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statistics multi-part question and need an explanation and answer to help me learn. Requirements: Reasonable 9-171-248REV: SEPTEMBER 29, 2006 ________________________________________________________________________________________________________________ Professor William B. Whiston prepared this case. HBS cases are developed solely as the basis for class discussion. Cases are not intended to serve as endorsements, sources of primary data, or illustrations of effective or ineffective management. Copyright © 1970 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call 1-800-545-7685, write Harvard Business School Publishing, Boston, MA 02163, or go to http://www.hbsp.harvard.edu. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means—electronic, mechanical, photocopying, recording, or otherwise—without the permission of Harvard Business School. WILLIAM B. WHISTON Harmon Foods, Inc. John MacIntyre, general sales manager of the Breakfast Foods Division of Harmon Foods, Inc., was having difficulty in forecasting the sales of Treat. Treat was a ready-to-eat breakfast cereal with an important share of the market. It was the main product in those company plants that manufactured it. MacIntyre was responsible for sales forecasts from which production schedules were prepared. In past months, actual Treat sales had varied from 50% to 200% of his forecast. The greatest difficulty in preparing forecasts arose from the wide variability in historical sales. (See Exhibit 1. Sales were debited on the day of shipment; therefore, Exhibit 1 represents unit shipments as well as sales. Consumer Packs and Dealer Allowances, which are discussed later, are also shown in Exhibit 1.) Manufacturing Problems Accurate production forecasts were essential for the health of the entire business. The plant managers received these forecast schedules and certified their ability to meet them. A plant manager’s acceptance of a schedule represented a promise to deliver: crews and machines were assigned, materials ordered, and storage space allocated to meet the schedule. Schedule changes were expensive. On the one hand, the lead time on raw material orders was several weeks, so that ordering too little not only caused expensive shortages in lost production time but also disappointed customers. Reducing schedules, on the other hand, created a surplus of raw material. Lack of storage space required materials to be left on the trucks, railroad cars, or barges that brought them. Retaining these vehicles resulted in expensive demurrage charges.1 Overshadowing the storage problem was the problem of efficient use of the work force. Tight production schedules prevented unnecessary costs. Overtime was avoided because it was expensive and interfered with weekend maintenance. The labor force was highly skilled and difficult to increase in the short run. Layoffs, however, were avoided to preserve the crew’s skills. This job security was an important part of the company’s labor policy, and it created high employee morale. 1 Demurrage charges are assessments made by a carrier against a consignee for delays in the unloading (or the initiation of unloading) of a transport vehicle. Usually one free hour is allowed after the normal unloading time for trucks. Railcars and barges have typical allowances of three days and one day, respectively, including unloading time. Charges for delays beyond these allowances range from $20 an hour for a truck and $32 a day for a railcar to $4,000 a day for a barge. This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. 171-248 Harmon Foods, Inc. 2 Thus, the production manager attempted to make production schedules efficient for a constant-size work force while using as little overtime as possible. Advertising Expenditures Inaccurate sales forecasts also reduced the effectiveness of Treat’s advertising expenditures. Most of Treat’s advertising dollars were spent on Saturday morning network shows for children. This time was purchased up to a year or more in advance and cost $80,000 per one-minute commercial. The brand managers in the Breakfast Foods Division, however, believed that these network programs delivered the best value for each advertising dollar spent. This opinion was based upon cost per million messages delivered, viewer-recall scores, and measures of audience composition. Like many other companies, Harmon Foods budgeted advertising expenditures at a fixed amount per unit sold. Each year the monthly budgets for advertising were established, based on forecast sales. Brand managers tended to contract for time on network programs to the limit of their budget allowance. When shipments ran high, however, brand managers tended to increase advertising expenditures in proportion to actual sales. In such circumstances, they would seek contracts for time from other brand managers who were shipping below budget. Failing this, they would seek network time through the agencies, or if such time were unavailable, they would seek spot advertising as close to prime program time as possible. Thus, unplanned advertising expenditures could result in time that gave lower value per advertising dollar spent than did prime time. Budgets and Controls The controller of the Breakfast Foods Division also complained about forecasting errors. Each brand manager prepared a budget based on forecast shipments. This budget promised a contribution to division overhead and profits. Long-term dividend policy and corporate expansion plans were partly based on these forecasts. Regular quarterly increases in earnings over prior years had resulted in a high price-earnings ratio for the company. Because the owners were keenly interested in the market value of the common stock, profit planning played an important part in the management control system. Discretionary overspending on advertising, noted earlier, amplified the problems of profit planning. These expenditures did not have budgetary approval, and until a new budget base (sales forecast) for the fiscal year was approved at all levels, such overspending was merely borrowing ahead on the current fiscal year. The controller’s office charged only the budgeted advertising to sales in each quarter and carried the excess over, because it was unauthorized. This procedure resulted in spurious accounting profits in those quarters where sales exceeded forecast, with counterbalancing profit reductions in subsequent quarters. The significant effect of deferred advertising expenditures on profits had been demonstrated in the past fiscal year. Treat and several other brands had overspent extensively in the early quarters; as a result, divisional earnings for the fourth quarter were more than $4 million below corporate expectations. The division manager, her sales manager, brand managers, and controller had felt very uncomfortable in the meetings that were held because of this shortage of reported profits. The extra profits recorded in earlier quarters had offset the shortages of other divisions, but in the final quarter, no division was able to offset the Breakfast Foods shortage. This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. Harmon Foods, Inc. 171-248 3 The Brand Manager Donald Carswell, the brand manager for Treat, prepared his brand’s budget based on a set of monthly, quarterly, and annual forecasts that governed monthly advertising and promotional expenditures. These forecasts, along with forecasts from the division’s other brand managers, were submitted to MacIntyre for approval. This approval was necessary because, in a given month, the salesforce could only support the promotions of a limited number of brands. Once approved, the brand managers’ forecasts were the basis for MacIntyre’s official forecasts. The production schedule, in turn, was based upon MacIntyre’s official forecast. This required mutual confidence and understanding. MacIntyre provided information on Harmon’s and also competitors’ activities and pricings at the stores. The brand managers furnished knowledge of market trends for their brands and their brands’ competitors. The brand managers also kept records of all available market research reports on their brands and similar brands and were aware of any package design and product formulations under development. As Treat’s brand manager, Carswell knew that it was his responsibility to improve the reliability of sales forecasts for Treat. After talking to analysts in the Market Research, Systems Analysis, and Operations Research departments, he concluded that better forecasts were possible. Robert Haas of the Operations Research Department offered to work with him on the project. MacIntyre and the controller enthusiastically supported Carswell’s undertaking. Although such projects were outside the normal scope of a brand manager’s duties, Carswell recognized this as an opportunity to find a solution to his forecasting problem that would have companywide application. Factors Affecting Sales Carswell and Haas delved into the factors that influenced sales. A 12-month moving average of the data in Exhibit 1 indicated a long-term rising trend in sales. This trend confirmed the A.C. Nielsen store audit, which reported a small but steady rise in market share for Treat and a steady rise for the commodity group to which Treat belonged. Besides trend, Carswell felt that seasonal factors might be important. In November and December, sales slowed down as inventory levels among stores and jobbers were drawn down for year-end inventories. Summer sales were often low because of plant shutdowns and sales personnel vacations. There were fewer selling days in February. Salespeople often began the fiscal year with a burst of energy, jockeying for a strong quota position for the rest of the year. Carswell obtained data made available by the National Association of Cereal Manufacturers, showing seasonal effects on shipments of breakfast cereals in the United States. These indexes appear in Exhibit 2. Nonmedia promotions, which represented about 25% of Treat’s advertising budget, strongly influenced sales. The two main types of promotions were consumer packs and dealer allowances. Promotions targeted directly at the consumer were called consumer packs, so named because the consumer was reimbursed in some way for each package of Treat that was purchased. Promotions that sought to increase sales by encouraging the dealer to push the brand were called dealer allowances, so called because allowances were made to dealers to compensate them for expenditures incurred in promoting Treat. Consumer packs and dealer allowances were each offered two or three times a year during different canvass periods. (A sales canvass period is the time required for a salesperson to make a complete round to all customers in the assigned area. Harmon Foods scheduled 10 five-week canvass periods each year. The remaining two weeks—one at mid-summer and one at year-end—were for holidays and vacations.) This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. 171-248 Harmon Foods, Inc. 4 Consumer Packs Consumer packs were usually a 20-cent-per-package reduction in the price the consumer paid. The promotion could also be made as a coupon, an enclosed premium, or a mail-in offer. Based on the results of consumer-panel tests of all such promotions, however, Carswell was confident that these forms were roughly equivalent to the 20-cent price reduction in its return to the brand. Consequently, he decided not to make a distinction among the different kinds of consumer packs. (Exhibit 1 shows the history of consumer pack shipments.) Consumer packs, supporting advertising material, and special cartons were produced before the assigned canvass period for shipment throughout the five-week period. Any packs not shipped within this period would be allocated among the salespeople for shipment in periods in which no consumer promotion was officially scheduled. From a study of historical data that covered several consumer packs, Haas found that approximately 35% of a consumer-pack offering moved out during the first week, 25% during the second week, 15% during the third week, and approximately 10% during each of the fourth and fifth weeks of the canvass period. Approximately 5% was shipped after the promotional period. Because they saw no reason for this historical pattern to change, Haas and Carswell were confident that they could predict with reasonable accuracy future monthly consumer pack shipments. Total shipments were favorably affected, of course, during the month in which the consumer packs were shipped. Because the consumer ate Treat at a more or less constant rate over time, Carswell was convinced that part of the increase in total shipments resulted from inventory build-ups by jobbers, stores, and consumers. Thus, he thought that the consumer packs might have a negative influence on total shipments in subsequent months as these excess inventories were depleted in the first, or possibly the second, month after the packs were shipped. Dealer Allowances Sales seemed even more sensitive to allowances offered to dealers for cooperative promotional efforts. Participating dealers received a $4 to $8 per-case discount on their purchases during the allowance’s canvass period. The total expenditure for dealer allowances during a given promotional canvass period was budgeted in advance. As with consumer packs, any unspent allowances would be allocated to the salespeople for disbursement after the promotional period. The actual weekly expenditures resulting from these allowances followed approximately the same pattern as the one for the shipment of consumer packs. Consequently, Carswell believed that the monthly expenditures resulting from any given schedule of future dealer allowances could also be predicted with reasonable accuracy. Dealers promoted Treat by using giant, spectacular end-of-aisle displays, newspaper ads, coupons, fliers, and so forth. Such efforts could affect sales dramatically. For example, an end-of-aisle display located near a cash register could do an average of five weeks’ business in a single weekend. As with consumer packs, however, Carswell believed that much of the sales increase was attributable to inventory build-ups, and therefore he expected reactions to these build-ups as late as two months after the initial sales increase. Actual expenditures made for dealer allowances from 1983 to 1987 appear in Exhibit 1. This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. Harmon Foods, Inc. 171-248 5 Conclusion Carswell and Haas felt that they had identified, to the best of their abilities, the important factors affecting sales. They knew that competitive advertising and price moves were important but unpredictable, and they wished to restrict their model to variables that could be measured or predicted in advance. Haas agreed to formulate the model, construct the data matrix, and write an explanation of how the model’s solution could be used to evaluate promotional strategies, as well as to forecast sales and shipments. Carswell and Haas would then plan a presentation to divisional managers. This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. 171-248 Harmon Foods, Inc. 6 Exhibit 1Case Shipments, Consumer Packs, Dealer Allowances, 1983–1987 Month Case Ship- mentsa Con- summer Packs (cases)a Dealer Allow- ance Month Case Ship- ments Con- summer Packs cases Dealer Allow- ance Jan-83 #N/A 0 $396,776 Jan-86 655,748 544,807 $664,712 Feb-83 #N/A 0 $152,296 Feb-86 270,483 43,708 $536,824 Mar-83 #N/A 0 $157,640 Mar-86 365,058 5,740 $551,560 Apr-83 #N/A 0 $246,064 Apr-86 313,135 9,614 $150,080 May-83 #N/A 15,012 $335,716 May-86 528,210 1,507 $580,800 Jun-83 #N/A 62,337 $326,312 Jun-86 379,856 13,620 $435,080 Jul-83 #N/A 4,022 $263,284 Jul-86 472,058 101,179 $361,144 Aug-83 #N/A 3,130 $488,676 Aug-86 254,516 80,309 $97,844 Sep-83 #N/A 422 $33,928 Sep-86 551,354 335,768 $30,372 Oct-83 #N/A 0 $224,028 Oct-86 335,826 91,710 $150,324 Nov-83 #N/A 0 $304,004 Nov-86 320,408 9,856 $293,044 Dec-83 #N/A 0 $325,872 Dec-86 276,901 107,172 $162,788 Jan-84 425,075 75,253 $457,732 Jan-87 455,136 299,781 $32,532 Feb-84 315,305 15,036 $254,396 Feb-87 247,570 21,218 $23,468 Mar-84 367,286 134,440 $259,952 Mar-87 622,204 157 $4,503,456 Apr-84 429,432 119,740 $267,368 Apr-87 429,331 12,961 $500,904 May-84 347,874 135,590 $158,504 May-87 453,156 333,529 $0 Jun-84 435,529 189,639 $430,012 Jun-87 320,103 178,105 $0 Jul-84 299,403 9,308 $388,516 Jul-87 451,779 315,564 $46,104 Aug-84 296,505 41,099 $225,616 Aug-87 249,482 80,206 $92,252 Sep-84 426,701 9,391 $1,042,304 Sep-87 744,583 5,940 $4,869,952 Oct-84 329,722 942 $974,092 Oct-87 421,186 36,819 $376,556 Nov-84 281,783 1,818 $301,892 Nov-87 397,367 234,562 $376,556 Dec-84 166,391 672 $76,148 Dec-87 269,096 71,881 $552,536 Jan-85 629,402 548,704 $0 Feb-85 263,467 52,818 $315,196 Mar-85 398,320 2,793 $703,624 Apr-85 376,569 27,749 $198,464 May-85 444,404 21,887 $478,880 Jun-85 386,986 1,110 $457,172 Jul-85 414,314 436 $709,480 Aug-85 253,493 1,407 $45,380 Sep-85 484,365 376,650 $28,080 Oct-85 305,989 122,906 $111,520 Nov-85 315,407 15,138 $267,200 Dec-85 182,784 5,532 $354,304 a 1 case contains 24 packs. This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023. Harmon Foods, Inc. 171-248 7 Exhibit 2Seasonal Effects on Breakfast Cereals Shipments Seasonal Indices for Treat Breakfast Cereal Shipments Month Index January 113 February 98 March 102 April 107 May 119 June 104 July 107 August 81 September 113 October 97 November 95 December 65 This document is authorized for use only in Jennifer Shang©s Statistical Analysis: Uncertainty at University of Pittsburgh from Dec 2022 to Jun 2023.