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Problem of the Day--Pricing Delivery Incentives

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Don Mansfield

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Pricing Delivery Incentives  

9 members have voted

  1. 1. Considering only the total amount the Government would expect to pay, which quote do you think is best?

    • Supplier A
      0
    • Supplier B
      6
    • Supplier C
      3

Assume you are soliciting quotes for an item of supply. Suppliers A, B, and C each sell the item for about $100/unit. However, the probability of late delivery is different for each supplier. Supplier A has a 31% chance of delivering late, Supplier B has a 21% chance of delivering late, and Supplier C has a 4% chance of delivering late. There’s a 100% chance that all suppliers will deliver no later than one week after the delivery date and any damages due to late delivery will be negligible.

Your solicitation requests that vendors quote both a unit price and a per-unit delivery incentive. The supplier can only earn the delivery incentive if delivery is on time. Otherwise, the Government only pays the unit price.

Supplier A quotes a per-unit price of $71 and a $41/unit delivery incentive.

Supplier B quotes a per-unit price of $65 and a $41/unit delivery incentive.

Supplier C quotes a per-unit price of $59 and a $41/unit delivery incentive.

Considering only the total amount the Government would expect to pay, which quote do you think is best?

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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.

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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.

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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.

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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.

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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

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