Reddick's Specialty Electronics makes weatherproof surveillance systems for parking lots. Demand estimates for the next four quarters are 25, 9, 13, and 17 units

The firm is preparing an aggregate plan that uses inventory, regular time and overtime and back orders. Subcontracting is not allowed. Regular time capacity is 15 units for quarters 1 and 2, 18 units for quarters 3 and 4. Overtime capacity is 3 units per quarter. Regular time cost is $2000 per unit, while overtime cost is $3000 per unit. Back order cost is $300 per unit per quarter; inventory holding cost is $100 per unit per quarter. Beginning inventory is zero.

The data inputs for this problem, and the optimal solution, generated by microcomputer software, appear below. Answer the following questions based on the scenario and the solution.
a. How many total units will be produced in quarter 1 for delivery in quarter 1?
b. How many units in total will be used to fill back orders over the four quarters?
c. What is the cost to produce one unit in Quarter 4 using overtime to deliver in quarter 1 (filling a back order)?
d. At the end of quarter 3, what is the ending inventory of finished systems?
e. What is the total cost of the solution?
f. What is the average cost per unit?

Reddick's Specialty Electronics
Period 1 Period 2 Period 3 Period 4 Supply
RT 1 2,000 2,100 2,200 2,300 15
OT 1 3,000 3,100 3,200 3,300 3
RT 2 2,300 2,000 2,100 2,200 15
OT 2 3,300 3,000 3,100 3,200 3
RT 3 2,600 2,300 2,000 2,100 18
OT 3 3,600 3,300 3,000 3,100 3
RT 4 2,900 2,600 2,300 2,000 18
OT 4 3,900 3,600 3,300 3,000 3
Demand 25 9 13 17

Reddick's Specialty Electronics Solution
Optimal cost =
$132,200 Period 1 Period 2 Period 3 Period 4 Dummy
RT 1 15.
OT 1 3.
RT 2 6. 9.
OT 2 3.
RT 3 4. 13. 1.
OT 3 3.
RT 4 17. 1.
OT 4 3.

a. 15;
b. 10;
c. $3,900;
d. 0;
e. $132,200;
f. 132200 / 64 = $2,066