Problem 1. 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 stockouts 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; straight 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.

Summary of the Information above Forecast Fall Winter 10000 Spring 8000 Summer 7000 12000 beginning inventory current # of workers temporary workers Overtime hiring cost (temporary) laying off cost (each worker) Inventory holiding cost (per unit-quarter) backorder cost Straight time (per hour) overtime (per hour) productivity (per worker hour) workhours a day workdays a season 500 30 hired at the beginning of summer and laid off at the end of summer use regular workforce on overtime during winter or spring, not available on fall $100 $200 $5 $10 $5 $8 0.5 unit a workhour 8 hours a day 60 days a season Fall Winter 10000 500 9500 19000 14400 Spring 8000 -2300 10300 Summer 7000 12000 0 200 14400 14400 14400 6200 14400 7200 -2300 0 200 Forecast Beginning inventory Production required Production hours required(#of products/productivity(.5)) Production hours available (30 workers*8*60) Overtime hours Temp workers (Temp workers to be hired= (23,600-14400)/(8*60) = 19.17 workers) Temp worker hours available Total hours available Actual production Ending inventory Workers hired Workers laid off Costs Straight time (production hours*$5) Overtime (overtime hours * $8) Inventory (Ending inventory*Holding cost($5) Backorder (backorder *backorder cost ($10) Hiring(Temp workers hiring cost ($100)) Layoff (temp workers*laying off cost ($200)) Total (Quarter) Total(year) $ 72,000.00 $ 72,000.00 $