Question

Problem 1 (Aggregate planning): Martin Trailers (MT) is a manufacturer of small camping and snowmobile trailers in Ontario (lvey case #9A82D006). The demand for the camping trailers occurs between Jan and Jun of each year (mostly in Apr and May). Aggregate demand (in units) is: Jan 450 Feb 525 Mar 675 Apr 1005 May 1,125 Jun. 600 MT employs 40 permanent workers who are paid $20 per hour and each worker works 150 hours per month. Together they make approx. 600 camping trailers per month during regular time if the components are available. They can also work up to 50% more as overtime and get paid 1.5 times the regular wage rate. In addition, MT could hire up to 40 additional temporary workers to work during a second shift. Hiring/training cost is approx. $1,000 per temp worker. Assume that their wage rate and productivity are the same as permanent workers. Inventory holding cost per camping trailer per month is $90, charged to average inventory level during a month. Before Jan, MT had no camping trailers on hand, and it desires no inventory at the end of Jun. Any shortage during a period is backordered at the cost of $300 per camping trailer per month. a. Suppose MT only uses permanent workers during only regular time. Determine the no. of trailers short during each month and the total cost of the plan. [10 Marks] b. Suppose MT hires temp workers to meet the shortages (in addition to perm workers during regular time). Compare temp production (0,0,0,255, 525,0" with (0, 0, 30, 225,525, 0) in terms of the total cost. [5 Marks] Suppose MT wishes to improve the solution in Part b above by using overtime production. Compare the solution of part b with the case in which there are both temp and overtime productions in addition to the regular production (temp production of (0, 0, 30, 195, 495, 0)* and overtime production of (0,0,0, 30, 30, 0)) [5 Marks] "number of units in Jan, Feb Mar Apr May Jun) [Hint: you can use hourly pay rate to estimate the costs of producing one unit through different options (regular, temp., and overtime)]

Answer 1

1. a) From the Problem given above, we able to obtain the following figures:

- Units Produced

- Cost of Production

- Demand per month

Using the above data we are able to calculate the Inventory, Excess, Shortage and Cost.

The calculations are give below:

Month	Opening Inventory	Inventory Holding Cost (Opening Inventory * 90)	Production	Number of Workers	Cost of Production (Hourly Wage * Number of hours worked per month)	Demand/ Supply (in units)	Shortage (in units)	Cost of Backordering (Shortage * 300)	Excess (Production - Demand)	Closing Stock	Total Cost per month (Inventory Holding Cost + Production Cost + Backordering Cost)
Jan	0	0	600	40	$ 3000	450	0	0	150	150	$ 3000
Feb	150	$ 13500	600	40	$ 3000	525	0	0	225	225	$ 16500
Mar	225	$ 20250	600	40	$ 3000	675	0	0	150	150	$ 23250
Apr	150	$ 13500	600	40	$ 3000	1005	255	$ 76,500	0	0	$ 93000
May	0	0	600	40	$ 3000	1125	525	$ 157,500	0	0	$ 160500
Jun	0	0	600	40	$ 3000	600	0	0	0	0	$ 3000

Thus we can calculate the total cost of the plan by adding the figures in the last column of the table.

Total Cost of the Plan = $ 299,250

There are only shortages during the month of April and May for 255 and 525 units aproximately.

b. Comparing temp production in case 1 and case 2.

Using the data given in the problem we know that the temp workers have the same wages and production capacity as the regular workers. But they have to be trained with an additional cost of 1000 per head. Thus adding the total shortage and dividing with the number of months that there has been a shortage we are able to arrive at how many temps we need to hire (upper cap being 40 persons)

Case 1:

Month	Inventory	Inventory Holding Cost	Number of temp workers	Training Cost	Wages	Units Produced	Total units in stock	Shortage	Excess	Closing Stock	Total Cost per month
Jan	0	0	0	0	0	0	0	0	0	0	0
Feb	0	0	0	0	0	0	0	0	0	0	0
Mar	0	0	0	0	0	0	0	30	240	240	0
Apr	0	0	26	$ 26000	$ 78000	390	390	255	135	135	$ 116150
May	135	$ 12,150	26	0	$ 78000	390	525	525	0	0	$ 78000
Jun	0	0	0	0	0	0		0	0		0

Cost of production when temp workers are hired is $ 194,150 in case 1.

Case 2:

Month	Inventory	Inventory Holding Cost	Number of temp workers	Training Cost	Wages	Units Produced	Total units in stock	Shortage	Excess	Closing Stock	Total Cost per month
Jan	0	0	0	0	0	0	0	0	0	0	0
Feb	0	0	0	0	0	0	0	0	0	0	0
Mar	0	0	18	$ 18,000	$ 54,000	270	270	30	240	240	$ 72000
Apr	240	$ 21,600	18	0	$ 54,000	270	510	255	255	255	$ 75600
May	255	$ 22950	18	0	$ 54,000	270	525	525	0	0	$ 76950
Jun	0	0	0	0	0	0		0	0		0

Cost of production when temp workers are hired is $ 224,550 in case 2.

Thus from both the cases we are able to see that in case 2 the total production cost by the temp workers are greater than the one in case 1.