Here's my initial understanding of the problem--

• Supplier A = $112/ea for on-time delivery, or $71/ea for late delivery, with about a 1-in-3 chance of late delivery;
• Supplier B = $106/ea for on-time delivery, or $65/ea for late delivery, with about a 1-in-5 chance of late delivery; and
• Supplier C = $100/ea for on-time delivery, or $59/ea for late delivery, with about a 1-in-25 chance of late delivery.

Am I understanding correctly?

Or does the quoted price include the delivery incentive?--

• Supplier A = $71/ea for on-time delivery, or $30 for late delivery, with about a 1-in-3 chance of late delivery;
• Supplier B = $65/ea for on-time delivery, or $24 for late delivery,  with about a 1-in-5 chance of late delivery; and
• Supplier C = $59/ea for on-time delivery, or $18 for late delivery, with about a 1-in-25 chance of late delivery.

16 minutes ago, ji20874 said:

Here's my initial understanding of the problem--

• Supplier A = $112/ea for on-time delivery, or $71/ea for late delivery, with about a 1-in-3 chance of late delivery;
• Supplier B = $106/ea for on-time delivery, or $65/ea for late delivery, with about a 1-in-5 chance of late delivery; and
• Supplier C = $100/ea for on-time delivery, or $59/ea for late delivery, with about a 1-in-25 chance of late delivery.

Am I understanding correctly?

Yes.

I presume that we can make our own assumptions with regards to orders vs units (i.e. 1 order for a 100 units or 100 orders for 1 unit each) and for the number of customers placing orders (i.e. 1 customer with 100 orders or 100 customers with 1 order each) and that on-time probability applies to the entire order and not to an individual unit within an order; and that what is best for the government means what is best for any one individual customer’s cost or budget.

2 hours ago, Whynot said:

I presume that we can make our own assumptions with regards to orders vs units (i.e. 1 order for a 100 units or 100 orders for 1 unit each) and for the number of customers placing orders (i.e. 1 customer with 100 orders or 100 customers with 1 order each) and that on-time probability applies to the entire order and not to an individual unit within an order; and that what is best for the government means what is best for any one individual customer’s cost or budget.

You may be making things too complicated. I suggest you just work out the problem for 1 unit.

I would say B, but only if $41 delivery incentive has already been factored into the likelihood of late delivery.

I said B, too. 

Expected Price of A = $71 + (.69)($41) = $99.29

Expected Price of B = $65 + (.79)($41) = $97.39

Expected Price of C = $59 + (.96)($41) = $98.36

All suppliers have the same delivery incentive, so the $41 is a wash.

All suppliers will deliver no later than 1 week, so the delivery schedule is a wash.

This leaves the price per unit the only consideration, and Supplier C has the best price, $59.