Question

Ram Roy’s firm has developed the following supply, demand, cost, and inventory data. Allocate production capacity to meet demand at a minimum cost using the transportation method. What is the cost? Assume that the initial inventory has no holding cost in the first period and backorders are not permitted.

Initial Inventory 20 Units

Regular Time cost per unit $100

Overtime cost per unit $160

Sub contract cost per unit $250

Carrying cost per unit per month $6

Supply Table

Period	Regular Time	Overtime	Subcontract	Demand Forecast
1	30	15	5	40
2	30	15	5	45
3	40	15	5	55

Answer 1

Total Demand Forecast for three periods = 140

Inventory in Hand = 20

Period 1:

Production for Period 1 = 30 Regular + 20 Inventory = 50 units

Demand for Period 1 = 40 units

Inventory after period 1 = 10 units

Cost for Period 1 = 30*$100 = $3000

Inventory Carrying Cost from Period 1 to Period 2 = 10*$6 = $60

Period 2:

Production for Period 2 = 30 Regular + 10 Inventory + 5 Overtime = 45 units

Demand for Period 2 = 45 units

Inventory after period 2 = 0 units

Cost for Period 3 = 30*$100 + 5*$160 = $3800

Inventory Carrying Cost from Period 2 to Period 3 = $0

Period 3:

Production for Period 3 = 40 Regular + 15 Overtime = 55 units

Demand for Period 3 = 55 units

Inventory after period 3 = 0 units

Cost for Period 3 = 40*$100 + 15*$160 = $6400

Inventory Carrying Cost from Period 2 to Period 3 = $0

Total Cost

Total Cost = Period 1 + period 2 Period 3

= $3000+ $60 + $3800 + $6400

= $13260