Duck Lovers Unlimited (DLU) Inc. assembles specially configured light jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the upcoming fiscal year are:

Quarter:                      1                        2                      3                  4               

Forecast (units):         11                       17                     8                  15

It takes an average of 2500 direct labor hours to assemble each aircraft. Currently, 48 full-time production workers are employed by DLU, working a single 8-hour shift each day. As of now, there is no inventory of completed or semi-finished units. Demand backlogging is possible, but 20% of backlogged demand eventually turns out to be lost sales, representing an opportunity loss of $80,000 per unit (aircraft). Under-time or overtime work may be resorted to, the latter being restricted to 4 hours per day for each worker. The average regular time labor wage rate is $10/hour, with a 50% premium for overtime work. Finished goods inventory holding costs are $16,000/unit/year and backordering costs are estimated to be $9,500/quarter for each aircraft. The inventory holding and backlogging costs, if any, are charged to end-of-quarter finished goods inventories and backorders, respectively. The workforce size can be varied through hires or layoffs (done at the beginning of any quarter) at $3,200 or $3,000, respectively, per worker. For simplicity, assume that there are about 500 regular-time hours in a typical quarter. Material and overhead costs per aircraft amount to $20,000. 

(a) Using the information given above, develop a minimum-cost, 4-quarter aggregate sales and operations plan (SOP) for DLU, such that the workforce size is constant throughout the year (after initial hires or layoffs, as necessary), allowing no overtime, backorders, lost sales or part-time employees. Summarize your SOP in a tabular format shown below and compute the resulting total relevant cost for the next fiscal year.

Demand          Production      Ending Inventory        Workforce

Quarter      (Units)                (Units)                (Units)                 (No. of Workers)

      1               11

      2               17

      3                8

      4               15                                                                                                   _

(b) In order to cope with demand uncertainty, DLU management has decided on a safety stock policy, requiring that at the end of each quarter, the planned finished goods inventory be at least 10% of that quarter's demand forecast. Repeat part (a) with this policy in effect.

(c) Removing all restrictions outlined in part (a), but with the safety stock policy (b) in effect, develop an algebraic linear programming model ( i.e. clearly define all decision variables used and formulate the objective function and all constraints) for determining the optimal SOP for DLU. Solve this model using Excel/Solver, showing the optimal aggregate plan and the resulting minimum total relevant cost for the next fiscal year.