1. Speed and Schedule Stability in Supply Chains Michael G H Bell Professor of Transport Operations Imperial College London P O R T e C GCSL2006, Hong Kong, December, 2006

2. PORTeC members Civil and Environmental Engineering: –Prof. Mike Bell –Prof. Andrew Evans –Prof. John Polak –Prof. Robert Cochrane –Dr. Sheila Farrell –Khalid Bichou –Panagiotis Angeloudis –Gianluca Barletta –Konstantinos Zavitsas Tanaka Business School: –Dr Elaine Hadjiconstantinou –Nang Laik

3. Security and port efficiency (Khalid Bichou) Changing security regimes after 9/11 IDEF process mapping of security measures Panel data for port inputs and outputs DEA and not SFA efficiency analysis

4. Robust AGV Scheduling (Panagiotis Angeloudis) Robust optimisation of assignment of jobs to AGVs Simulation of an automated container terminal

5. Managing supply chain uncertainty (Gianluca Barletta) Sources of uncertainty Technological solutions (for example, RFID) Organisational structures and information flows

6. Optimisation of transport and stacking in yards (Nang Laik) MIP formulation of movement and stacking problem Exact and heuristic solutions

7. Global energy supply security (Konstantinos Zavitsas) Construction of a global network model for shipping Application to oil and gas Analysis of security

8. Contents Background Stability at a single terminal Stability for two terminals Stability for N terminals Stochastic stability Conclusions

9. Inventory in the supply chain Time Cumulative number of items Production Shipments Arrivals Consumption Waiting for transport Number being transported Waiting for consumption Travel time Wait Wait = Travel time + Max headway

10. Bus bunching Newell and Potts (1964) model: – Applied to study bus service reliability – Passengers arrive more-or-less continuously but depart in batches when a bus arrives – Stability requires that passengers board at a rate that is more than twice the rate at which they arrive – Instability leads to bus bunching, longer queues and longer waits

11. Model applied to a container terminal: – Passengers = containers, buses = ships – Containers arrive at terminal continuously – Ship arrives late => Containers stack up – Longer loading time => Ship leaves even later – Fewer containers for next ship => Next ship leaves early – Ship bunching may occur – Ship bunching increases average yard inventory Container terminals

12. Arrival and departure headways  = Ratio of arrival to loading rate of containers h = Arrival headway of vessels (assumed to be uniform) =n th departure headway (arrival headway at the next port of call) (1) (2), assuming

13. Deviations from equilibrium At equilibrium:(3) Implies d = h Subtracting equation (3) from (2): (4)

14. Stability (4) Positive deviation from equilibrium departure headway leads to a subsequent negative deviation from the equilibrium departure headway Stability requires that, otherwise ship bunching eventually occurs

15. Single terminal example Simulation: – Port where ships call every 24 hours, h=24 – Deviation to the initial departure headway – It is assumed that or

16. Successive headways (1)

17. Stability for two ports of call (5) (6)

18. Two port example Simulation: – Two ports in series – At the first terminal h=24 and – It is assumed or

19. Successive headways (2)

20. Stability for N terminals For N terminals, stability requires: which implies for i = 1.. N

21. Stochastic stability Travel time may vary The arrival headway will now be considered random around mean h:

22. Departure headway variance For 1 st port of call: – Departure headway variance: – Finite variance requires: For 2 nd port of call – Departure headway variance: –Finite variance requires:

23. Headway variance for 4 ports in sequence (h = 24 +/- 1 hours, with uniform distribution) HeadwaysMeanSimulated varianceCalculated variance Arrival at 1 st port24.01510.3387 Arrival at 2 nd port24.01470.83330.8467 Arrival at 3 rd port24.01412.99503.0693 Arrival at 4 th port24.013913.7513 Stochastic stability (1)

24. Headway variance for 4 ports in sequence (h = 24 +/- 1 hours, with uniform distribution) HeadwaysMeanSimulated varianceCalculated variance Arrival at 1 st port24.01510.3387 Arrival at 2 nd port24.01480.66890.6774 Arrival at 3 rd port24.01431.65371.6934 Arrival at 4 th port24.01384.8555 Stochastic stability (2)

25. Conclusions Loading speed determines schedule stability Schedule instability leads to bunching, which increases average yard inventory The condition for schedule stability is that the ratio of the arrival to loading rate should be less than half Analytic solutions for departure headway variance at the 1 st and 2 nd ports of call derived Next: Look at global container liner stability

26. Thank you for your attention!