We analysed H&M's supplier selection and order allocation phases and implemented a quantitative model on Excel using linear and integer programming in order to reach our objective and effectively allocate the initial resources, keeping hypothetical constraints in mind and testing the model through sensitivity analysis.

1. Supplier selection
and order allocation
for H&M
Andrea Bendandi 774610
Carol Bortolotto 774431
Marco Cersosimo 773626
Alberto Giannone 774434
Marta Pozzar 774609

2. □Swedish multinational
fashion retailer
□Second biggest retailer
□Two main collections per
year plus some sub-
collections to meet fashion
trends
Introduction
H&M does NOT own any factories, but it
outsources manufacturing to more than 800
independent suppliers in Europe and Asia

3. Problem Identification
Supplier selection and order allocation
□ obtain the number of products j ordered from supplier i and
delivered with k transportation channels
Train = 1 Ship = 2
□ minimizing the total costs and respecting the budget
□ respect H&M’s demand
□ respect the production capacity
□ not go below the minimum inventory of each supplier, otherwise penalty
costs would be applied
□ consider custom fees
□ and costs deriving from suppliers’ lead times
□ total deliveries by train should not exceed 10%
□ at least 20% of products for each category should be ordered from
European suppliers
□ suppliers should not exceed the maximum limit of CO2 emissions

4. Variables
𝑥𝑖𝑗𝑘 = number of products j ordered from supplier i
delivered with k transportation channel
𝑢𝑖 =
1,
0,
if the order from supplier 𝑖 is less than 𝑞𝑖
otherwise
𝑣𝑖
=
1,
0,
if supplier 𝑖 is selected
otherwise
𝑤𝑖 =
1,
0,
if both 𝑢𝑖 and 𝑣𝑖 are 1
otherwise

5. Objective function
𝑖=1
𝑛
𝑗=1
𝑚
𝑘=1
𝑝
𝑐𝑖𝑗 + 𝑠𝑐𝑖𝑗𝑘 + 𝑡𝑐𝑖𝑗𝑘 + 𝑐𝑓𝑖𝑗 𝑥𝑖𝑗𝑘 +
𝑖=1
𝑛
𝑝𝑐𝑖 × 𝑤𝑖
Product cost
Security cost
Transportation cost
Custom fees
Penalty cost
Minimize z =

6. Origin Constraint
□At least 20% of each product 𝑗 must be ordered
from European suppliers
𝑖=1
𝑛1
𝑘=1
𝑝
𝑥𝑖𝑗𝑘 − 0,2 ×
𝑖=1
𝑛
𝑘=1
𝑝
𝑥𝑖𝑗𝑘 ≥ 0; 𝑗 = 1,2, … , 𝑚

7. Transportation constraint
□We decided to consider two types of transportation
means: train and ship. Indeed they are most
environmentally friendly and efficient means of
transportation
□Transportation by ship is more secure than the train
□Therefore we assumed that no more than 10% of
deliveries can be completed via train, while the
remaining 90% will occur via sea
𝑖=1
𝑛
𝑗=1
𝑚
𝑥𝑖𝑗2 − 0,1 ×
𝑖=1
𝑛
𝑗=1
𝑚
𝑘=1
𝑝
𝑥𝑖𝑗𝑘 ≤ 0 (𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

8. Transportation costs
□Since the transportation cost is based on the volume in
m3, we have estimated the total volume for each product.
□After that we assigned the costs of delivery involved
from European and Asian countries
□Finally, we multiplied each volume of product with the
cost of transportation

9. Security cost
□ First component: risk of each supplier multiplied by the
value of the products
□ Second component: risk of each mean of transportation
multiplied by the cost of transportation
□ Finally we added the first with the second component

10. Custom fees
□Custom fees are applied whenever the firm imports
goods from extra European countries
□Custom fees have been calculated as 12% of the value
of goods

11. Max n° of Supplier Constraint
□ Maximum number of suppliers 𝑖 that can
be selected, according to H&M’s
corporate policy
𝑖=1
𝑛
𝑣𝑖 ≤ 𝑁

12. Final Constraints
𝑖=1
𝑛
𝑗=1
𝑚
𝑘=1
𝑝
𝑐𝑗 + 𝑠𝑐𝑖𝑗𝑘 + 𝑡𝑐𝑖𝑗𝑘 + 𝑐𝑓𝑖𝑗 𝑥𝑖𝑗𝑘 +
𝑖=1
𝑛
𝑝𝑐𝑖 × 𝑤𝑖 ≤ 𝐵 (𝑏𝑢𝑑𝑔𝑒𝑡 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)
𝑗=1
𝑚
𝑘=1
𝑝
𝑥𝑖𝑗𝑘 ≤ 𝑠𝑖; 𝑖 = 1,2, … , 𝑛 (𝑠𝑢𝑝𝑝𝑙𝑦 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)
𝑖=1
𝑛
𝑘=1
𝑝
𝑥𝑖𝑗𝑘 = 𝑑𝑗 ; 𝑗 = 1,2, … , 𝑚 (𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)
𝑖=1
𝑛
𝑣𝑖 ≤ 𝑁; (𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟𝑠 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)
𝑥𝑖𝑗𝑘 ≥ 0 𝑎𝑛𝑑 𝑎𝑟𝑒 𝑠𝑒𝑡 𝑜𝑓 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 (𝑛𝑜𝑛 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑖𝑡𝑦 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)
𝑤𝑖, 𝑢𝑖, 𝑣𝑖 = 0 𝑜𝑟 1 𝑜𝑛𝑙𝑦 𝑓𝑜𝑟 𝑖 = 1,2, … , 𝑛

13. Sensitivity analysis
1. Increasing the limit of trains to 50% increases
the amount of products delivered by train.
□ Aim: understand how our variables impact on the
order allocation and objective function
Total costs decrease by 1.47%

14. Sensitivity analysis
2. We ignored the 20% limit of firms in europe
- Most of the production would be then allocated to Asian
suppliers
- Problem: clashes with the need to have close production
facilities for urgent orders
Total costs decrease by 10.72%

15. Sensitivity analysis
3. No cap of maximum 8 suppliers and each
supplier respects the maximum emissions of CO2
- Inefficient order allocations
- Penalty costs applied because of orders not reaching
suppliers’ minimum inventory levels
Total costs increase by 6.31%

16. Limitations
□ Suppliers produce all the products indifferently and
the product offering has been simplified compared
to H&M’s actual collection
□ Only 12 suppliers were considered in the model due
to technical limitations of Excel
□ Adopting pollution per capita in suppliers’
evaluation, due to the lack of relevant data linked to
unitary production emissions

17. Strengths of the model
□ We tailored our model to H&M’s needs
□ Fast fashion industry companies mainly localize the
production of basic items in Asia, whereas seasonal
collections come from Europe
□ Sustainability issues that relate to H&M’s
environmental standards.
□ The reliability of each supplier in terms of the rate
of non delivery toincorporate the qualitative factor
of supplier risks

18. Thank you!