Flexible Services and Manufacturing Journal

, Volume 30, Issue 4, pp 764–784 | Cite as

A stochastic online algorithm for unloading boxes from a conveyor line

  • Reinhard Bürgy
  • Pierre Baptiste
  • Alain HertzEmail author
  • Djamal Rebaine
  • André Linhares


This article discusses the problem of unloading a sequence of boxes from a single conveyor line with a minimum number of moves. The problem under study is efficiently solvable with dynamic programming if the complete sequence of boxes is known in advance. In practice, however, the problem typically occurs in a real-time setting where the boxes are simultaneously placed on and picked from the conveyor line. Moreover, a large part of the sequence is often not visible. As a result, only a part of the sequence is known when deciding which boxes to move next. We develop an online algorithm that evaluates the quality of each possible move with a scenario-based stochastic method. Two versions of the algorithm are analyzed: in one version, the quality of each scenario is measured with an exact method, while a heuristic technique is applied in the second version. We evaluate the performance of the proposed algorithms using extensive computational experiments and establish a simple policy for determining which version to choose for specific problems. Numerical results show that the proposed approach consistently provides high-quality results, and compares favorably with the best known deterministic online algorithms. Indeed, the new approach typically provides results with relative gaps of 1–5% to the optimum, which is about 20–80% lower than those obtained with the best deterministic approach.


Sequencing Real-time scheduling Heuristics Conveyor line Stochastic online optimization 



Reinhard Bürgy’s work was partially funded by the Swiss National Science Foundation under Grant P2FRP2_161720.


  1. Baptiste P, Rebaine D, Brika Z (2012) Chargement de camions d’une ligne de production: comparaison d’heuristiques. In: Conférence ROADEF 2012Google Scholar
  2. Baptiste P, Hertz A, Linhares A, Rebaine D (2013) A polynomial time algorithm for unloading boxes off a gravity conveyor. Discret Optim 10(4):251–262MathSciNetCrossRefGoogle Scholar
  3. Baptiste P, Bürgy R, Hertz A, Rebaine D (2017) Online heuristics for unloading boxes off a gravity conveyor. Int J Prod Res 55(11):3046–3057CrossRefGoogle Scholar
  4. Bartholdi JJ, Platzman LK (1986) Retrieval strategies for a carousel conveyor. IIE Trans 18(2):166–173CrossRefGoogle Scholar
  5. Bozma HI, Kalalıoğlu ME (2012) Multirobot coordination in pick-and-place tasks on a moving conveyor. Robot Comput Integr Manuf 28(4):530–538CrossRefGoogle Scholar
  6. Dyer JS, Glover F (1970) A barge sequencing heuristic. Transp Sci 4(3):281–292CrossRefGoogle Scholar
  7. Ghosh JB, Wells CE (1992) Optimal retrieval strategies for carousel conveyors. Math Comput Model 16(10):59–70CrossRefGoogle Scholar
  8. Lee SD, Kuo YC (2008) Exact and inexact solution procedures for the order picking in an automated carousal conveyor. Int J Prod Res 46(16):4619–4636CrossRefGoogle Scholar
  9. van den Berg JP (1996) Multiple order pick sequencing in a carousel system: a solvable case of the rural postman problem. J Oper Res Soc 47(12):1504–1515CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Reinhard Bürgy
    • 1
  • Pierre Baptiste
    • 1
  • Alain Hertz
    • 1
    Email author
  • Djamal Rebaine
    • 2
  • André Linhares
    • 3
  1. 1.GERAD & École Polytechnique de MontréalMontrealCanada
  2. 2.GERAD & Université du Québec à ChicoutimiSaguenayCanada
  3. 3.University of WaterlooWaterlooCanada

Personalised recommendations