1 A power plant in California uses coal at the rate of 10000

1. A power plant in California uses coal at the rate of 100,000 pounds each day. It also uses MRO material at the rate of 1,000 pounds each day. The coal comes from Wyoming and the MRO material comes from Chicago. Coal costs $0.01 per pound, whereas MRO material costs S10 per pound, on average. Holding costs at the power plant are 25 percent. Transportation choices available are as follows Truck Lead time 4 days Minimum cost $100 Up to 10,000 pounds at $0.08 per pound Between 10,000 and 20,000 pounds at $0.07 per pound for entire load Between 25,000 and 40,000 pounds at S0.06 per pound for Train Lead ime 15 days Carload (100,000 pounds) at $400 per carload Full train (70 cars) at $15,000 per train entire load Small TL (40,000 pounds) for $2,000 Large TL (60,000 pounds) for $2,600 Safety inventory of coal and MRO materials is kept at twice the consumption during the lead time of supply. What mode of transport do you recommend for each of the two products? Why?

Solution

Given that,

Train

Lead Time = 15 days

Transportation cost: Carload(100,000 pounds) at $400 per carload and Full train (70 cars) at $15,000

Truck

Lead time = 4 days

Transportation cost: Min of $100, LTL at $0.06 to $0.08 per pound

Small TL (40,000 pounds) for $2,000 and Large TL (60,000 pounds) for $2600.

To find the suitable mode of transportation, we need to estimate the total Cost, which is sum of the Transportation cost and inventory cost.

Total Cost = Transportation cost + inventory holding cost

For Coal, D = 100,000 pounds/ day and cost $0.01/pound

Using train, since lead-time is 15 days, the total quantity has to be 15 x 100,000 pounds = 1,500,000 pounds to be carried each time

Transportation Cost (TC) = 400 * 15 = $6,000

Cycle inventory = shipment size (Q) / 2

In transit inventory = Leadtime x demand (D)

Safety inventory = Leadtime x demand (D)*2

Average inventory = cycle inventory + in transit inventory + safety inventory = 1,500,000/2 + 15 * 100,000 + 15 * 100,000 * 2 = 3.5 * 1,500,000 = 52,50,000 units

Inventory costs = 52,50,000 * 0.25 * 0.01 = $13,125

Thus, Total Cost = Transportation cost + inventory holding cost = $6,000 + $13,125 = $19,125

The same estimates using train, will be 4 x 100,000 pounds = 4,00,000 pounds to be carried each time which requires 4,00,000/ max capacity of truck = 4,00,000/60,000 = 6 LTL and 1 STL

Transportation Cost (TC) = 6 LTL and 1 STL = 6 * $2600 + $2,000 = $17,600

Inventory costs = 14,00,000 * 0.25 * 0.01 = $3,500

Thus, Total Cost = Transportation cost + inventory holding cost = $17,600+ $3,500 = $21,100

Comparing both the costs, we can conclude that shipping coal using train is recommend solution.

For MRO, D = 1,000 pounds/ day and cost $10/pound

Contrary to the coal, MRO has low demand and high unit cost, which makes the product to have short lead-time availability and lesser inventory.

Since, Truck can ship smaller quantities than the train while the minimum train carload capacity starts at 100,000 pounds, it is recommended to ship MRO using Truck.

Thanks.