one call or multiple calls to resolve it. Thus, the number of cases is always less than or equal to the number of calls.

You know you only have case volume data for the decentralized center, and you certainly do not want to compare apples and oranges. You therefore ask if case volume data exist for the new centralized center. Mark gives you a wicked grin and nods his head. He sees where you are going with your forecasts, and he tells you that he will have the data for you within the hour.

At the end of the hour, Mark arrives at your desk with two data sets: weekly case volumes for the decentralized center and weekly case volumes for the centralized center. You ask Mark if he has data for daily case volumes, and he tells you that he does not. You therefore first have to forecast the weekly demand for the next week and then break this weekly demand into daily demand.

The decentralized center was shut down last year when the new centralized center opened, so you have the decentralized case data spanning from week 44 of two years ago to week 5 of last year. You compare this decentralized data to the centralized data spanning from week 44 of last year to week 5 of this year. The weekly case volumes are shown in the table below.

(1) Find a mathematical relationship between the decentralized case volume data and the centralized case volume data.

(2) Now that you have a relationship between the weekly decentralized case volume and the weekly centralized case volume, you are able to forecast the weekly case volume for the new center. Unfortunately, you do not need the weekly case volume; you need the daily call volume. To calculate call volume from case volume, you perform further analysis and determine that each case generates an average of 1.5 calls. To calculate daily call volume from weekly call volume, you decide to use the seasonal factors as conversion factors. Given the following case volume data from the decentralized center for Week 6 of last year, forecast the daily call volume for the new center for Week 6 of this year.

(3) Using the actual call volumes given in part (b), calculate the mean absolute deviation and evaluate the effectiveness of this forecasting method.

(d) Which forecasting method would you recommend Mark use and why? As the call center continues its operation, how would you recommend improving the forecasting procedure?

Introduction to Operations Research

10th edition

Authors: Frederick S. Hillier, Gerald J. Lieberman

ISBN: 978-1259162985

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