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Speed and Schedule Stability in Supply Chains

P O R T e C. GCSL2006, Hong Kong, December, 2006. Speed and Schedule Stability in Supply Chains. Michael G H Bell Professor of Transport Operations Imperial College London. PORTeC members. Civil and Environmental Engineering: Prof. Mike Bell Prof. Andrew Evans

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Speed and Schedule Stability in Supply Chains

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

  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. 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 Security and port efficiency (Khalid Bichou)

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

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

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

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

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

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

  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. Container terminals • 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

  12. Arrival and departure headways = Ratio of arrival to loading rate of containers h = Arrival headway of vessels (assumed to be uniform) =nth 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 1st port of call: Departure headway variance: Finite variance requires: For 2nd port of call Departure headway variance: Finite variance requires:

  23. Stochastic stability (1) Headway variance for 4 ports in sequence (h = 24 +/- 1 hours, with uniform distribution)

  24. Stochastic stability (2) Headway variance for 4 ports in sequence (h = 24 +/- 1 hours, with uniform distribution)

  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 1st and 2nd ports of call derived Next: Look at global container liner stability

  26. Thank you for your attention!

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