Exploring delivery fairness and work allocation using public datasets and a scalable heuristic approach. Part of flipgig: http://flipgig.org

1. Exploring fairness in
food delivery routing
and scheduling
problem
Antonio (Toni) Martinez-Sykora
a.Martinez-Sykora@soton.ac.uk

2. Outline
• Introducing fairness for the Gig-economy couriers
• Exploring deeper the meal delivery problem – MDP
• Mathematical model
• Construction heuristic – current strategies
• VNS (Variable Neighbourhood Search)
• Results and discussion
• Introducing packing challenges

3. Toy example…
Collection
Delivery
How to achieve fairness?

4. Understanding the problem
- One job assigned
- 1 h cycling
- No waiting
- Four jobs assigned
- 1.5 h cycling
- 0.5 h waiting
- Three jobs assigned
- 1 h cycling
- 2 h waiting
- Two jobs assigned
- 1.5 h cycling
- 0.5 h waiting
- Three jobs assigned
- 1 h cycling
- 1 h waiting
- Three jobs assigned
- 1 h cycling
- 1 h waiting
- Four jobs assigned
- 2 h cycling
- 0.5 h waiting
- Three jobs assigned
- 1.5 h cycling
- 1 h waiting
Not working

5. Meal delivery problems
• Orders mainly from restaurants
• Couriers (Gig economy workers) need to do the delivery just after
collecting the meals.
• Collection must happened as soon as possible
• Workers are paid per job (most common case)
• Some platforms rank the Gig workers and use some preference
system

6. Objectives
𝐽 set of couriers and 𝐼 set of orders
1. 𝐽 is minimised
2. Range is minimised
3. Travelling time between jobs is minimised
4. Waiting time minimised
5. Balancing proportion of waiting time

7. Notation
• 𝑅! set of all feasible routes for transport mode 𝑚 ∈ 1, … , '
𝑚
• 𝑅 = ⋃!∈ #,…, &
! 𝑅!
• 𝑟 = 𝑖#, … , 𝑖|(| , 𝑟 ∈ 𝑅
• 𝑟 = 𝑐)!
, 𝑑)!
, 𝑐)"
, 𝑑)"
, … , 𝑐)|$|
, 𝑑)|$|
• 𝑊
( waiting time of route 𝑟 ∈ 𝑅
• Travelling time within the jobs of route 𝑟 ∈ 𝑅
𝐷(
* = 0
)∈+
𝑡,%,-%
!
• Travelling time between the jobs of route 𝑟 ∈ 𝑅
𝐷(
. = 0
)∈{#,…, ( 0#}
𝑡-%,,%&!
!

8. Decision variables
𝑥2 = 4
1 𝑖𝑓 𝑟𝑜𝑢𝑡𝑒 𝑟 𝑖𝑠 𝑏𝑒𝑖𝑛𝑔 𝑢𝑠𝑒𝑑
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
∀𝑟 ∈ 𝑅
𝑦345, 𝑦367 ∈ 𝑍
𝑧345, 𝑧367 ∈ 𝑍
Maximum and minimum number of jobs
Maximum and minimum proportion of waiting time

9. Objective function: 𝑤! > 𝑤"> 𝑤#> 𝑤$> 𝑤%
𝐹 = 𝑤! $
"∈$
𝑥" + 𝑤% 𝑦&'( − 𝑦&)* + 𝑤+ $
"∈$
𝐷"
,𝑥" + 𝑤- $
"∈$
𝑊
"𝑥" + 𝑤.(𝑧&'( − 𝑧&)*)
Minimise number of couriers
Minimise range – balancing shifts
Minimise distance travelled –
common OF – route efficiency
Minimise total waiting time –
scheduling efficiency
Minimise range – balancing
shifts

10. Constraints
$
"∈$,)∈$
𝑥" = 1
𝑦&'( ≥ 𝑟 𝑥"
𝑦&)* ≤ 𝑟 + 𝑀(1 − 𝑥")
𝑍&'( ≥ 𝑊
"𝑥"
𝑍&)* ≤ 𝑊
" + 𝑀(1 − 𝑥")
𝑥" ∈ 0,1
∀𝑖 ∈ 𝐼
∀𝑟 ∈ 𝑅
∀𝑟 ∈ 𝑅
∀𝑟 ∈ 𝑅
∀𝑟 ∈ 𝑅
∀𝑟 ∈ 𝑅

11. Construction heuristic - Policies
1
3
2
4
J: Sorted by preference

12. How to sort the workers?
1. Priority
2. Waiting time
3. Time to get to next collection

13. VNS
INSERTION SWAP

14. Computational results
Dataset used to generate
problems randomly with
40,50 and 60 orders

15. Small problems (40-60 orders)

16. US data
• 240 problems
• 54 to 323 restaurants
• 242 to 3212 orders

17. Conclusions
• We present a new model to capture different aspects of fairness.
• Mathematical (exact) model can solve consistently problems with up
to 60 orders
• Heuristic (VNS) algorithm can handle problems with over 3000 orders.
• Mathematical model vs Heuristic achieve same level of fairness but
driving/riding time can go up to 25% in the heuristic.
• Some packing considerations have been explored.

18. Routing meets Packing
1.- No packing

19. Routing meets Packing
2.- No routing:
Logistics centre
Distribution centre
Orders per day
Day Product
1 100 beers
200 kg
potatoes
50 cereals
100 soap
2 250 cokes
500 sauces
200 rice
…
Point-to-point transportation problem
Products
Pallets Trucks

20. Ceschia, Schaerf, J. Heuristics 2011
Positioning: Multi-drop

21. 6
Routing meets Packing: 2D
8
5
3
2
1
D
7
4

22. Routing meets Packing: 3D
Vehicle 1

23. Routing meets Packing: pallet
loading
3.- Routing and Packing

24. Thank you
Antonio (Toni) Martinez-Sykora
A.Martinez-Sykora@soton.ac.uk