The demand forecasts for the next four quarters pertaining to a firm, that produces a single product line, are: 1200, 2000, 1500 and 1000 standard product units, respectively. Each standard product requires 10 direct labor hours to produce. The production facility operates on the basis of a single 8 - hour shift per day and each quarter consists of approximately 500 regular time hours. Overtime work is allowed to the extent that no worker works more than a total of 10 hours on any given day. Average regular time wages are $10 per hour, with a 50% premium for overtime. Material and overhead costs amount to about $100 per standard product. The inventory holding cost is estimated to be $80/standard product unit/year and backordering is allowable at a cost of about $50/standard product unit /quarter. Hiring and layoff costs are, respectively, $500 and $350 per employee. Currently, 24 production workers are employed and the finished goods inventory consists of 100 standard product units (no in - process inventory). The maximum workforce size for this facility is 30 employees. Management desires that there be no finished goods inventory or any backorders at the end of the current planning horizon.
(a) Formulate (i.e. clearly define all decision variables, then construct the objective function and all constraints in algebraic format) a linear optimization model for finding the optimal SOP for this firm.
(b) Determine this firm’s optimal aggregate sales and operations plan via Excel/Solver.