Question

Here is an operations planning case analysis. You are expected to do the following questions and submit them for marking at the end of the semester via utsonline and in hard copy to your tutor in week 10. A company has the following demand forecast next year, expressed in six bimonthly periods: Forecast Demand: Period 1 = 4,500 units Period 4 = 6,500 units Period 2 = 3,000 units Period 5 = 5,100 units Period 3 = 4,800 units Period 6 = 5,500 units The company begins the planning year with 500 units of inventory as safety stock and finish the year with the same inventory amount. The following cost data have been obtained: Each employee works 160 regular working hours per month Each unit requires 2 standard hours to produce The labour costs are $20 per normal hour and $27 per overtime hour It costs $4 per month to hold an item in the warehouse

Answer 1

Question3:

In this problem we need to first use the overtime level. Only if that is not sufficient then we hire. Next, if we have additional capacity, we fire people till we can manage with bare minimum workers and their overtime. Hence overtime is preferred over hiring or firing. This makes the most of the steps easy till we reach period 5 and 6. At this point we need to find the number of workers hired and fired in such a way that we maintain minimum possible inventory, we use their complete overtime capacity and also we end with 25 workers.

In order to do this, we will use excel solver at the period 5 and 6. The solver setup is shown below

fc =SUM(B11:611) Solver Parameters D 3 E 4 6500 F 5 5100 G 6 5500 T To Set Objective: SGS7 4500 3000 4800 2 To: O Max O Min O Value of: 42 31 86 25 17 50 18 68 18 By Changing Variable Cells: SF55:5656 19 0 Subject to the Constraints: SF$11:$G$11 >= 0 SFS5:SGS6 = integer SG$7 = 25 Add 50 86 Change 0 61 25 4000 2000 42 6720 3360 672 32 : x А 1 Period 2 Demand 3 4 #workers beginning 5 hired 6 fired 7 #workers end 8 Labor hour avl 9 Regular production 10 Overtime production 11 End inventory 12 13 14 15 Hour/worker 16 Hour/unit 17 Regular cost 18 Overtime cost 19 Inventory cost/period 20 Hire cost 21 Fire cost 11 31 4960 2480 496 8 68 10880 5440 1088 36 8000 4000 800 8 13760 6880 1376 3192 Delete 400 - 92 Reset All Load/Save ✓ Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options 160 Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. 20 27 Help Solve close 400 500

The optimum solution is shown below

H11 1 x fc =SUM(B11:511) D I J K L M N B 1 4500 C 2 1 Period 2 Demand E 4 6500 F 5 5100 G 6 5500 H Total 29400 3000 4800 Solver Results 25 42 31 50 17 19 18 72 72 Solver found an integer solution within tolerance. All Constraints are satisfied. Reports Answer O Keep Solver Solution 4 #workers beginning 5 hired 6 fired 7 #workers end 8 Labor hour avl 9 Regular production 10 Overtime production 11 End inventory 42 6720 3360 11 31 4960 2480 496 8 50 8000 4000 800 8 6 8 18 0 86 13760 6880 1376 3192 68 10880 5440 1088 36 O Restore Original Values 86 0 61 25 4000 2000 400 92 48320 24160 4832 3368 672 Return to Solver Parameters Dialog Outline Reports 32 - OK Cancel Save Scenario... 12 Solver found an integer solution within tolerance. All constraints are satisfied. It is possible that better integer solutions exist. To make sure Solver finds the very best solution, set the integer tolerance in the options dialog to 0%. 160 13 14 15 Hour/worker 16 Hour/unit 17 Regular cost 18 Overtime cost 19 Inventory cost/period 20 Hire cost 21 Fire cost 27 400 500

a)

Employment levels are shown in the image above.

b)

Total payroll related cost includes labor cost, hire cost and fire cost. That will be

Labor cost = 48320*20 = 966400

Overtime cost = 0.2*48320*27 = 260928

Hire cost = 72*400 = 28800

Fire cost = 72*500 = 36000

Total payroll cost = 1292128

c)

Total labor cost is 966400 + 260928 = 1227328

Total units produced = 29400-500 = 28900

Cost per unit = 1227328/28900 = 42.46

This is an increase of 42.46-20 = 22.46 or 22.46/20 = 1.12 or 112% increase

d)

The total cost is 1292128 + 3368*8 = 1319072