La Poste – Urban Logisticsidei.fr/sites/default/files/medias/doc/conf/pos/papers...Need for Urban Logistics Infrastructure and Fleet Optimization March 23, 2012 4P.R. Kleindorfer,

Excellence in Management Education

A MIXED INTEGER LINEAR PROGRAMMING MODEL FOR SOLVING LARGE-SCALE INTEGRATED LOCATION-ROUTING PROBLEMS FOR URBAN LOGISTICS APPLICATIONS AT GROUPE LA POSTE

Working paper at the Kuehne Foundation Endowed Chair in Logistics Management WHU – Otto Beisheim School of Management Joint research project of Groupe La Poste, INSEAD and WHU Presented at the 7th bi-annual conference on "The Economics of the Postal Sector in the Digital World“ Toulouse, March 23, 2012 Alain Roset, Groupe La Poste Matthias Winkenbach, WHU

Authors P.R. Kleindorfer INSEAD, Boulevard de Constance, 77305 Fontainebleau, France B. Lemarié, C. Levêque, A. Roset Groupe La Poste, 44 Boulevard de Vaugirard, 75757 Paris, France S. Spinler, M. Winkenbach WHU - Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany Contact M. Winkenbach [email protected] +49 (0)261 / 65 09 - 435

Outline

March 23, 2012 P.R. Kleindorfer, B. Lemarié, C. Levêque, A. Roset, S. Spinler, M. Winkenbach 2

Motivation I

Specific Problem Setting II

Preliminary Analyses IV

Managerial Implications V

Optimization Model III

MOTIVATION Section I


Need for Urban Logistics Infrastructure and Fleet Optimization


Urban Logistics as a requirement for sustainable development Trends and developments leading to a continuing increase in the demand for urban goods transportation Ongoing urbanization Ongoing boom of e-commerce Transportation intensive trends in supply chain and production

management Increasingly severe conflicts of interest between stakeholders Accessibility and congestion Emissions, noise, smell and vibration Energy consumption Need for tighter coordination and consolidation of individual consignments of different shippers and carriers within the same vehicles and facilities. No longer consider each shipment, transportation provider, and vehicle

individually. Instead they should be seen as components of an integrated logistics system.

Urban Logistics as a strategic option for postal operators POs are facing serious challenges due to the deterioration of their revenue base from established business models At the same time the increasing demand for urban transportation and the related problems offer a strategic opportunity for POs to broaden their product portfolio Potential synergies of ULS with existing postal

operations Existing infrastructure and know-how could be

used for ULS

Need for more sophisticated consolidation and coordination of urban goods transportation.

Need to develop optimization and simulation models to quantitatively evaluate possible strategic moves for postal operators in the domain of Urban Logistics Services, especially with respect to optimal infrastructure and fleet design.

SPECIFIC PROBLEM SETTING Section II


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4 9 20 80 39 7 6 2 11 55 148 149 42 2 73 35 12 20 53 152 8 29 21 33 1 114 182 69 95 253 146 4 3 36 30 24 61 5 40

1 1 2 5 23 95 179 150 18 40 12 2 34 97 204 22 252 97 5 2 377 76 3 2 72 222 20 112 114 261 42 17 25 48 6 91 129 209 40

5 2 1 2 1 25 152 155 199 269 59 111 59 207 201 9 3 2 14 222 67 173 44 1 11 258 194 26 200 266 146 27 18 112 131 3 32 38 107 218 260 221 42

5 9 11 5 3 4 21 74 226 234 183 84 10 22 530 253 4 9 5 145 163 110 112 157 91 142 4 115 21 5 26 239 312 107 5 3 50 70 90 37 141 140 194 266 11 1

4 4 1 12 4 10 14 20 22 39 49 67 2 13 7 5 40 81 78 290 286 182 182 370 424 277 63 22 15 5 239 166 24 71 122 166 312 51 161 10 18 273 175 118 6

31 5 10 62 4 7 13 3 3 8 2 18 25 2 1 15 85 198 334 192 309 103 448 327 218 343 186 52 222 231 94 185 138 142 140 234 287 319 215 38 48 94

2 5 12 29 5 36 46 10 18 7 7 45 2 4 3 10 6 75 61 75 387 316 207 246 377 89 82 296 112 313 49 28 106 50 78 301 291 215 179 74 125 10

2 1 13 11 8 3 6 13 4 3 10 23 59 20 3 4 1 21 7 4 164 341 286 159 391 115 142 59 67 4 153 286 116 366 255 202 207 56 144 292 176 204 4 2 3

1 10 13 5 4 77 8 7 6 7 6 1 16 13 11 13 12 16 42 211 6 66 209 221 268 428 399 440 386 344 161 90 311 374 126 115 389 274 52 31 145 86 12

1 1 17 12 3 29 12 9 1 15 4 32 8 2 15 26 22 46 144 57 6 18 31 300 455 342 490 660 461 28 333 431 402 423 336 177 83 294 83 2 4 9 77

1 2 13 3 31 98 109 5 10 6 1 84 18 60 161 17 54 43 24 50 37 6 18 197 310 325 173 238 176 597 394 671 670 322 536 538 316 427 339 411 387 40 13 94 1 14 40 4

3 3 11 123 239 157 61 6 4 37 155 153 83 7 8 38 93 54 27 54 225 220 372 91 241 407 247 741 540 338 266 359 172 346 363 352 3 1 36 32 1

1 6 11 118 193 306 223 242 457 87 132 281 355 438 120 43 40 220 193 162 57 13 88 332 324 183 278 424 367 471 631 542 178 557 202 271 463 523 196 54 10

1 5 14 175 3 361 486 206 218 245 107 78 93 282 96 2 337 349 264 298 126 5 70 214 393 411 627 400 492 376 368 308 713 244 210 229 198 6 22 9 2 26

55 62 6 7 34 101 13 63 6 2 10 10 2 17 1 2 1 146 224 301 258 202 38 27 71 190 274 347 338 685 761 452 297 669 574 471 165 93 34 24 3 169 196 138 22 90 24 2

13 18 2 3 2 61 49 51 166 326 338 15 151 9 2 37 56 24 225 120 14 15 73 3 36 196 189 375 507 495 661 357 222 48 68 185 77 31 165 30 18 12 90 24 43 36 68 212 221 11 18 28 12

15 4 4 5 8 3 12 33 273 211 34 105 1 135 2 4 54 2 2 600 202 145 10 51 5 32 12 55 231 550 405 735 503 522 76 6 74 322 190 30 33 86 55 202 433 323 405 531 32 134 265 94 33 23 16 23 39 8

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2 3 1 4 25 163 290 93 25 77 107 121 12 176 340 509 160 200 38 62 71 295 102 259 17 100 124 55 139 2 32 54 18 9 4 2 32 5

6 6 21 30 90 2 27 7 73 1 6 104 10 90 261 95 131 295 103 48 1 139 92 17 80 135 179 198 175 37 133 15 11 2 45 3 4 35

7 54 43 39 3 4 9 29 28 97 44 24 172 263 229 142 8 51 12 25 196 78 48 223 160 337 208 49 33 10 51 21

59 4 2 1 11 14 65 37 20 20 45 4 48 93 25 191 142 2 20 216 144 154 26 102 24 19 110 58 104 13

1 2 1 5 1 1 11 15 17 204 130 77 20 71 110 27 182 61 38 1 4 39

3 18 104 201 233 4 65 25 18 3 3 55 55 5 35 1 2

5 222 363 74 102 27 28 31 24 61 104 2 46 30

2 30 5 134 163 61 33 26 16 17 24 13 3

3 27 34 28 31 5 2 1 7 5 33 50 45 48 67 10

32 1 1 6 1 13 4 98 103 9 27

32 1 15 42 2 15 22 12

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Accomodation of complex geographies and demand distributions


Heterogeneous pickup and delivery demand 1.0

0.4

0.8

0.6

0.4

0.2

0.0

0.7 delivery items / stop

pickup items / stop

11111 Pr

obab

ility

[0

..1]

Parcel size [cm³] 𝜶

Prob

abili

ty

[0..1

] Parcel size [cm³] 𝜶

Prob

abili

ty

[0..1

]

Parcel size [cm³]

a

b

c

… …

𝜶

Heterogeneous size distributions of pickup and delivery demand

city segmentation

Parallel network architectures & mixed fleets


Small items

Indirect delivery via intermediate depots

Employed vehicle types

Pick

up

dem

and

Item size [cm³]

Deliv

ery

dem

and

Large items

Cut-off: 𝜶

Direct delivery from city hub

Employed vehicle types

Joint optimization of upstream and downstream

item flow

Item pickup and delivery are considered simultaneously

ILLUSTRATIVE

Pedestrian Bike Van Truck Pedestrian Bike Van Truck

OPTIMIZATION MODEL Section III


Model Structure & Theoretical Contribution


Cost data

Vehicle data

Location data

Data & Parameters

Demand data

Model parameters

Vehicle access restrictions To facilities To segments

Facility capacities

Vehicle capacities

Maximum service times

Constraints

Existing / blocked infrastructure

Active depot locations

Allocations of segments to depots and vehicle types for small item transport

Decision variables

City hub location

Allocations of segments to vehicle types for large item transport

Total Cost Routing Stop & service Inter stop transit Tour setup

Equipment Infrastructure Handling

Objective function

Augmented Routing Cost Approximation

Formula

1 Mixed Integer Linear

Programming Model (MILP)

Two-step optimization heuristic

GUROBI simplex solver

2

Optimization

Optimal facility count Optimal facility locations Optimal facility influence

area definition Optimal modal choice for

each segment Optimal vehicle routing

within segments

Output

Augmented routing cost approximation


0.60.70.80.9

11.1

1 4 9 16 25 36 49 64 81 100

fit w

ith C

WS

# of segments

5 stops/km²

20 stops/km²

50 stops/km²

100 stops/km²

200 stops/km²

Performance comparison

Very flexible regarding the problem setting Transparent and comprehensible result generation

No algorithm required Suitable for an optimization routine Results for a wide range of arguments

+ Long computation time Not suitable for direct use with optimization solver

Regressions required to construct function

Certain constraints are difficult to implement while keeping the problem linear

Approximation error needs to be assessed –

Explicit routing simulation [e.g. Clarke Wright Savings] Closed-form routing cost approximation

Vehicle routing cost as a function of vehicle characteristics

(capacity, speed, time requirements, cost, …) city segment characteristics

(distance from facility, size, …) demand characteristics

(stop density, item size distribution, pickup/delivery, …)

Increasing performance gains vs.

decreasing precision losses

Two-step optimization heuristic


Decision dimensions

Number of facilities

Facility locations

Allocation of city segments to facilities

Modal choice

Vehicle routing

Constraints

Vehicle capacities

Facility capacities

Vehicle Access Restrictions

Max. service times

Single-stage optimization Two-stage optimization

Stage II Stage I

Number of facilities fixed for each model run; changed iteratively to find optimum

Augmented Routing Cost Approximation formula assumes optimal routing

relaxed

fixed

lowest cost choice assumed

Cost result deviation [Percent]

Calculation time [10³ seconds]

10

8

6

4

2

0 240

+1.0%

0.0%

Model size [# of decision variables in thousands]

1,215 15

optimal cost deviation

two-stage calculation time

single-stage calculation time

PRELIMINARY ANALYSES Section IV


Relative vehicle competitiveness


stop density: low stop density: high

Cost

per

stop

[€]

Distance to segment [km]

stop density: medium



Pedestrians

Bikes

Vans

Bikes are strongly dominant vehicle choice. Pedestrians only to be preferred for very short line-haul distances and very high stop densities. Vans only become optimal for very long line-haul distances and low stop densities.

By allowing for mixed fleets, each city segment can be served by its cost optimal vehicle choice,

lowering total cost of transportation.

Optimal threshold between parallel network infrastructures


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

minimum total cost [€] cost optimal number of intermediate depots

alpha (i.e. the percentage of item sizes starting from the smallest that is directed through the indirect transportation network

consisting of the city hub and the intermediate depots)

# depots opt

TC min

Distinct optimal load balance between parallel network infrastructures and corresponding degree of consolidation can be identified

Snapshot: Influence area definition & modal choice


3 7 7

5 10 33 46 1

2 1 90 5

3 11 2

3 46 66 13

4 24 136 15 3 3 1 2 5 24 7 27 26

3 10 24 3 6 17 4 9 3 19 14 70 3 7 36 4

14 14 121 5 29 26 4 1 75 11 14 3 28 12 1 8 14 8 4

2 12 16 101 237 171 152 49 24 1 89 4 38 17 8 1 6 2 1

2 5 5 8 7 6 1 1 1 196 89 282 11 1 7 3 14 23 259 195 99 23 3 11 3

11 7 1 14 2 9 3 4 3 1 29 3 124 423 179 3 5 4 8 36 1 157 270 243 85 9 2 1 6 1 2 5 2

3 5 12 1 5 4 5 12 5 1 2 2 5 32 3 34 145 292 226 26 3 1 78 11 25 565 308 192 23 19 56 157 9 3 5 2 1

6 11 2 10 7 3 4 1 4 3 6 5 2 17 2 57 59 48 134 170 174 54 18 145 119 71 44 84 79 9 13 8 1 12 3 17 7 7

2 3 7 30 13 9 8 1 1 2 4 5 2 6 2 49 26 22 66 199 53 103 50 5 2 8 53 115 11 3 3 2 14 7 2 100 3 16 21 3

10 2 12 1 8 3 7 5 3 24 84 70 33 7 9 35 14 3 6 235 102 13 36 62 12 18 31 243 189 62 64 19 30 30 39 72 75 51 54 14 7 2 5

4 9 20 80 39 7 6 2 11 55 148 149 42 2 73 35 12 20 53 152 8 29 21 33 1 114 182 69 95 253 146 4 3 36 30 24 61 5 40

1 1 2 5 23 95 179 150 18 40 12 2 34 97 204 22 252 97 5 2 377 76 3 2 72 222 20 112 114 261 42 17 25 48 6 91 129 209 40

5 2 1 2 1 25 152 155 199 269 59 111 59 207 201 9 3 2 14 222 67 173 44 1 11 258 194 26 200 266 146 27 18 112 131 3 32 38 107 218 260 221 42

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1 2 13 3 31 98 109 5 10 6 1 84 18 60 161 17 54 43 24 50 37 6 18 197 310 325 173 238 176 597 394 671 670 322 536 538 316 427 339 411 387 40 13 94 1 14 40 4

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2 2 32 17 4 25 37 49 335 81 169 178 221 192 8 21 99 103 5 413 37 19 7 10 66 49 24 138 218 164 44 7 10 6 8 184 62 103 128 386 206 239 322 324 342 24 115 148 124 45 12 90 155 83 17 6 1

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15 81 61 281 271 339 236 162 31 16 8 2 8 25 17 74 142 550 250 158 163 378 178 148 224 362 156 343 223 22 107 240 108 41 93 25 17 50 95 14 39 42 7 8 6 22

1 24 74 91 156 70 86 134 10 4 4 14 60 10 2 110 303 392 442 81 447 329 444 526 271 303 525 379 498 89 248 68 96 92 80 108 130 14 16 16 81 9 110 44 2 25 8 3 4

16 2 5 54 1 35 111 125 107 259 481 162 9 17 24 372 305 112 31 200 298 425 394 634 262 192 69 217 359 181 36 98 47 191 123 86 62 16 46 55 10 3 24 9 24 36 25

5 4 20 60 64 285 234 86 110 110 4 29 113 69 206 514 229 344 458 199 168 175 54 203 113 210 26 31 86 230 59 12 49 32 23 70 25 28 15 3 15 1 1

2 3 1 4 25 163 290 93 25 77 107 121 12 176 340 509 160 200 38 62 71 295 102 259 17 100 124 55 139 2 32 54 18 9 4 2 32 5

6 6 21 30 90 2 27 7 73 1 6 104 10 90 261 95 131 295 103 48 1 139 92 17 80 135 179 198 175 37 133 15 11 2 45 3 4 35

7 54 43 39 3 4 9 29 28 97 44 24 172 263 229 142 8 51 12 25 196 78 48 223 160 337 208 49 33 10 51 21

59 4 2 1 11 14 65 37 20 20 45 4 48 93 25 191 142 2 20 216 144 154 26 102 24 19 110 58 104 13

1 2 1 5 1 1 11 15 17 204 130 77 20 71 110 27 182 61 38 1 4 39

3 18 104 201 233 4 65 25 18 3 3 55 55 5 35 1 2

5 222 363 74 102 27 28 31 24 61 104 2 46 30

2 30 5 134 163 61 33 26 16 17 24 13 3

3 27 34 28 31 5 2 1 7 5 33 50 45 48 67 10

32 1 1 6 1 13 4 98 103 9 27

32 1 15 42 2 15 22 12

7 12 5 13 8 3

62 10 1

Small item transportation

Large item transportation

MANAGERIAL IMPLICATIONS Section V


Some results for La Poste


A first complete model representation of parcel delivery at the city level (extensible to other similar products): number and location of facilities, choice of vehicle type, facility influence area definition.

A model splitting the global cost of a parcel delivery within a city into about 10 elementary cost (handling, line haul, setup, etc..) and showing the evolution of these elementary cost when the input parameters change.

A confirmation by the model of our actual operational choices of the best vehicles to deliver according to the line haul distances.

The antagonistic link between the number of depots and the number of vehicles to serve a city with an optimal choice.

Optimum costs and relevant variables


The optimum cost is a balance between line haul: cost of the vehicles and of the postmen number of depots: real estate cost With the model parameters (cost per m² of facilities, vehicle operating cost, postmen salary, etc.) being set close to the actual observable figures of La Poste the optimum is flat: The model shows a large range of number of depots with similar parcel

delivery costs The flat shape of the optimum may however change if the input parameters evolve with divergence. The model gives La Poste the capability to react e.g. to increases in the cost

of transportation by a reduction of the cost of depots.

QUESTIONS? Thank you.


Documents

La Poste – Urban Logisticsidei.fr/sites/default/files/medias/doc/conf/pos/papers...Need for Urban Logistics Infrastructure and Fleet Optimization March 23, 2012 4P.R. Kleindorfer,