Suppose Generic has to select one of two products, A or B, to introduce into a certain market. Because of their different characteristics, A and B are expected to perform differently in the market.

Specifically, A has a 5% chance of encountering very low demand, 20% chance of somewhat low demand, 20% of fairly high demand, and 55% of very high demand. Product B is expected to behave differently: there is a 60% chance that B will have low demand, 15% chance of medium demand, and 25% chance of high demand.

The expected revenues (in $M) are as follows:

A |
B |
||

$M | $M | ||

Very low | 100 | Low | 100 |

Somewhat low | 180 | Medium | 200 |

Fairly high | 400 | High | 300 |

Very high | 500 |

Finally, product A will cost $160M to introduce, while B will cost $30M to introduce. Use decision analysis to answer the following questions. (Show your work!)

(a.) With an expected value criterion, which product will you choose to introduce? (Over if necessary.)

(b.) Using a maximin criterion, which product will you choose, and why? (Show work.)

Problem 2 (20 points)

Consider, for a certain product, the following regional sales data that have been collected over the past six months. Assume there are no seasonal effects.

Use Excel to perform the following, using two decimal places. WRITE YOUR ANSWERS IN THE TABLE BELOW.

(a.) An exponential smoothing forecast for June through November with a = 0.2 and a starting value of 250 for May. Find the MAD for these forecasts as well.

(b.) A set of regression forecasts for May through November, and the MAD for these forecasts.

Month |
Period |
Sales ($K) |
a = 0.2 |
Error(0.2) |
Regression |
Regr. Error |

May 22 | 1 | 250 | 250 | |||

Jun 22 | 2 | 259 | ||||

Jul 22 | 3 | 257 | ||||

Aug 22 | 4 | 259 | ||||

Sep 22 | 5 | 252 | ||||

Oct 22 | 6 | 258 | ||||

Nov 22 | 7 | ? |

What is the equation of the trend line?

(c.) Which forecast method performed best for this data set? Explain your answer.

(d.) What is the r^{2 }value? State in plain English what this means in the forecasting context.

Problem 3 (20 points)

Consider an item with the following six-step assembly. Task times are in seconds.

Immediate

Taskpredecessortime (sec.)

A — 30

B — 50

C A,B 95

D B 45

E C,D 60

F D 50

(a.) What is the minimum possible cycle time?

(b.) Now consider a two minute (= 120 sec.) cycle time. Use the default (longest task time) assignment rule to assign tasks to work stations. Show the assignment you obtain! Calculate its efficiency.

(c.) Now suppose only three work stations are available. How would you now assign the tasks

to three work stations in order to maximize output? Compare the resulting output to the

situation in (b.). *Hint*: being shortstaffed, there’s no way you can do as well as in (b.).

Problem 4 (20 points)

Consider a bank branch that has three distinct customer arrival patterns throughout the day, as measured by average arrival rates (below).

Morning (8:30 – 11:30):l_{1} = 35/hour.

Lunch (11:30 – 1:30):l_{2} = 55/hour.

Afternoon (1:30 – 4:00):l_{3} = 31/hour.

Regardless of the time of day, the average time it takes for a teller to serve customers is 3 minutes, 8 seconds.

(a.) First, write down the service rate (per teller, per hour).

(b.) Use the Excel template to determine, for each of the three periods, the minimum number of tellers necessary to ensure that the average customer wait before service is less than 8 minutes.

(c.) For each of the three periods, and for the decisions you made in (a.) above, what is the average total number of customers present?

Problem 5 (20 points)

Generic manufactures a personal communication device called the iFell Tower that they hope can compete with the iPhone. Right now they plan to test distribution and sales of the “Tower” through four channels in their Philadelphia test market.

1. Mobile stores2. Office equipment retailers3. The Worst Buy big box chain, and4. Web sales.

Generic has an advertising budget of $5,000 and they are willing to devote up to 1,800 hours of sales force time for this test market. They plan to produce and distribute exactly 600 Tower units in the test market, and to test the effectiveness of their contract with Worst Buy, they will allocate at least 150 of the 600 units solely for the Worst Buy stores. The different channels have different costs and characteristics and these differences are summarized in the table below.

Distribution Channel | Profit per unit sold | Advertising cost per unit sold | Personal sales effort per unit sold |

Mobile stores | $90 | $10 | 2 hours |

Office equipment stores | 84 | 8 | 3 hours |

Worst Buy stores | 70 | 9 | 3 hours |

Web distribution | 60 | 15 | None |

(a.) First notice that Generic’s objective in this test market is to sell all of the 600 units in the most profitable way. To aid in this planning, Generic will develop a linear programming (LP) model. Define the decision variables that Generic will want to use in this LP. DO NOT TRY TO SOLVE!

(b.) Now write down the objective function, using the variables from part (a.).

(c.) Now write down all the constraints for this LP, using the variables that you defined as well as all of the information above. REPEAT: DO NOT TRY TO SOLVE!

(d.) Below is some output involving the optimal solution for this problem.

Variable |
x1 | x2 | x3 | x4 |

Value |
25.0 | 425.0 | 150.0 | 0.0 |

Constraint |
Slack/surplus |
Shadow prices |

Advertising budget | 0.00 | 3.00 |

Sales force limitation | 25.00 | 0.00 |

Exactly 600 units to sell | 0.00 | 60.00 |

150 sold through Worst Buy | 0.00 | -17.00 |

Would you propose increasing the sales force hours beyond the 1,800 originally specified? Why or why not