6 Managing freight transport

Transcription

1 6 Managing freight transport 6.1 Introduction 6.2 Freight traffic assignment problems 6.3 Service network design problems 6.4 Vehicle allocation problems 6.5 A dynamic driver assignment problem 6.6 Fleet composition 6.7 Shipment consolidation 6.8 Vehicle routing problems 6.9 Real-time vehicle routing problems 6.10 Integrated location and routing problems 6.11 Vendor-managed inventory routing 6.12 Case study: Air network design at Intexpress 6.13 Case study: Meter reader routing and scheduling at Socal 6.14 Case study: Dynamic vehicle-dispatching problem with pickups and deliveries at ecourier 6.15 Questions and problems G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 1 / 10

2 Introduction 6 Managing freight transport Vehicle allocation problems - VAPs are faced by carriers that generate revenue by transporting full loads over long distances, as in TL trucking and container shipping; - once a vehicle delivers a load, it becomes empty and has to be moved to the pickup point of another load, or has to be repositioned in anticipation of future demands; - deterministic single-vehicle VAP: amounts to deciding the loads to be accepted and the ones to be rejected, as well as repositioning empty vehicles; - modelled as a minimum-cost flow problem on a time-expanded directed graph. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 2 / 10

3 Introduction 6 Managing freight transport Vehicle allocation problems - VAPs are faced by carriers that generate revenue by transporting full loads over long distances, as in TL trucking and container shipping; - once a vehicle delivers a load, it becomes empty and has to be moved to the pickup point of another load, or has to be repositioned in anticipation of future demands; - deterministic single-vehicle VAP: amounts to deciding the loads to be accepted and the ones to be rejected, as well as repositioning empty vehicles; - modelled as a minimum-cost flow problem on a time-expanded directed graph. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 2 / 10

4 Introduction 6 Managing freight transport Vehicle allocation problems - VAPs are faced by carriers that generate revenue by transporting full loads over long distances, as in TL trucking and container shipping; - once a vehicle delivers a load, it becomes empty and has to be moved to the pickup point of another load, or has to be repositioned in anticipation of future demands; - deterministic single-vehicle VAP: amounts to deciding the loads to be accepted and the ones to be rejected, as well as repositioning empty vehicles; - modelled as a minimum-cost flow problem on a time-expanded directed graph. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 2 / 10

5 Introduction 6 Managing freight transport Vehicle allocation problems - VAPs are faced by carriers that generate revenue by transporting full loads over long distances, as in TL trucking and container shipping; - once a vehicle delivers a load, it becomes empty and has to be moved to the pickup point of another load, or has to be repositioned in anticipation of future demands; - deterministic single-vehicle VAP: amounts to deciding the loads to be accepted and the ones to be rejected, as well as repositioning empty vehicles; - modelled as a minimum-cost flow problem on a time-expanded directed graph. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 2 / 10

6 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

7 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

8 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

9 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

10 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

11 Deterministic single-vehicle VAP (1/7) - Planning horizon composed of a finite number {1,...,T} of time periods; - N: set of points (e.g. cities) where the (full) loads have to picked up and delivered; - d ijt, i N, j N, t = 1,...,T: number of requested loads to be moved from origin i to destination j at time period t; - τ ij, i N, j N: travel time from point i to point j; - p ij, i N, j N: profit (revenue minus direct operating costs) derived from moving a load from point i to point j; - c ij, i N, j N: cost of moving an empty vehicle from point i to point j; - m it, i N, t = 1,...,T: number of vehicles that enter the system in time period t at point i. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 3 / 10

12 Deterministic single-vehicle VAP (2/x) - x ijt, i N, j N, t = 1,...,T: decision variables representing the number of vehicles that start moving a load from point i to point j at time period t; - y ijt, i N, j N, t = 1,...,T: decision variables representing the number of vehicles that start moving empty from point i to point j at time period t. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 4 / 10

13 Deterministic single-vehicle VAP (2/x) - x ijt, i N, j N, t = 1,...,T: decision variables representing the number of vehicles that start moving a load from point i to point j at time period t; - y ijt, i N, j N, t = 1,...,T: decision variables representing the number of vehicles that start moving empty from point i to point j at time period t. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 4 / 10

14 Deterministic single-vehicle VAP (3/7) Maximize T t=1 i N j N,j i (p ij x ijt c ij y ijt ) (1) subject to (x ij1 +y ij1 ) = m i1, i N (2) j N (x ijt +y ijt ) (x ki(t τki ) +y ki(t τki )) y iit 1 = m it, j N k N,k i:t>τ ki i N,t {2,...,T} (3) x ijt d ijt, i N,j N,t {1,...,T} (4) x ijt 0, i N,j N,t {1,...,T} y ijt 0, i N,j N,t {1,...,T} G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 5 / 10

15 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

16 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

17 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

18 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

19 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

20 Deterministic single-vehicle VAP (3/7) - Objective function (1): total discounted profit over the planning horizon; - constraints (2) and (3): impose flow conservation at the beginning of each time period (flow: number of vehicles); - due to constraints (2) and (3), the decision variables x iit and y iit, i N, j N, t = 1,...,T, have integer values implicitly; - constraints (4): number of loaded movements of vehicles at each time period t = 1,...,T between each pair origin i destination j, i N, j N, is bounded above by the demand; - d ijt x ijt, i N, j N, t = 1,...,T: loads should be rejected; - y iit, i N, t = 1,...,T: vehicles staying idle (inventory movements). G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 6 / 10

21 Deterministic single-vehicle VAP (4/7) Murthy Murthy is a motor carrier operating in the Andhraachuki region (India). Last July 11, four TL transport requests were made: from Chittoor to Khammam on July 11, from Srikakulam to Ichapur on July 11 and from Ananthapur to Chittoor on July 13 (two loads). On July 11, one vehicle was available in Chittoor and one in Khammam. A further vehicle was currently transporting a previously scheduled shipment and would be available in Chittoor on July, 12. Transport times between terminals are shown in Table 1. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 7 / 10

22 Deterministic single-vehicle VAP (5/7) Murthy Ananthapur Chittoor Ichapur Khammam Srikakulam Ananthapur Chittoor Ichapur Khammam 0 2 Srikakulam 0 Table 1: Travel times (in days) between terminals in the Murthy problem. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 8 / 10

23 Deterministic single-vehicle VAP (6/7) Murthy The revenue provided by a truck carrying a full load is 1.8 times the transport cost of a deadheading truck, estimated equal to rupees for each journey day. The problem to solve for Murthy is a VAP in which T = {July 11, July 12, July 13} = {1,2,3} and N = {Ananthapur, Chittoor, Ichapur, Khammam, Srikakulam} = {1,2,3,4,5}. The cost c ij of a journey from city i, i N, to city j, j N, is simply obtained by multiplying the cost of each journey day by the journey days τ ij from city i to city j. Consequently, the profit p ij, i,j N, is equal to τ ij. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 9 / 10

24 Deterministic single-vehicle VAP (7/7) Murthy The number of available vehicles m it, i N, t = 1,...,T, are all zero except the following: m 12 = 1; m 21 = 1; m 41 = 1. The values d ijt, i N, j N, t = 1,...,T, are also equal to zero, except the following: d 241 = 1; d 531 = 1; d 123 = 2. The optimal VAP solution is x241 = 1, x 123 = 1, y 441 = 1, y 112 = 1, y442 = 1, y = 2, while the values of the remaining decision 443 variables are zero. The corresponding optimal cost is rupees. It is worth noting that the requests from Srikakulam to Ichapur on July 11 are not satisfied and from Ananthapur to Chittoor on July 13 are partially satisfied. G. Ghiani, G. Laporte, R. Musmanno Introduction to Logistics System Management John Wiley & Sons, Ltd 10 / 10