Production Scheduling Delivery Service - Restaurants Benoît Lagarde – bl2506 Soufiane Ahallal– sa3103 Malek Ben Sliman– mab2343

Agenda I- Background II- Algorithm III- Simulation & Results 2

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 3

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 4

II- Algorithm Input: N umber of restaurants, number of simulations, number of delivery men for each case (centralized and decentralized), restaurant locations Process: How it works 5 Generate Orders Model 1: Decentralized Model 2: Centralized Outputs -rj: time of order -(xi, yi): customers’ coordonates -rj: time of order -Cj= rj+CT+ travel time

II- Algorithm Models: At each unit of time t How it works 6 Order at t? Assign a delivery man Update delivery men positions Outputs YES NO Update delivery men positions Update Customers List (rj, Cj)

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 7

III- Simulation & Results Same # drivers – Mean(Lj) 2) Results – Delivery ONLY 8 55%

III- Simulation & Results Same # drivers – Variance(Lj) 2) Results – Delivery ONLY 9 87%

III- Simulation & Results Lower # drivers - Still 33% improvement of the variance 2) Results – Delivery ONLY 10 19%

Conclusion 11 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 ImprovementComments Average delivery time (travel) 55% More deliveries possible & better service Variance85% Lower number of angry customers Fewer delivery men20% Cut costs with a better variance Same number of delivery men Lower number of delivery men

Thank you! 12