Management Science and Operations Technology

MS$-3053$

Simulation Project $(80$ Points$)$

Please read the problems carefully, build a simulation model for each problem and answer

each part accordingly. Question Part Points

Problem $11$ Simulation model $20$

a $5$

b $5$

c $5$

d $5$

Problem $12$ Simulation model $25$

a $5$

b $5$

c $5$

Total $80$

$11.$ In preparing for the upcoming holiday season, Fresh Toy Company $($FTC$)$ designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $$100,000.$ The variable cost, which includes material, labor, and shipping costs, is $$34$ per doll. During the holid$1$ay selling season, FTC will sell the dolls for $$42$ each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $$10$ per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of $60,000$ dolls with a standard deviation of $15,000.$

The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce $60,000$ units $($the same as average demand$),$ but it wants to conduct an analysis regarding this production quantity before finalizing the decision.

a$.$ Create a what$-$if spreadsheet model using a formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand $(60,000$ units$)?$

b$.$ Modeling demand as a normal random variable with a mean of $60,000$ and a standard deviation of $15,000,$ simulate the sales of the Dougie doll using a production quantity of $60,000$ units. What is the estimate of the average profit associated with the production quantity of $60,000$ dolls? How does this compare to the profit corresponding to the average demand $($as computed in part $($a$))?$

c$.$ Before making a final decision on the production quantity, management wants an analysis of a more aggressive $70,000-$unit production quantity and a more conservative $50,000-$unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each?

In addition to mean profit, what other factors should FTC consider in determining a production quantity? Compare the three production quantities $(50,000,60,000,$ and $70,000)$ using all these factors. What trade$-$offs occur? What is your recommendation?

$12.$ South Central Airlines $($SCA$)$ operates a commuter flight between Atlanta and Charlotte.

The regional jet holds $50$ passengers, and currently SCA only books up to $50$ reservations.

Past data show that SCA always sells all $50$ reservations, but on average, two passengers do not show up for the flight. As a result, with $50$ reservations the flight is often being flown with empty seats. To capture additional profit, SCA is considering an overbooking strategy in which they would accept $52$ reservations even though the airplane holds only $50$ passengers. SCA believes that it will be able to always book all $52$ reservations. The probability distribution for the number of passengers showing up when $52$ reservations are accepted is estimated as follows:

Passengers Showing Up The table shows the following:

$$ There is a $5\%$ chance $(0\mathrm{.}05)$ that $48$ passengers will show up$.$

$$ There is a $25\%$ chance $(0\mathrm{.}25)$ that $49$ passengers will show up$.$

$$ There is a $50\%$ chance $(0\mathrm{.}50)$ that $50$ passengers will show up $($this is the most likely outcome$).$

$$ There is a $15\%$ chance $(0\mathrm{.}15)$ that $51$ passengers will show up$.$

$$ There is a $5\%$ chance $(0\mathrm{.}05)$ that $52$ passengers will show up$.$

SCA receives a marginal profit of $$100$ for each passenger who books a reservation $($regard$-$less whether they show up or not$).$ The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $$150$ per passenger. Develop a spreadsheet simulation model for this overbooking system and simulate the number of passengers that show up for a flight.

a$.$ What is the average net profit for each flight with the overbooking strategy?

b$.$ What is the probability that the net profit with the overbooking strategy will be less than

the net profit without overbooking $(50*$$$100=$ $$5000)?$

c$.$ Explain how your simulation model could be used to evaluate other overbooking levels such as $51,53,$ and $54$ and for recommending a best overbooking strategy.