Question

Four suppliers each with a specific product provide service to ESS, a retailer with eight stores in Saskatoon. Transportation can be done by a single truck owned by ESS or using the trucks of a 3PL.

Jack, the operations manager of ESS, has gathered the following information about the two options:

The retailer’s truck:

• Capacity: 20,000 kilograms.
• Cost of shipping: $1,000 per load, $100 per delivery.
• Due to the scheduling limitations, truck is only able to serve one store per trip (direct shipping).

The 3PL’s trucks:

• Capacity: 30,000 kilograms.
• Cost of shipping: flat rate of $2,000 per load.
• The 3PL does not have scheduling limitations and serves two stores per trip (milk run).

Jack has calculated the holding cost per kilogram of the products to be $0.5 per year. Jack is interested in finding the breakeven demand amount between the two options.

Answer 1

Let us say the overall demand for the retailer is x

Now to meet the demand in the eight stores, the retailer will have to run 8 trips with $1000 per load $100 per delivery i.e. $1100 per trip i.e. total of $8800

So if the total supply to the 8 stores is 20,000 kg each, the remaining inventory with the retailer is x-160000

The cost of this will be 0.5 X (x-160000)

So overall cost incurred by the retailer is 0.5x – 80000 + 8800 = 0.5x -71200

Nor for the 3PL provider, capacity is 30000 kg and there is flat cost of $2000 per load

Now to meet the 20000 kg supply to each of the 8 stores, the 3PL provider can run fewer trips since it can serve two stores per tip; The total trips will be 6 as follows:

Trip 1 will cover store 1 and store 2 -> 20000 kg and 10000 kg

Trip 2 will cover store 2 and store 3 -> 10000 kg and 20000 kg

Trip 3 will cover store 4 and store 5 -> 20000 kg and 10000 kg

Trip 4 will cover store 5 and store 6 -> 10000 kg and 20000 kg

Trip 5 will cover store 7 and store 8 -> 20000 kg and 10000 kg

Trip 6 will cover store 8 -> 10000 kg

So total cost will be 2000 X 6 = $12000

For breakeven demand, the cost for retailer and 3PL should be same

So 0.5x – 71200 = 12000

i.e. 0.5x = 83200

i.e. x = 166,400