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An efficient MILP-based decomposition strategy for solving large-scale scheduling problems in the shipbuilding industry

  • Natalia P. Basán
  • Mariana E. Cóccola
  • Alejandro García del Valle
  • Carlos A. MéndezEmail author
Research Article
  • 3 Downloads

Abstract

This work presents a novel hybrid and systematic MILP-based solution approach for the resolution of multi-stage scheduling problems arising in the shipbuilding industry. The manufacturing problem involves the processing of a large number of sub-blocks and blocks, which should be rigorously produced and assembled with the aim of finalizing a project on time. Firstly, this paper presents three alternative rigorous MILP mathematical formulations relied on a continuous-time representation for solving the problem under study. Although the objective values reported by these exact optimization approaches outperform the results found through other solution techniques proposed in the literature to solve the same problem instances, the main drawback of the MILP models is the high computation time. Therefore, this work proposes an algorithm for solving the mathematical models in a decomposable way with the goal of accelerating the resolution times. The applicability of our proposal is demonstrated by effectively coping with several instances of a real-world case study dealing with the construction of a ship for the development of marine resources. Computational results show that the proposed decomposition method is able to obtain high-quality solutions in few seconds of CPU time for all examples considered.

Keywords

Multi-stage scheduling problem Shipbuilding process MILP model Decomposition strategy 

List of symbols

Indices

\(i\)

Product order (block or sub-block)

\(k\)

Processing unit

\(s\)

Processing stage

\(p\)

Time slot

Sets

\(I\)

Set of product orders

\(K\)

Set of processing units

\(S\)

Set of processing stages

\(P\)

Set of time slots

\(I^{b}\)

Set of blocks

\(I^{sb}\)

Set of sub-blocks

\(SB_{i}\)

Subset of sub-blocks that integrate a block \(i \in I^{b}\)

\(S^{b}\)

Available processing stages \(s\) to process block \(i \in I^{b}\)

\(S^{sb}\)

Available processing stages \(s\) to process sub-block \(i \in I^{sb}\)

\(S^{a}\)

Available processing stages \(s\) to assemble sub-blocks \(i \in I^{sb}\)

\(P_{k}\)

Set of time slots for processing unit \(k\) (slot-based continuous time formulation)

\(K_{s}\)

Set of parallel processing units \(k\) in processing stage \(s\)

Parameters

\(pt_{is}\)

Processing time of product order \(i\) at stage \({\text{s}}\)

\(M\)

Constant for big-M constraints

\(iter\)

Number of block to be inserted at each iteration

\(active_{i}\)

Indicating if product i is active in the current iteration

\(sY_{ik}\)

Saving assignment decisions

\(sW_{{ii^{\prime}s}}\)

Saving sequencing decisions

\(BestSol\)

Saving the best solution found in the improvement stage

\(CurrentSol\)

Saving the last solution found by the improvement stage

Continuous variables

\(Ts_{is}\)

Start time of product \(i\) in processing stage \(s\)

\(Tf_{is}\)

Final time of product \(i\) in processing stage \(s\)

\(Ts_{pk}\)

Start time of time slot \(p\) in processing unit \(k\) (slot-based continuous time formulation)

\(Tf_{pk}\)

Final time of time slot \(p\) in processing unit \(k\) (slot-based continuous time formulation)

MK

Makespan

Binary variables

\(W_{ipk}\)

Defining if product \(i\) is allocated to the time slot \(p\) of processing unit \(k\) (slot-based continuous time formulation)

\(W_{{ii^{\prime}s}}\)

Defining if product \(i\) is processed before of product \(i'\) in processing stage \(s\) (global general precedence formulation)

\(W_{{ii^{\prime}k}}\)

Defining if product \(i\) is processed exactly before than \(i'\) in processing unit \(k\) (unit-specific direct precedence formulation)

\(Y_{ik}\)

Defining if product order \({\text{i}}\) is processed in processing unit \({\text{k}}\)

\(YF_{ik}\)

Defining if product order \(i\) is first processed in unit \(k\)

Notes

Acknowledgements

The authors gratefully acknowledge the financial support from CONICET under Grant PIP 112 20150100641, from Universidad Nacional del Litoral under Grant CAI+D 2016 PIC 50420150100101LI and from ANPCyT under Grant PICT-2014-2392.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Natalia P. Basán
    • 1
  • Mariana E. Cóccola
    • 1
  • Alejandro García del Valle
    • 2
  • Carlos A. Méndez
    • 1
    Email author
  1. 1.INTEC (UNL –CONICET)Santa FeArgentina
  2. 2.University of A CoruñaFerrolSpain

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