Alveva is an online beauty subscription service that sends subscribers a monthly box of four to seven curated make-up and beauty products. Alveva’s monthly subscription service allows consumers to test in-trend products before purchasing them at a full price from Alveva’s website. Table 1 below displays the per unit wholesale cost of each product that can be used to create different boxes each month.

Table 1. Per unit wholesale cost of available products

List of Products	Cost
Moisturizer A	$ 15.00
Moisturizer B	$ 18.00
Moisturizer C	$ 11.00
Moisturizer D	$ 18.00
Lipstick A	$ 10.00
Lipstick B	$ 7.00
Lipstick C	$ 20.00
Lipstick D	$ 9.00
Concealer A	$ 24.00
Concealer B	$ 6.00
Concealer C	$ 14.00
Concealer D	$ 24.00
Highlighter A	$ 19.00
Highlighter B	$ 19.00
Highlighter C	$ 5.00
Highlighter D	$ 6.00
Nail polish A	$ 27.00
Nail polish B	$ 15.00
Nail polish C	$ 6.00
Nail polish D	$ 9.00

After customers receive their subscription boxes, they can indicate the products they did not enjoy through a monthly survey. The Analytics Department at Alveva uses this information to categorize customers into 10 subscriber types. The number of customers that belong to each subscriber type is given in Table 2. In addition to collecting subscribers’ feedback, the firm also keeps track of the products that the customers receive each month to ensure the delivery of new items in each box. The ones in Table 2 indicate a product that a subscriber type must not receive in their next box. For example, subscriber type 1 must not receive moisturizer A, lipstick C, concealer B, highlighters A and B, and nail polish D in their next monthly box. The same box should be sent to all subscribers of the same type. At most 80000 units of each product type can be produced due to resource limits.

Table 2. Subscriber types and requirements

List of Products	Subscriber 1	Subscriber 2	Subscriber 3	Subscriber 4	Subscriber 5	Subscriber 6	Subscriber 7	Subscriber 8	Subscriber 9	Subscriber 10
Moisturizer A	1	0	0	0	0	0	0	0	0	0
Moisturizer B	0	0	0	1	0	0	0	0	0	0
Moisturizer C	0	0	0	0	0	0	0	1	0	0
Moisturizer D	0	1	1	0	0	0	1	0	0	0
Lipstick A	0	0	0	0	0	1	0	0	0	1
Lipstick B	0	0	0	0	0	1	1	1	1	1
Lipstick C	1	0	0	0	0	0	0	1	0	1
Lipstick D	0	0	0	0	0	0	0	0	0	0
Concealer A	0	0	0	0	0	0	0	0	0	1
Concealer B	1	1	1	1	0	0	0	0	0	0
Concealer C	0	0	0	0	0	0	0	0	0	0
Concealer D	0	0	1	1	0	0	0	0	0	0
Highlighter A	1	0	0	0	0	0	0	0	0	0
Highlighter B	1	0	0	0	0	0	0	0	0	0
Highlighter C	0	0	1	0	0	1	1	0	0	1
Highlighter D	0	0	0	1	0	0	0	0	0	1
Nail polish A	0	0	1	0	0	0	0	0	0	0
Nail polish B	0	0	0	0	0	0	0	0	1	0
Nail polish C	0	1	0	0	0	1	1	0	0	1
Nail polish D	1	0	0	0	0	0	0	0	0	0
Total # of customers	8264	5248	7676	5497	23140	12723	20746	22761	6922	3966

If Alveva charges $8 per item in the monthly subscription box, how should the boxes be curated and assigned to different subscribers to maximize the total profit?

1. Write the algebraic formulation for this optimization problem.
2. Solve using Excel or GAMS and report your findings.

The CEO of Alveva would like to keep the number of different boxes created to a maximum of 3 to process boxes faster. (Please ignore the 80000 resource constraint for this problem.) What should be included in these 3 boxes, how should they be assigned to different subscribers, and what is the optimal profit? Solve using Excel or GAMS. Hint: I recommend using GAMS and solver BONMIN for this portion of the problem. Remember you can select your solver by adding the following before the model statement:

Answer rating: 100% (QA)

Here is the optimization formulation for maximizing Alvevas total profit from their monthly su... View the full answer