Liner Shipping Single Service Design Problem with Arrival Time Service Levels

Transcription

1 Liner Shipping Single Service Design Problem with Arrival Time Service Levels Kevin Tierney (Joint work with Ann Campbell, Jan Fabian Ehmke and Daniel Müller) Department of Business Information Systems University of Paderborn Paderborn, Germany October 4, 2017

2 Outline Outline I Motivation & background I Data analysis: container ship lateness I Chance constrained mathematical model for designing services I Computational results & business insights Liner Shipping Single Service Design Problem with Arrival Time Service Levels 2/21

3 Motivation & Background Liner Shipping 1600 Millions of tons of containers Year Data source: UNCTAD Review of Maritime Transport 2016 Vessels Over 4900 ships in operation (WSC) Services: Over 500 services (cyclical routes) available Containers: Over 180 million twenty-foot equivalent units (TEU) transported in 2016 Liner Shipping Single Service Design Problem with Arrival Time Service Levels 3/21

4 Motivation & Background Liner Shipping: Looking to the Future Mærsk Mc Kinney Møller Walter Rademacher / Wikipedia A major threat to the future of complex liner service networks lies in increased schedule unreliability. Notteboom and Rodrigue (2008) Liner Shipping Single Service Design Problem with Arrival Time Service Levels 4/21

5 Motivation & Background Liner Shipping Services Subset of Maersk Line s network in 2010 Key properties of a liner shipping service: Periodic: A port is visited on the same day, at the same time, every week (or two weeks, etc.) Cyclical: Enduring: A service has no start or end; it loops Most services last months or years Liner Shipping Single Service Design Problem with Arrival Time Service Levels 5/21

6 Motivation & Background Liner Shipping Services Subset of Maersk Line s network in 2010 Liner Shipping Single Service Design Problem with Arrival Time Service Levels 5/21

7 Motivation & Background Contribution This work provides: 1. A data-driven investigation of liner shipping travel time distributions 2. A mathematical model for designing services with punctuality guarantees 3. A simulation study of the effectiveness of the model We show that: 1. Punctual services can be designed in reasonable amounts of computation time 2. Guaranteeing punctuality is extremely expensive and in many cases likely not worth it Liner Shipping Single Service Design Problem with Arrival Time Service Levels 6/21

8 Motivation & Background Slow Steaming 1.0 Cost (Millions of USD) Travel time (days) Sailing cost from Boston, USA to Copenhagen, Denmark Challenge: Incorporate sailing costs and punctuality into the service design process. Liner Shipping Single Service Design Problem with Arrival Time Service Levels 7/21

9 Data analysis: Container ship lateness Data Analysis: Travel Time Distributions Data gathering: AIS tracking of all vessels on 25 COSCO services in 2014 Total of 1872 port to port transits around the world Key question: What distribution best models vessel travel times? Liner Shipping Single Service Design Problem with Arrival Time Service Levels 8/21

10 Data analysis: Container ship lateness Data Analysis: Travel Time Distributions Data gathering: AIS tracking of all vessels on 25 COSCO services in 2014 Total of 1872 port to port transits around the world Key question: What distribution best models vessel travel times? Aggregated, normalized, region-to-region histograms Intra-Europe China/Japan to S. Mediterranean Three-Parameter Log-logistic (LL3P) Intra-Western North America Normal Liner Shipping Single Service Design Problem with Arrival Time Service Levels 8/21

11 Mathematical model Designing Liner Shipping Services Given: A set of ports with pre-negotiated time windows A set of vessels A set of container demands between ports Goal: Plan a route between the ports minimizing: 1. The sailing cost of the vessels 2. The total number of vessels Optional: 3. Maximize profit from container demands Liner Shipping Single Service Design Problem with Arrival Time Service Levels 9/21

12 Mathematical model Model phases Phase 1: Design speed All ports must be visited exactly once Require all demand to be carried within specified path duration Only sail at the vessel design speed Phase 2: Optimized speed Phase 1 and... Allow vessels to speed up or slow down Phase 3: Optimized speed with maximum path durations Phase 2 and... Earn revenue from carrying demand Allow rejection of demand Liner Shipping Single Service Design Problem with Arrival Time Service Levels 10/21

13 Mathematical model Mathematical Model P Ports A Arcs Sets/Parameters: (o k, d k, a k ) K Demands ti WS, ti WE Time window c S, c C Sailing/charter costs Decision variables: w i N Week at port i x ij {0, 1} 1 iff arc (i, j) used i, τi E, τi A R Service start, end, arrival port i τ S f kij Demand k flow on (i, j) Objective function: min c C w p+1 + (i,j) A c S ij x ij Liner Shipping Single Service Design Problem with Arrival Time Service Levels 11/21

14 Mathematical model Mathematical Model P Ports A Arcs Sets/Parameters: (o k, d k, a k ) K Demands ti WS, ti WE Time window c S, c C Sailing/charter costs Decision variables: w i N Week at port i x ij {0, 1} 1 iff arc (i, j) used i, τi E, τi A R Service start, end, arrival port i τ S f kij Demand k flow on (i, j) Objective function: min c C w p+1 + (i,j) A c S ij x ij Number of vessels on the service Liner Shipping Single Service Design Problem with Arrival Time Service Levels 11/21

15 Mathematical model Mathematical Model P Ports A Arcs Sets/Parameters: (o k, d k, a k ) K Demands ti WS, ti WE Time window c S, c C Sailing/charter costs Decision variables: w i N Week at port i x ij {0, 1} 1 iff arc (i, j) used i, τi E, τi A R Service start, end, arrival port i τ S f kij Demand k flow on (i, j) Objective function: min c C w p+1 + (i,j) A c S ij x ij Number of vessels on the service Phase 1 fixed sailing cost Liner Shipping Single Service Design Problem with Arrival Time Service Levels 11/21

16 Mathematical model Mathematical Model: Constraints x ij = 1 j P except 1 (i,j) A (i,j) A x ij = 1 i P except p + 1 Liner Shipping Single Service Design Problem with Arrival Time Service Levels 12/21

17 Mathematical model Mathematical Model: Constraints x ij = 1 j P except 1 (i,j) A (i,j) A x ij = 1 i P except p + 1 τi S τi E = t WS i + 168w i i P = t WE i + 168w i i P Week 1 Week 2 Liner Shipping Single Service Design Problem with Arrival Time Service Levels 12/21

18 Mathematical model Mathematical Model: Constraints τ E i + t S ij τ A j + M(1 x ij ) (i, j) A Time feasibility (Also acts as subtour elimination) Liner Shipping Single Service Design Problem with Arrival Time Service Levels 13/21

19 Mathematical model Mathematical Model: Constraints j P\{o k } j P\{d k } f kokj = a k k K f kjdk = a k k K f kji = f kij k K, i P \ {o k, d k } (j,i) A (i,j) A f kij ux ij (i, j) A k K Container demands modelled as a multicommodity flow Liner Shipping Single Service Design Problem with Arrival Time Service Levels 14/21

20 Mathematical model Modelling Punctuality Guarantees τ E i + t α ij τ A j + M(1 x ij ) (i, j) A Amount of buffer necessary to ensure a service level of α for arc (i, j) t α ij Liner Shipping Single Service Design Problem with Arrival Time Service Levels 15/21

21 Computational results Evaluation Procedure Instances: Generated using COSCO service data and the LINERLIB (Brouer et al. 2013) 44 instances with between 6 and 13 vessels (COSCO schedule) Testing procedure: 1. Solve Phase 1/2/3 deterministic and stochastic models 2. Simulate the optimal solution using the LL3P distribution 3. Analyze the expected performance versus the simulated performance Liner Shipping Single Service Design Problem with Arrival Time Service Levels 16/21

22 Computational results Phases 1/2 Simulation Results Phase 1: Optimization Simulation Distribution c C c S Total c S Late Late / P Faster Speed Deterministic % 16.9 Norm % 14.1 Norm % 13.4 LL3P % 14.6 LL3P % 13.2 LL3P % 12.7 Phase 2: Optimization Simulation Distribution c C c S Total Speed c S Late Late / P Faster Speed Deterministic % 15.1 Norm % 13.3 Norm % 12.8 LL3P % 13.8 LL3P % 12.6 LL3P % 12.5 Liner Shipping Single Service Design Problem with Arrival Time Service Levels 17/21

23 Computational results Phase 3: Demand Carried (Det/LL3P) Service Cargo carried (%) Transit inc. (%) Det abx aesa awe awe awe awe awe cen ces ese Liner Shipping Single Service Design Problem with Arrival Time Service Levels 18/21

24 Computational results Sample solutions ll3p CHS 4 det 6 ll3p ILM 5 det 7 ll3p PUS 7 det 4 ll3p SAV 6 det 5 ll3p SHA 8 det 3 HKG ll3p YTN 9 det 1 ll3p ZLO 2 det 9 ll3p 0 det 0 KHH ll3p 1 det 2 Deterministic Log-Logistic (3P) 0.9 ll3p PCN 3 det 8 Phase 1 optimization of the AWE3 service Liner Shipping Single Service Design Problem with Arrival Time Service Levels 19/21

25 Computational results Conclusion Services can be designed with puncutality guarantees at low computational cost However, the operational costs may be high Acceptance from shippers is necessary to implement such services Liner Shipping Single Service Design Problem with Arrival Time Service Levels 20/21

26 Literature Literature Overview Article Wang and Meng (2012) Unif. & Norm. (NL) NL stoch. prog. Wang and Meng (2012) Any Truncated (NL) NL stoch. prog. Qi and Song (2012) Unif./Norm. (NL) Sim. stoch. approx. Song and Dong (2013) (NL) Heuristic Decomp. Plum et al. (2014) Branch-Cut-and-Price Lee et al. (2015) Normal/Any (NL) Markov chains Song et al. (2015) Trunc. Norm. (NL) NSGA-II Reinhardt et al. (2016) (SAX) MILP Wang and Wang (2016) (NL) P time alg. This paper log-logistic 3P (SAX) MILP Routing Distribution Speed opt. NL = Non-linear; SAX = Secant approximation Method Liner Shipping Single Service Design Problem with Arrival Time Service Levels 21/21