Case Study: Analyzing Free Shipping Strategies

As the promotion manager of a company that sells a single product, you are tasked with evaluating

different free shipping strategies to maximize profits. The company's product is bought from the

supplier for $$20$ per unit and sold to customers for $$50$ per unit. Customers are interested in

buying as many units as possible within their budget, but they will not purchase more than $3$

units. The shipping cost for any order is $$25,$ regardless of the number of units purchased.

Free Shipping Strategies:

The company is considering four free shipping strategies:

$1.$ Offering free shipping for purchases of $4$ or more items, which effectively means no free

shipping since customers do not buy more than $3$ items.

$2.$ Offering free shipping for purchases of $3$ or more items.

$3.$ Offering free shipping for purchases of $2$ or more items.

$4.$ Offering free shipping for any purchase, including just $1$ item.

Customer Purchase Decisions:

In terms of customer purchase decisions, customers aim to buy as many items as possible within

their budget, with a maximum limit of three items.

For instance, if a customer's budget is $$120,$ their purchasing behavior would vary based on the

free shipping policy in place.

Under Strategy $-1$: Without any free shipping offer:

$$ The customer would only buy $1$ item.

$$ The remaining budget after shipping costs, which is equal to $$120-$$$25=$ $$95,$ would not

allow for the purchase of a second item.

Under Strategy$-2$: If a free shipping is offered for buying $3$ or more items:

$$ The customer would only be able to buy $1$ item, since buying $3$ products is out of her

budget. That is$,3$x$$50=$ $$150>$ $ $120.$

$$ The customer needs to pay for $$25$ shipping cost, and her remaining budget, $$120-$$$25=$

$$95,$ would allow her to buy at most $1$ item.

Under Strategy$-3$: If a free shipping is offered for buying $2$ or more items:

$2$

$$ The customer would opt to buy $2$ items, because the cost of buying $2$ items is within the

budget of the customer as her order qualifies for free shipping. That is $2$x$$50=$ $$100<$

$$120.$

Under Strategy$-4$: If free shipping is available for any purchase:

$$ The customer would still buy $2$ items, maximizing her budget's potential.

Company's Net Profit Calculation:

The company's net profit from a customer is calculated as the sales profit minus the shipping cost.

The sales profit is determined by the number of items bought multiplied by the profit per unit, which

is $$30.$ The shipping cost will either be $$0$ or $$25,$ depending on the free shipping policy in effect.

The number of items bought by the customer will depend on the free shipping policy and the

customer's budget.

Using the above example, we can calculate the company$$s net profit for different free shipping

strategies, as follows.

Once again, let a customer's budget be $$120.$ Then, the company$$s net profit would vary based on

the free shipping policy in place.

Under Strategy $-1$: Without any free shipping offer:

$$ The customer would only buy $1$ item and would pay the shipping cost.

$$ The company$$s net profit would be $1$x$$30=$$$30$ since the company does not incur any

shipping cost.

Under Strategy$-2$: If a free shipping is offered for buying $3$ or more items:

$$ The customer would only buy $1$ item and would pay the shipping cost.

$$ The company$$s net profit would be $1$x$$30=$$$30$ since the company does not incur any

shipping cost.

Under Strategy$-3$: If a free shipping is offered for buying $2$ or more items:

$$ The customer would buy $2$ items and would not pay for shipping as her order qualifies

for free shipping.

$$ The company$$s net profit would be $2$x$$30-$ $ $25=$$$35$ since the company would pay for

the shipping.

$$

Under Strategy$-4$: If free shipping is available for any purchase:

$$ The customer would buy $2$ items and would not pay for shipping.

$$ The company$$s net profit would be $2$x$$30-$ $ $25=$$$35$ since the company would pay for

the shipping.

$3$

Monte Carlo Simulation:

For the Monte Carlo Simulation, the customer's budget is considered a random variable with a

normal distribution. The mean of this distribution is twice the sum of the digits in your student ID$,$

and the standard deviation is the sum of the digits in your student ID$.$ The goal is to simulate the

behavior of $500$ customers under each free shipping strategy to determine which one is most

beneficial for the company. The simulation will calculate the total number of items sold, total

sales profit, total shipping cost paid by the company, and total net profit for each strategy.

Task:

Your task is to analyze the results of the simulation to compare the strategies in terms of total

number of items sold, total shipping cost incurred by the company, and total net profit. Based on

this analysis, a final recommendation will be made on which strategy should be selected and why.

Submission Guidelines:

Your submission should consist of an Excel file containing two sheets, as detailed below:

Sheet $1$: Monte Carlo Simulation and