Assignment #1:  due Tuesday, Sep. 3

Assignment #1:  due Tuesday, Sep. 3

(Collected at beginning of class; no late submissions accepted)

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NAME:  _______________________________________

INSTRUCTIONS:

1. Type your answers in red in the indicated areas.
2. This is an individual assignment, not a group assignment. It is to be completed by you entirely on your own.

Consider the following information for Questions 1 through 6:

Paul is the proprietor of several retail jewelry stores (all of which operate under the name “Taylor Diamonds and Jewelry”) in the Philadelphia area.  He must submit orders for bracelets for the upcoming merchandise season.  Bracelets are an important part of Taylor’s product line, along with other jewelry items such as earrings, watches, wedding and engagement rings, and other fashion accessories.   

The supplier from which Paul buys bracelets sells bracelets only in “lots” (i.e., batches or multiples) of ten.  The cost per bracelet is $40 if Paul orders 10 bracelets, $39 if he orders 20 bracelets, $37 if he orders 30 bracelets, $36 if he orders 40 bracelets, and $34 if he orders 50 bracelets.  Regardless of the cost to Taylor of purchasing the bracelets, Paul intends to price the bracelets at $50 each to customers in his retail stores. 

Paul knows that if there are any bracelets remaining at the end of the merchandise season, he can sell them in a clearance sale for $24 each.  Paul also knows that if his stores run of bracelets during the season, Taylor will suffer a “goodwill” loss with customers, estimated at about $6 per customer unable to purchase a bracelet.   

Paul estimates that the demand for bracelets in the upcoming season will be 15, 25, 35, or 45 bracelets, with probabilities of 0.35, 0.25, 0.20, and 0.20.  So, for example, the demand for 15 bracelets has a probability of 0.35, while the demand for 35 bracelets has a probability of 0.20, etc.. 

Using the above information, the payoff table (in $), with “ordering options” (i.e., the decision alternatives) and demand “states of nature,” is shown below:

Note:  the states of nature and decision alternatives in the payoff matrix are “flipped” from how presented in the Parvaderm case.   

* Example 1 payoff table calculation:  if Paul buys 40 bracelets, and demand turns out to be 15, then:

He purchases 40 bracelets at $36 each, for an expenditure of $1,440. Selling 15 bracelets at $50 each results in revenue of $750.  The 25 bracelets left over at season’s end will be sold at $24 each, for $600.  So, the entry in the payoff table in this example is:  $750 – $1,440 + $600 = -$90.

* Example 2 payoff table calculation:  if Paul buys 20 bracelets, and demand turns out to be 45, then:

The money spent to buy the bracelets is 20 x $39 = $780.  Upon selling the 20 bracelets, revenue is 20 x $50 = $1,000.  But 25 customers who wanted a bracelet couldn’t get one, so the loss of goodwill is 25 x $6 = $150.  So, the entry in the payoff table in this example is:  $1,000 – $780 – $150 = $70.

(1) Using the minimax regret criterion, which alternative will be chosen, and what is the dollar value of the maximum regret corresponding to the chosen alternative?

(i) In the “regret matrix” below, enter all 16 “regret” (also called “opportunity loss”) values corresponding to the cells of the payoff table:

(ii) ________________ Alternative chosen based on the minimax regret criterion?

(iii) _______________ Dollar value of the maximum regret corresponding to the chosen

alternative?

(2) Using the maximin decision criterion, which alternative will be chosen, and what is the dollar amount ($) of the minimum payoff corresponding to the chosen alternative?

(i) ________________ Alternative chosen based on the maximin criterion?

(ii) _______________ Dollar value of the minimum payoff corresponding to the

selected alternative?

(3) Using the maximax decision criterion (Note:  this decision criterion is described by Heizer and Render; see reading for details), which alternative will be chosen, and what is the dollar amount ($) of the maximum payoff corresponding to the chosen alternative?

(i) ________________ Alternative chosen based on the maximax criterion?

(ii) _______________ Dollar value of the maximum payoff corresponding to the

selected alternative?

(4)(a) ___________What is the expected monetary value (i.e., EMV) of the order option “Buy 10”?  (SHOW CALCULATION)

(b)  ___________What is the EMV of the order option “Buy 20”?  (SHOW CALCULATION)

(c)  ___________What is the EMV of the order option “Buy 30”?  (SHOW CALCULATION)

(d)  ___________What is the EMV of the order option “Buy 40”?  (SHOW CALCULATION)

(e)  ___________What is the EMV of the order option “Buy 50”?  (SHOW CALCULATION)

(5) _______________ What is the EMV of an order decision made with perfect information (i.e., under certainty) about the states of nature?   (SHOW CALCULATION)

(6) _______________ What is the EMV of perfect information (i.e., EMV(PI))?  (Note:  Heizer and Render refer to this value as “EVPI”)  (SHOW CALCULATION)

For Questions 7 and 8 below, assume the same information as above, except that now demand for 15, 25, 35, or 45 bracelets in the merchandise season has probabilities of occurrence of 0.1, 0.2, 0.6, and 0.1, respectively.

(7)(a) ___________What is the EMV of the order option “Buy 10”?  (SHOW CALCULATION)

(b)  ___________What is the EMV of the order option “Buy 20”?  (SHOW CALCULATION)

(c)  ___________What is the EMV of the order option “Buy 30”?  (SHOW CALCULATION)

(d)  ___________What is the EMV of the order option “Buy 40”?   (SHOW CALCULATION)

(e)  ___________What is the EMV of the order option “Buy 50”? (SHOW CALCULATION)

(8) _______________ What is the EMV of perfect information (i.e., EMV(PI))?  (SHOW CALCULATION)