Question

George, the Room Service Supervisor at the London Inn, just received the forecast for the weekend orders. Based on this forecast, he has to decide whether the regular hours of his staff will be sufficient, if he needs to prepare them to do some overtime (maximum 20% of the forecasted demand) or, as a last resort, if he needs to hire temporary workers (subcontracting) to be able to deliver all orders.

The associated costs are:

Regular-time cost per order	$5.00
Overtime cost per order	$7.50
Subcontract cost per order	$10.00
Idle time cost per order	$15.00

Forecasted requirements are:

Room Service Orders		Capacity
Period	Forecast	Regular	Overtime	Subcontract
Saturday AM	50	75	25	100
Saturday PM	130	100	30	100
Sunday AM	150	75	25	100
Sunday PM	100	75	25	100

Constraints on overtime are:

Period	Overtime Max (20% of the forecasted demand)
Saturday AM	10
Saturday PM	26
Sunday AM	30
Sunday PM	20

1. Develop a schedule plan that minimizes costs using the transportation method. Due to the nature of the business, there's no inventory, no stock out and no back order. On the other hand, if the regular staff capacity for the period is larger than the demand, there will be a cost for idle time.
2. State the corresponding schedule plan and its total costs?

Answer 1

Solution:

Schedule plan :

Saturday AM 50 + 75 = 125 * $5 =$625

Saturday PM 130 +100=230 * $5 =$1,150

Sunday PM 150+75=225 * $5=$1,125

Sunday PM 100+75=175 * $5=$875

Overtime

Overtime = 25 + 10 * $7.50=$262.50

Overtime= 30+ 26 * $7.50=$420

Overtime = 25+30 * $7.50=$412.50

Overtime= 25+ 20*$7.50=$337.50

Subcontract:

100 * $10 = $1,000

100 * $10 = $1,000

100 * $10 = $1,000

100 * $10 = $1,000

Period Regular overtime Subtract Availability

Saturday AM $625 $262.50 $1,000 50

Saturday PM $1,150 $420 $1,000 130

Sunday AM $1,125 $412.50 $1,000 150

Sunday PM $875 $337.50 $1,000 100

Total NIL $1,432.50 $4,000

Least is $625

50 = 50

130=150

150 - 50=100

100=100

Saturday PM $420 $1,000 130

Sunday AM $412.50 $1,000 150

Sunday PM $337.50 $1,000 100

Saturday PM $420 $100 13

Sunday AM $412.50 $100 15

Sunday PM $337.50 $100 10

Saturday PM $420 $10 13

Sunday AM $412.50 $10 15

Sunday PM $337.50 $10 0

Saturday PM $84 $10 13

Sunday AM $82.50 $10 3

Sunday PM $67.50 $10 0

Total Cost =$84 + $10 + $82.50 + $10 + $67.50 +$10

=$264