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A decomposition-based approach to the scheduling of identical automated yard cranes at container terminals

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Abstract

In today’s ports, the storage area is often the bottleneck in the serving of a vessel. It is therefore an important influencing factor in the minimization of the turnaround time of the vessels, which is the main objective in operational planning in container terminals. The operational planning of the yard cranes strongly impacts the yard’s efficiency. This planning task comprises the assignment of jobs to cranes, the sequencing of jobs per crane and the scheduling of crane movement and job executions subject to time windows and precedence constraints. A common yard configuration is a block storage system with two identical automated gantry cranes, called twin cranes. These cranes are subject to non-crossing constraints and therefore often exclusively serve either the landside or the seaside of the terminal. A polynomial-time algorithm for the scheduling subproblem of the cranes is introduced. As the sequencing and assignment part of this planning task is NP-hard, the overall problem is solved heuristically with a branch and bound procedure that includes the introduced scheduling algorithm as an evaluation subroutine. A computational study is presented to test the performance of this approach against a mathematical program solved by CPLEX.

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Notes

  1. Following the classification in Boysen et al. (2017), the considered crane scheduling problems are

    $$\begin{aligned}&[2\text {D}, 2\,| \, \text {M},\text {mv}^{\mathrm{XY}}, r^i,\delta ^i,\text {prec},\,\text {pos}\,|\,C^{\max }]\ \text {and}\\&[2\text {D}, 2, \text {ends}\,|\, \text {M},\text {mv}^{\mathrm{XY}}, r^i,\delta ^i,\text {prec}, \text {pos}\, | \,C^{\max }]. \end{aligned}$$

  2. The classification of Boysen and Stephan (2016) for this problem is \([\text {B} \mid \text {IO}^1 \mid \text {C}_{\max }]\).

  3. Briskorn and Angeloudis (2016) propose a polynomial algorithm for the yard crane scheduling problem without time windows, spreader movement or precedence constraints. For this problem setting, their solution algorithm can be used for the lower bound computation.

  4. For the remainder of this section the term “solved” means the procedure ended with an answer. This answer could be a feasible solution to a solvable instance or having proven infeasibility for an infeasible instance.

  5. CPLEX could prove that one instance in test set 2 is not feasible. This is the instance the B&B procedure could not solve.

  6. See footnote 5.

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  1. Institute of Operations Management, University of Hamburg, Moorweidenstraße 18, 20148, Hamburg, Germany

    Amelie Eilken

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Eilken, A. A decomposition-based approach to the scheduling of identical automated yard cranes at container terminals . J Sched 22, 517–541 (2019). https://doi.org/10.1007/s10951-019-00611-z

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