Production SchedulingDelivery Service - Restaurants

Benoît Lagarde – bl2506Soufiane Ahallal– sa3103

Malek Ben Sliman– mab2343

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Agenda

I- Background

II- Algorithm

III- Simulation & Results

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I- Background

• Questions:- How can we decrease customers’ waiting time?- How can we decrease costs of delivery?

• Current situation:- A restaurant owner owns N restaurants- Each restaurant has its own fleet of delivery men and each faces problems with their delivery service.

• The idea:Centralize delivery by only having a unique fleet of deliverymen that would work for the whole network of restaurants

1) The problem

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I- Background

• Average Restaurant:- Frequency: 50 orders/lunch (Normal Distribution over lunch)- Nb of delivery men: 3 delivery men- Cooking time: 18 minutes

• Distances from a restaurant to its customers

2) Inputs

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

P(X<d) for d straight distance in miles

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II- Algorithm

• Input:Number of restaurants, number of simulations, number of delivery men for each case (centralized and decentralized), restaurant locations

• Process:

How it works

Generate Orders

Model 1:Decentralize

d

Model 2:Centralized

Outputs

- rj: time of order- (xi, yi):

customers’ coordonates

- rj: time of order

- Cj= rj+CT+ travel time

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II- Algorithm

• Models:At each unit of time t

How it works

Order at t?

Assign a delivery man

Update delivery men

positions

Outputs

YES

NO

Update delivery men

positions

Update Customers

List(rj, Cj)

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III- Simulation & Results

• Scenarios:- Same number of delivery men: How does it impact the waiting time?- Fewer delivery men: How much can we decrease the number of delivery men while keeping the same average waiting time?

• Parameters- Different restaurant densities: 1 restaurant/ 0.1 mile, 0.3 mile and 0.5 mile- Different number of restaurants: 4, 9, 16 and 25 restaurants (on a square 3x3…)- Average on 3000 simulations

1) Simulation

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III- Simulation & Results

• Same # drivers – Mean(Lj)

2) Results – Delivery ONLY

0 5 10 15 20 25 3010.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

50.0%

55.0%

60.0%

Low DensityMedium DensityHigh Density

55%

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III- Simulation & Results

• Same # drivers – Variance(Lj)

2) Results – Delivery ONLY

0 5 10 15 20 25 3045.0%

50.0%

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

85.0%

90.0%

Low DensityMedium DensityHigh Density

87%

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III- Simulation & Results

• Lower # drivers - Still 33% improvement of the variance

2) Results – Delivery ONLY

0 5 10 15 20 25 304.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

20.0%

Low DensityMedium DensityHigh Density

19%

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Conclusion

• It works pretty well:

• To go further:Have a more complex model:- More than 1 order/ delivery man- Possibility to take orders from different restaurants at the same time- When a delivery man is free, where to go (not to the closest restaurant)- Stochastic Parameters: cooking time, travel time, number of orders

Improvement Comments

Average delivery time (travel)

55%More deliveries

possible & better service

Variance 85%Lower number of angry customers

Fewer delivery

men

20%Cut costs with a better variance

Same number of delivery men

Lower number of delivery men

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Thank you!