Tables $3$ and $4$ give estimates for the cost of a procuring a generator and for the lost profit

experienced in the event of a shortage of generators. Based on these scenarios, construct a

newsvendor model for the problem of selecting the number of generators that will minimize

expected cost by completing each table.

$2.$ Based on the data from the tables in Problem $1,$ answer the following questions:

a$.$ Suppose that experience indicates that the region will be without electricity for three days

following a major hurricane and that lost profits are estimated at $$5,000$ per day. How

many generators should be purchased to minimize the expected cost?

Page $11$

b$.$ What is the impact of your decision about the number of generators to purchase if

electricity is actually out for four days?

c$.$ What are the advantages and disadvantages of using a model that minimizes expected

cost in determining how many generators to procure?

$3.$ Now suppose the realized demand for generators is D and the total quantity of generators

purchased is Q$.$ Estimates indicate that electricity will be out for three days in the event of a

major hurricane and lost profit at stores unable to open is projected to be $$5,000.$ Generators

cost $$1,000.$ Complete the following steps to analyze the generator procurement problem

using an alternative objective, namely to minimize the maximum regret experienced.

a$.$ Express the realized cost of a decision to purchase Q generators, including procurement

cost for generators and the cost of lost sales, in terms of Q and D$.$

b$.$ If a planner knew a priori what the total demand for generators would be$,$ what is the

optimal cost the planner would incur? Express this cost in terms of Q and D$.$

c$.$ Regret is defined as the difference between the realized cost of a procurement decision

and the cost of an optimal decision that would have been made with a priori knowledge

of the demand for generators. Express the regret incurred as a result of a decision to

purchase Q generators when D are actually needed in terms of these two variables.

d$.$ Using the expressions you developed, complete Table $5,$ which summarizes the realized

costs and the regret of procurement decisions. In this scenario, assume that the maximum

number of generators that could possibly be needed in a season is $16.$

$4.$ Based on your analysis in Problem $3,$ answer the following questions:

a$.$ Suppose once again that your operations management team estimates from experience

that the region is likely to be without electricity for three days following a storm and that

lost profits are $$5,000$ per day. How many generators should be purchased to minimize

the maximum regret?

b$.$ What is the impact of your decision about the number of generators to purchase if

electricity is actually out for four days?

c$.$ What are the advantages and disadvantages of using a model that minimizes maximum

regret in determining how many generators to procure?

$5.$ In Problems $14,$ the decision about the number of generators to purchase was made based

on estimates for the number of days without electricity and the lost profits that result from the

inability to open stores. Historical data and management expertise can help improve these

estimates, but uncertainty still exists. In this question, we will examine the effects of this

uncertainty on the procurement decisions made under the two objectives.

a$.$ Using the approach from Problem $3,$ calculate the value of Q that minimizes maximum

regret if daily profit loss is $$3,000$ and electricity is out for $2,3,$ or $4$ days. Do the same if

daily profit loss is $$5,000$ and electricity is out for $2,4,$ or $5$ days.

b$.$ How do these values compare to those from Problem $1$ for each scenario, where the

objective was to minimize expected cost? How do the Q values change under each

objective as the number of days without electricity and the anticipated profit loss

increase?

c$.$ What implications do these trends have for supply chain managers and their decisions

about procuring emergency equipment in the face of uncertain scenarios?

$6.$ Based on your findings from the previous problems, how many generators will you

purchase? Explain your reasoning for this recommendation.