Problem $1[28$ Marks$]$

Swift Shipping is a $20-$year$-$old Glasgow$-$based clothing retailer specialising in next$-$day

delivery of its affordable, stylish office attire for working women. Recently, Swift has struggled

to maintain its competitive edge as more clothing brands focus on speedy shipping. Swift

prides itself on using only local Scottish couriers for reliability. Lately, tensions between

management and couriers' unions have increased. The possibility of postal strikes could

severely impact Swift's shipments right before its busy season ramps up$.$

Swift's Operations Manager must decide whether to ship orders now as usual via its Scottish

couriers or wait to see if strikes occur. If Swift ships as normal and strikes happen, costs from

delays and rerouting through England would total $60,000.$ If no strikes occur, regular Scottish

shipping would run $4,000.$ If Swift postpones Scottish shipping pre$-$emptively, delay costs

would hit $10,000$ regardless of strikes. The Operations Manager knows Strikes could seriously

impact the company's shipping capacity right before the busy season. But postponing

shipping may upset customers expecting Swift's signature next$-$day delivery. She must

carefully weigh the costs and benefits of potential actions based on the likelihood of strikes

occurring. Let p equal the probability that strikes affect Swift's courier shipments.

a$.$ For what values of p does Swift minimize expected total cost by postponing shipping?

Build a decision tree with trial values of p and determine the approximate probability p

that minimises expected cost. $[$Consider using data table to determine EMV for various

values of p$][6]$

b$.$ Suppose Swift pays $1000$ to purchase strike likelihood data. Based on similar strike threats

in the past, the company assesses that if there will be a strike, the information will predict

a strike with probability $0\mathrm{.}75,$ and if there will not be a strike, the information will predict

no strike with probability $0\mathrm{.}85.$ Provided that p$=0\mathrm{.}15,$ what strategy should Swift Shipping

pursue to minimize its expected total cost? $[8]$

c$.$ Using the analysis in Part B$,$ find the EVI when p$=0\mathrm{.}15.$ Then use a data table to find EVI for

p from $0\mathrm{.}05$ to $0\mathrm{.}30$ in increments of $0\mathrm{.}05.$ and chart EVI versus p$.[5]$

d$.$ Write a formal report that summarises your analysis and provides recommendations to the

Operations Manager at Swift Shipping. The report should include: $[9]$

$4$

$-$ An executive summary highlighting the key findings from your analysis in question

a$,$ b$,$ and c$.(3)$

$-$ Clearly stated recommendations on whether Swift should postpone shipping or

proceed as normal before the postal strike threat. $(2)$

$-$ Quantitative support for your recommendations using calculations from the

questions. $(2)$

$-$ A discussion of the limitations$,$ risks, and mitigation strategies related to your

recommendation. $(2)$

Problem $2[23$ Marks$]$

The credit union branch at Newcastle University frequently sees mismatches between

customer demand and service staffing levels. Customers face long queues on busy days, yet

idle staff at other times. Branch manager Michael Kaluuya sees this issue but lacks data

analytics expertise to optimize staff scheduling.

Michael believes accurate demand forecasting is key to balancing staff productivity, costs and

customer service. He compiled a dataset with over a year's worth of daily customer arrival

figures, along with potential demand drivers like the day of the week, whether the day was a

staff or faculty payday, and whether the day was the day before or after a holiday. Data for this

problem is in the file $$Problem $2\_$Data$.$ However, Michael cannot reliably analyse the patterns

himself to create robust forecasts of each day$$s customer arrivals.

a$.$ Build a statistical forecasting model to predict the credit union branch$$s daily customer

arrivals using Michael's dataset. $[$Hint$]$ you will need to create Dummy variables. $[8]$

b$.$ Develop an improved model using only significant variables. You might want to consider

if the first day of the month influences the demand. $[6]$

c$.$ In your consulting report for Michael: $[9]$

$-$ Concisely explain your final model methodology, variables, parameter estimates,

overall fit, etc. $(3)$

$-$ State model assumptions and evaluate their validity. $(4)$

$-$ Assess strengths $/$ limitations in capturing customer demand patterns $(2)$

$5$

Problem $3[26$ Marks$]$

The management of Zahret Company is trying to determine the amount of each of two

products to produce over the coming planning period. The following information concerns

labour availability, labour utilisation, and product profitability.

Table $1$

Labor$-$Hours Required $($hours$/$unit$)$

Department Product $1$ Product $2$ Hours Available

A $1\mathrm{.}000\mathrm{.}35100$

B $0\mathrm{.}300\mathrm{.}2036$

C $0\mathrm{.}200\mathrm{.}5050$

Profit contribution$/$unit $30\mathrm{.}0015\mathrm{.}00$

a$.$ Develop a linear programming model formulation of the Zahret Company problem. Solve

the model using Solver and determine the optimal production quantities of products $1$