Optimization in container terminals

Transcription

1 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 1/23 Optimization in container terminals Hierarchical vs integrated solution approaches Michel Bierlaire Matteo Salani Ilaria Vacca TRANSP-OR, Ecole Polytechnique Fédérale de Lausanne, CH IDSIA, Dalle Molle Institute for Artificial Intelligence, Lugano, CH 10th Swiss Transport Research Conference (STRC) September 2, Ascona, Switzerland

2 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 2/23 Outline Container terminals Berth Allocation Problem (BAP) Quay Cranes Assignment Problem (QCAP) Hierarchical vs Integrated solution approaches Computational results

3 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 3/23 Motivation Worldwide Singapore (+16%) (+21%) 2 Shanghai (+49%) (+29%) 3 Hong Kong (+07%) (+03%) Europe Rotterdam (+17%) (+12%) 2 Hamburg (+27%) (+10%) 3 Antwerp (+16%) (+23%) Table 1: Container traffic (in thousands TEUs).

4 Container terminals Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 4/23

5 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 5/23 Container terminals Scheme of a container terminal system (Steenken et al., 2004).

6 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 6/23 The Berth Allocation Problem (BAP) Input a set of vessels, a set of berths, a time horizon; an expected handling time for every vessel; a time window on the vessel s handling time; Output an assignment of vessels to berths; a scheduling of vessels over time; Objectives minimize the total delay; minimize the completion time; minimize the housekeeping costs.

7 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 7/23 Yard Housekeeping Costs In the context of a transshipment container terminal, we take into account the cost generated by the exchange of containers between ships in terms of traveled distance. Piecewise linear function depending on the distance and on the type of carrier used: < 600m : no housekeeping, straddle carriers m : housekeeping, straddle carriers > 1100 m : housekeeping, multi-trailer

8 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 8/23 The Quay Crane Assignment Problem (QCAP) Input a berth allocation plan; the workload of every vessel; the maximum number of available QCs; Output a quay crane assignment to vessels; Objectives minimize the turn-around time; minimize the completion time; maximize the monetary value associated to qc profiles.

9 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 9/23 Berth allocation plan with QC assignment BAP and QCAP are strictly interdependent: the expected handling time depends on the number of assigned QCs; given a berth allocation plan, the QC capacity must be satisfied.

10 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 10/23 The Tactical Berth Allocation Problem (TBAP) Integrated optimization of BAP and QCAP we solve the two problems simultaneously. Tactical decision level we analyze the problem from the terminal point of view, in order to provide decision support in the context of the negotiation between the terminal and shipping lines. Quay-crane profiles we introduce the concept of quay crane profile, i.e. the number of cranes assigned to a vessel over time. QC profiles can vary in length (number of shifts) and in size (number of QCs). Handling time the handling time becomes a decision variable, that depends on the assigned quay crane profile.

11 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 11/23 Hierarchical solution approach The hierarchical approach consists of the following steps: 1. determine the expected handling time for every ship; 2. BAP: solve the berth allocation problem, taking into account ships time windows and berths availability; 3. QCAP: assign a qc profile to every ship, taking into account the qc capacity constraint and the given berth allocation plan. Methodology: the BAP is solved exactly by a branch-and-price algorithm; the QCAP is solved by a general-purpose MIP solver.

12 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 12/23 Handling time estimation We consider 2 scenarios for the handling time: scenario A : longest feasible profile for every ship; scenario B : max-value profile for mother vessels, longest feasible profile for feeders. Scenario A represents a conservative approach (worst case scenario). Scenario B is more realistic, although it may lead to infeasibility of QCAP.

13 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 13/23 Integrated solution approach MIQP and MILP formulations for TBAP. Tabu search heuristic for TBAP. Dantzig-Wolfe reformulation. Column generation: master problem and pricing subproblem. Exact branch-and-price algorithm.

14 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 14/23 Results: 10 vessels, 1 week ( easy ) BAP+QCAP Scen.A BAP+QCAP Scen.B Integrated TBAP inst obj K t(s) obj K t(s) obj K t(s) %(A) %(B) H1_ % 0.16% H1_ % 0.16% H1_ % 0.16% H2_ % 0.00% H2_ % 0.41% H2_ % 0.41% L1_ % 0.17% L1_ % 0.58% L1_ % 0.58% L2_ % 0.56% L2_ % 0.56% L2_ % 0.56%

15 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 15/23 Results: 10 vessels, 4 days ( congested ) BAP+QCAP Scen.A BAP+QCAP Scen.B Integrated TBAP inst obj K t(s) obj K t(s) obj K t(s) %(A) %(B) H1_10 x x H1_ x % + H1_ x % + H2_10 x x H2_ % 0.23% H2_ % 0.40% L1_ x % + L1_ % 0.79% L1_ % 0.88% L2_ % 0.46% L2_ % 0.45% L2_ % 0.46%

16 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 16/23 Conclusions The hierarchical approach provides good and fast solutions on easy instances. The integrated approach performs significantly better for congested instances. The increased complexity of the simultaneous optimization allows for significant savings, both in terms of feasibility and utilization of resources.

17 Thanks for your attention! Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 17/23

18 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 18/23 The Tactical Berth Allocation Problem (TBAP) Decision variables berth assignment : y k i {0,1}; profiles assignment : λ p i {0,1}; ship scheduling : x k ij {0,1}, Tk i 0. Objective function : maximize total value of QC profile assignments & minimize the housekeeping yard cost of transshipment flows: max i N p P i v p i λp i 1 2 i N k M y k i j N w M f ij d kw y w j (1)

19 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 19/23 The Tactical Berth Allocation Problem (TBAP) Berth assignment k M y k i = 1 i N, (2) Flow constraints j N {d(k)} x k o(k),j j N {d(k)} x k i,d(k) i N {o(k)} x k ij j N {o(k)} j N {d(k)} x k ji = 1 k M, (3) = 1 k M, (4) = 0 k M, i N, (5) x k ij = yk i k M, i N, (6)

20 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 20/23 The Tactical Berth Allocation Problem (TBAP) Time computation Ti k + t p i λp i Tk j (1 xk ij )M k M, i N, j N d(k) (7) p P i To(k) k Tk j (1 xk o(k),j )M k M, j N, (8) Ship and Berth time windows a i yi k Tk i k M, i N, (9) Ti k b i yi k k M, i N, (10) a k To(k) k k M, (11) Td(k) k bk k M, (12)

21 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 21/23 The Tactical Berth Allocation Problem (TBAP) QC profile assignment & linking constraints k M QC total capacity a h h H s γ h i = p P i λ p i p P s i T k i bh (1 γ h i k M T k i (1 γ h i = 1 i N, (13) λ p i i N, s S, (14) )M h H, i N, (15) )M h H, i N, (16) ρ ph i λ p i +γh i 1 h H, i N, p P i, (17) i N p P i h ρ pu i q p(h u+1) i Q h h H s (18) u=max{h t p i +1;1}

22 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 22/23 TBAP linearization Additional decision variable z kw ij {0,1} i,j N, k,w M, set to 1 if y k i = yw j = 1 and 0 otherwise. Linearized objective function max i N p P i v p i λp i 1 2 i N j N k M w M f ij d kw z kw ij (19) Additional constraints k K w K z kw ij = g ij i,j N, (20) z kw ij y k i i,j N, k,w M, (21) z kw ij y w j i,j N, k,w M. (22)

23 Ilaria Vacca (EPFL) - Integrated optimization in container terminal operations p. 23/23 Master problem Objective function min 1 2 i N j N k M w M z kw ij f ijd kw k M r Ω k v r λ r (23) Serve every ship s.t. k M r Ω k α i r λ r = 1 i N, (24) QC total capacity Convexity constraints k M qrλ h r Q h h H, (25) r Ω k λ r 1 k M, (26) r Ω k

24 References Steenken, D., Voss, S. and Stahlbock, R. (2004). Container terminal operation and operations research - a classification and literature review, OR Spectrum 26: