Alveva Subscription Box Service
Advanced Business Analytics
Ali Fattahi
Alveva is an online beauty subscription service that sends its subscribers a monthly box of four to seven curated make-up and
beauty products. Alvevaàmonthly subscription service allows customers to test in-trend products before purchasing them at a full
price from Alvevaàwebsite. Table 1 (second column) shows the per unit wholesale cost of each product that can be used to create
different boxes each month.
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 the last row of Table 1. In addition to collecting subscribers&eedback, 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 1 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. Assume the same box
should be sent to all subscribers of the same type. At most 80000 units of each product type can be used in the subscription boxes
each month due to resource limits.
1)
2)
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?
a. Write the algebraic formulation for this optimization problem.
b. Solve using Excel or GAMS and report your findings.
The CEO of Alveva would like to limit the number of different boxes created to a maximum of 3 to process boxes faster.
In other words, at most 3 types of boxes will be produced, and each box type will be sent to multiple subscriber types
(e.g. box type 1 may be sent to subscriber types 1, 2, 5, and 8). What should be included in these 3 box types, how should
they be assigned to different subscribers, and what is the optimal profit? Solve using Excel or GAMS.
Hint for part 2: A (practically) desirable model for this part is a mixed-integer linear program. For this model, you need to introduce
a binary variable with three indices (for example, define binary variable ???????? , which takes a value of 1 if product ?? is included in
box ?? for subscriber type ??, and 0 otherwise). We recommend using GAMS for solving this model, because GAMS is a more
convenient platform for implementing variables with more than 2 indices. If you are unable to model this problem as a mixedinteger linear program, it is OK to model it as a nonlinear program. For this model, you do not need to define the binary variable
with three indices. If you adopt this second option, we recommend using GAMS and solver SCIP. Remember you can select your
solver by adding the following before the solve statement: ðtion solver=SCIP;Œist of
Unit
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
Total # of customers
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
8264
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5248
Table 1. Alveva case data
Subscriber Types
3
4
5
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7676
5497
23140
12723
7
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
20746
8
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
22761
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6922
10
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
3966
Model
Giant Motor Company
Assumptions
The Lyra and/or Libra plants can be retooled
The Hydra plant must stay open and cannot be retooled
There is no incentive to produce more than demand
Plant characteristics
Capacity (in millions)
Fixed cost (in $billions)
Lyra
1
2
Libra
0.8
2
Hydra New Lyra New Libra
0.9
1.6
1.8
2.6
3.4
3.7
Summary of opti
the Libra. Produc
Libras at the Libr
Hydras at the Hy
Profit margin (in $1000s) per car (large negative numbers mean the plant can’t make that car)
Lyra
Libra
Hydra New Lyra New Libra
Lyra
2
-100
-100
2.5
2.3
Libra
-100
3
-100
3
3.5
Hydra
-100
-100
5
-100
4.8
Demand (in millions)
Lyra
Libra
Hydra
1.4
1.1
0.8
Demand diversion matrix (from along side, to along top)
Lyra
Libra
Hydra
Lyra
NA
0.3
0.05
Libra
0
NA
0.1
Hydra
0
0
NA
Decisions on retooling (binary variables)
Retool Lyra?
1
Retool Libra?
0
Resulting plants open
Lyra
0
Libra
1
Hydra New Lyra New Libra
1
1
0
Production quantities (in millions)
Lyra
Lyra
0
Libra
0
Hydra
0
Total
0

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