Problem 1 [28 Marks] Swift Shipping is a 20-year-old Glasgow-based clothing reta

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 0.75, and if there will not be a strike, the information will predict
no strike with probability 0.85. Provided that p=0.15, 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=0.15. Then use a data table to find EVI for
p from 0.05 to 0.30 in increments of 0.05. 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]
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– 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)
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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 1.00 0.35 100
B 0.30 0.20 36
C 0.20 0.50 50
Profit contribution/unit £30.00 £15.00
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 and
2. [8]
b. In computing the profit contribution per unit, management does not deduct labour costs
because they are considered fixed for the upcoming planning period. However, suppose
that overtime can be scheduled in some of the departments. Which departments would
you recommend scheduling for overtime? How much would you be willing to pay per hour
of overtime in each department? [5]
c. Suppose that 10, 6, & 8 hours of overtime may be scheduled in departments A, B, and C,
respectively. The cost per hour of overtime is £18 in department A, £22.50 in department
B, and £12 in department C. Formulate and solve a linear programming model that can be
used to determine the optimal production quantities if overtime is made available. What
are the optimal production quantities, and what is the revised total contribution to profit?
How much overtime do you recommend using in each department? What is the increase
in the total contribution to profit if overtime is used? [8]
d. In the report, summarise answers to the above questions and discuss any additional insights
that would support decision making. [5]
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Problem 4 [23 Marks]
Management of Paxon Pharma, a leading UK manufacturer of generic prescription drugs, is
trying to control inventory costs for one of its highest volume products – the antibiotic drug
amoxicillin. The weekly holding cost for 1,000 cases (one unit) of amoxicillin is £30. The
marketing team estimates the average weekly demand from NHS trusts and UK pharmacies is
120 units, with a standard deviation of 15 units. Unmet demand is considered lost sales.
The production team at Paxon’s Manchester plant can manufacture at one of three weekly
rates: 110 units; 120 units; or 130 units. Changeover and recalibration between production
rates carries a fixed cost of £3,000.
Management aims to test the following production planning policy:
– If current UK amoxicillin inventory is below 30 units, produce 130 units next week.
– If inventory is above 80 units, produce 110 units next week.
– Otherwise, continue last week’s output rate.
Current UK inventory is 60 units following last week’s production of 120 units.
a. Build a 52-week Excel simulation model of this policy. Graph UK inventory over time and
calculate total cost (Inventory cost plus production cost). [7]
b. Run the simulation for 500 iterations by varying the upper threshold U from 30 to 80 units.
Estimate the average 52-week cost at each value of U. Keep L = 30 throughout. [5]
c. Determine the sample mean and standard deviation of costs for each value of U. Using the
simulated results, is it possible to construct valid 95% confidence intervals for the average
52-week cost for each value of U? In any case, graph the average 52-week cost versus U.
Identify the optimal U when lower threshold L is fixed at 30 units. [6]
d. Summarize findings and recommendations in a formal report. Synthesize numerical
analysis and qualitative context into strategic, actionable guidance for Paxon’s UK
executive team and manufacturing planners. Consider if other production policies could
be more useful to investigate?