Change a delivery boy needs to carry

Question

There are total 991 deliveries, to be done by N delivery boys. Each delivery boy can handle upto 40 deliveries. So the deliveries can be distributed in chunks of 40, in the same order of Delivery No, to each delivery boy.

Probability distribution: Each customer has a following likelihood of least denomination of notes he is paying with.

• 1000 - 2%

• 500 - 40%

• 100 - 30%

• 50 - 20%

• 20 - 5%

• 10 - 3%

Questions:

• What the amount of change, and in what denomination, should each delivery boy carry?
• What is the cost function of the model? What is being optimised, (maximized or minimized)?

What are the concepts required to solve this problem? I am beginner in data analytics or decision science, so please guide me.

Order number and order amount are given as excel sheet for all 991 orders. If required, can be provided.

Answer 1

This seems to be a combination of very precise data (in the Excel sheet) and very vague questions.

Here is one possible approach.

If a customer has only $1000$ denomination notes then the delivery boy will on average have to give the customer $500$ in change (in some cases it will be more than this, in other cases less). Out of $40$ deliveries the delivery boy expects $40 \times 2 \% = 0.8$ such customers on average. So he should carry $0.8 \times 500 = 400$ in change for these customers.

Go through the other groups of customers in the same way and add up the total amount of change that is required for each group of customers, and you get a total of $5226$ in change for each 24 delivery boys and for the 25th delivery boy delivering 31 deliveries, it will be 4050.

The "what denomination" part of the question is impossible to answer without more information. And the "cost function" is something that should be given in the question. Are we trying to minimize the amount of change carried by each delivery boy? Or the number of notes carried by each delivery boy? Or the probability that a delivery boy cannot give a customer change ? Or the average number of customers who cannot be given change? The question should provide this information.