Question

A manager is applying the Transportation Model of linear programming to solve an aggregate planning problem. Demand in period 1 is 100 units, and in period 2, demand is 150 units. The manager has 125 hours of regular employment available for $10/hour each period. In addition, 50 hours of overtime are available for $15/hour each period. Holding costs are $2 per unit each period. a. How many hours of regular employment should be used in period 1? (Assume demand must be met in both periods 1 and 2 for the lowest possible cost and that production is 1 unit per hour.) [Blank1] 65 125 100 50 150

the answer is NOT supposed to be 125. please show all your work on excel

Answer 1

Regular hours aviable for production = 125 hours

Regualr capacity = 125 Units per period (As every uint takes 1 hour per unit)

Price for regualr production =$10

Price for using over time for production =$15

Inv Holdin charges = $2

Case 1:

we production will be done as per requirement of particular period

	Period 1	Period 2
Demand	100	150
Production	100	150

Total cost for period 1= 100 *10 = $1000

Total cost for period 2= 125 *10 + 25 *15 = 1250 +375 =1625

Note: Here for over time produciton of 25 units more than the regular capacity the unit price for production is $15

Total cost = $1000+$1625 =$2625

The above planning is classic example when chase strategy of agrregate planning is used.

Case 2:

In Level planning of aggregate planning in every month the production will be same

Total demand = demand for period 1+ demand for period 2 = 100 +150 =250 Units

Level productioin = Total demand/ No of periods = 250/2 = 125 Units

Here we can produce 125 units every month

	Period 1	Period 2
Demand	100	150
Production	125	125
Ending Inventory	25	0
regular production cost ($10)	1250	1250
Inv Holding costs ($2)	50	0
Overtime costs ($15)	0	0

Here the total cost fro period 1= 1250 +50 =$1300

For period 2 = $1250

Total cost = 1300 +1250 =$2550

Here the ideal plan for production is level strategy (Case 2) which is cost saving.

Here coming back to question the actual requriement for production is 125 units, And we can have the monthly regular time for production is also 125 Hrs.

Hence here the answer to the question is 125 hrs is utilised in period 1

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