Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring if overtime is necessary to prevent stock-outs at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $100 for each temp; layoff, $200 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; regular time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer.

Fall Winter Summer Spring 7,000 Forecast 10,000 8,000 12,000 500 0 200 Beginning inventory Production required Production hours required 7,000 9,500 19,000 -2,300 10,300 20,600 14,400 6,200 14,000 11,800 23,600 14,400 Production hours available 14,400 14,400 Overtime hours 0 0 0 0 0 0 19 Temp workers Temp worker hours available 0 0 0 9,202 Total hours available 20,600 14,400 7,200 14,400 7,200 23,602 11,801 10,300 Actual production Ending inventory Workers hired -2,300 0 200 1 0 0 0 19 Workers bid off 10 Fall Winter Summer Spring 72,000 Regular time $ 72,000 $ 72,000 $ $ 118,008 Overtime 0 49,600 0 Inventory 0 0 1,000 4 x Backorder 23,000 0 0 0 0 0 0 Hiring Layoff 1,917 X 3,834 0 0 Total $ 95,000 $ 121,600 $ 73,000 $ 123,763 $ 413,363 Annual cost