1.  1  Storage Space Allocation in Container Terminals Chuqian Zhang *1, Jiyin Liu *1, Yat-wah Wan *1, Katta G. Murty *2, Richard Linn *3 *1 IEEM, HKUST, Clear Water Bay, HONG KONG *2 IOE, Univ. of Michigan, Ann Arbor, Michigan, USA *3 ISE, Florida International University, Miami, Florida, USA

2.  2  Outline  background  problem statement  solution approach  results and conclusion

3.  3   Busiest Container Ports  Throughput in TEU Rank200020012002 5 th 4 th 3 rd 2 nd 1st 6,274,556 7,425,832 7,540,387 17,086,900 18,098,000 6,334,400 7,540,525 8,072,814 15,571,100 17,826,000 8,493,000 8,620,000 9,453,356 16,940,900 19,144,000 20-foot equi- valent unit

4.  4  Rank200020012002 5 th 4 th 3 rd 2 nd 1st Shanghai Kaohsiung Pusan Singapore Hong Kong Shanghai Kaohsiung Pusan Singapore Hong Kong Singapore Pusan Kaohsiung Rotterdam  Busiest Container Ports  Throughput in TEU

5.  5  Impact of 19.14 m TEU (2002)  around 12 m TEU handled by container terminals  handling charge: at least NZ$ 2.5 b  2% improvement  NZ$ 50 m

6.  6  The Typical Container Terminal Layout Blocks of Containers & Yard Cranes Internal Tractors & Quay Crane Block, Internal Tractor, & Yard Crane Blocks, Yard Cranes, & Quay Cranes Quay Cranes & Container Vessel

7.  7  Types of Container Movements  vessel loading (VSLD: blocks to vessels)  vessel discharge (VSDS: vessels to blocks)  container grounding (CYGD: shippers to blocks)  container pickup (CYPI: blocks to consignees) need to consider the storage space allocationarrival times: random

8.  8  Comparing Different Terminals Delta (Netherlands) Long Beach (USA) HIT & COSCO-HIT throughput (TEU) 2.5 mill4.6 mill6.6 mill area (hectares) 280295122 yard cranes ~ 50 (+ AGV) ~ 50 (+ chassis, train) 167 ~ 18,000 TEU per day Tiny areaIntensive operations

9.  9  Comparing Different Terminals Delta (Netherlands) Long Beach (USA) HIT & COSCO-HIT throughput (TEU) 2.5 mill4.6 mill6.6 mill area (hectares) 280295122 yard cranes ~ 50 (+ AGV) ~ 50 (+ chassis, train) 167 HK: mix the storage of import (I/B) and export (O/B) containers

10.  10  Objectives of Hong Kong Container Terminals  various performance indicators, inter- related, and possibly contradictory to each other  two commonest objectives in HK  to max. the (average) throughput of QCs  to min. the (average) vessel berthing time

11.  11  Outline  background  problem statement

12.  12  location assignment (determining the exact locations of containers in blocks) storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block) QC allocation (allocating QCs to (bays of) vessels) berth allocation (allocating vessels to berths) RTGC deployment (deploying RTGCs in real time) IT deployment (deploying ITs in real time) schedule and stowage plan of vessels Operations Decisions in a Container Terminal

13.  13  location assignment (determining the exact locations of containers in blocks) storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block) QC allocation (allocating QCs to (bays of) vessels) berth allocation (allocating vessels to berths) RTGC deployment (deploying RTGCs in real time) IT deployment (deploying ITs in real time) schedule and stowage plan of vessels Operations Decision in this Research

14.  14  Our Problem: Storage Space Allocation  inputs  results of the berth allocation  results of the QC allocation  vessel arrival and departure times  workload requirements of vessels

15.  15  Our Problem: Storage Space Allocation  outputs  stor. space allocation for vessel discharge  interchangeable I/B containers  to determine for each vessel the number of I/B containers stored in each block  stor. space allocation for container grounding  interchangeable O/B containers  to determine for each vessel the number of O/B containers stored in each block  practical solution

16.  16  Our Problem: Storage Space Allocation  dynamics  deterministic arrival times of vessel loading and vessel discharge  stochastic arrival times of container grounding and container pick up  conversion of movements  container grounding turned into vessel loading  vessel discharge turned into container pickup

17.  17  Sketch of Outputs IB 525 OB 620 IB 28; OB 46 IB 525 OB 620

18.  18  Outline  Hong Kong terminals  problem statement  solution approach

19.  19  Difficulties of the Problem  inter-related problems & sub-problems  multiple objectives  large number of variables  integer variables hierarchical approach location assignment (determining the exact locations of containers in blocks) storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block) QC allocation (allocating QCs to (bays of) vessels) berth allocation (allocating vessels to berths) RTGC deployment (deploying RTGCs in real time) IT deployment (deploying ITs in real time) schedule and stowage plan of vessels Determine the total # of I/B and O/B containers of each block (to balance the workload in each period) Allocate I/B & O/B containers of vessels to blocks in each period (to minimize total distance traveled) Implement the decision for one day and update the information Information: blocks’ capacity, blocks’ status, arriving containers level 1 level 2

20.  20   inter-related problems & sub-problems  multiple objectives  large number of variables  integer variables  dynamic problem: vessels, trucks, etc. rolling horizon Difficulties of the Problem (cont.) Day 1Day 2Day 3Day 4Day 5 1 st planning horizon 2 nd planning horizon

21.  21   inter-related problems & sub-problems  multiple objectives  large number of variables  integer variables  dynamic problem: vessels, trucks, etc.  unknown data: grounding and picking ups beyond the planning horizon forecasting Difficulties of the Problem (cont.)

22.  22  storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block) Solution Approach Determine the total # of I/B and O/B containers stored in each block...............................................................

23.  23  Level 1: Determine the total # of I/B and O/B containers stored in each block shippers and consignees Vessel A YC 1 YC 2 the earliest departure time of Vessel A depends on the longest working time of YC 1 and YC 2

24.  24  Level 1  for yard cranes  balance the workload of yard cranes for vessels  rationale: yard cranes act as parallel servers; the longest processing time = vessel berthing time  output: # of I/B and O/B containers in each block for each time period

25.  25  Solution Approach level 1 Determine the total # of I/B and O/B containers stored in each block............................................................... (to balance the workload in each period)

26.  26  Level 1  decisions  D it : the total number of I/B containers discharged in period t that can be assigned to block i  G it : the total number of O/B containers delivered in period t that can be assigned to block i

27.  27  - balance the total number of containers - balance the number of vessel loading/discharging containers  the objective function Level 1 )]}(min)(max[ )](min)(max[{ }{ }{ 2 1 }{ }{ 1 it i i T t i i PGLDPGLDw LDLDwMin     Minimize the dispersion of the total number of containers among blocks Minimize the dispersion of vessel loading/discharging containers among blocks

28.  28  Level 1 ~ D t ~ D t0t0 ~ D t1t1 ~ D t,T-t  t... D 1t01t0 D 2t02t0 D Bt0... D 1t11t1 D 2t12t1 D Bt1... D 1t,T-t D 2t,T-t D Bt,T-t...  1t1t  2t2t  Bt......,,2,1;,2,1BiTtD it  0 D tT k itk      workload at period t block i...,,2,1;,2,1BiTtP it  1 0 )( 0 DP t k kkti      conservation of flow of containers total number of containers discharged at period t: from vessel records number of containers to be taken away at different time periods: from historical pattern storage blocks of such containers

29.  29  Level 1...,,1,0;,2,1 ~ 1 tTkTtDD B i itktk   ...,,1,0;,2,1 ~ 1 tTkTtGG B i itktk   ...,,2,1;,2,1 0 BiTtDD it tT k itkit     ...,,2,1;,2,1 0 BiTtGG it tT k itkit     ...,,2,1;,2,1 1 0 )( 0 BiTtGLL t k kktiit     ...,,2,1;,2,1 1 0 )( 0 BiTtDPP t k kktiit      TtBiLPDGVV ti...,,2,1;,2,1)]()[( )1(   TtBiCV iit...,,2,1;,2,1  flow conservation constraint on CYPI and VSLD containers block density constraints flow conservation constraint on CYGD and VSDS containers integer variables

30.  30  Solution Approach level 1 Allocate I/B & O/B containers of vessels to blocks in each period........................................................ Determine the total # of I/B and O/B containers stored in each block............................................................... (to balance the workload in each period)

31.  31  Level 2  known locations of vessels and blocks  known D it, D itk, G it, G itk (numbers of I/B and O/B containers in each block for each period) from level 1  unknown: the identification of vessels that contribute the containers (to blocks)  minimizing the travelling distance of ITs  minimizing the total processing time of vessels  standard transportation problems

32.  32  Level 2  X ijtk : the number of I/B containers discharged from vessel j in period t, picked up by customers in period t+k, that can be assigned to block i  ( or the number of O/B containers arrived in period t, headed for vessel j in period t+k, that can be assigned to block i)  decisions (separating I/B & O/B)

33.  33  1 2 StSt 1 2 B 1 B Sources (vessels) Destinations (blocks) N 1t N 2t N st U1t0U1t0 U2t0U2t0 U Bt0 U 1t2 U Bt(T-t) : : : d 11 : X 11t1 )( : tTtBS tt Xd  Level 2 number of different types of containers stored in each block number of containers for each vessel minimize the total distance travelled by ITs   

34.  34      B i S j tT k ijtkij t XdMin 110...,,1,0;,2,1 1 tTkBiUX t S j itkijtk   ...,,2,1 10 tjt B i tT k ijtk SjNX      X ijtk  0 i = 1, 2, …, B; j = 1, 2, …, S t ; k = 1, 2, …, T - t s.t. Level 2

35.  35  Solution Approach Implement the decision for one day and update the information Information: blocks’ capacity, blocks’ status, arriving containers level 1level 2 Allocate I/B & O/B containers of vessels to blocks in each period........................................................ (to minimize total distance traveled) Determine the total # of I/B and O/B containers stored in each block............................................................... (to balance the workload in each period)

36.  36  Outline  Hong Kong terminals  problem statement  solution approach  results and conclusion

37.  37  Numerical Study for Level 1  real data: 17 days, 6 periods per day  3-day rolling horizon  effective capacity = 83%  10 blocks (~ 4320 integer variables)  accept the first feasible integer solution

38.  38   ratio between the gap & the lower bound  min: 0.0%; average: 1. 84%; max: 6.58%  computation time  min: 16.5 s; average: 110 s; max: 542 s  average imbalance  all containers: 5.68/period  vessel related containers: 4.22/period Results of Level 1 upper bound lower bound optimal solution

39.  39  Conclusion  propose a procedure that possibly improves the terminal operations  further studies  more extensive numerical runs  different settings  larger sizes  approximate methods for solving level 1  actual benefits for terminals