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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.

This paper addresses the problem of minimising the number of moves to unload a set of boxes off a gravity conveyor by a forklift. If the input data are known in advance, the problem is efficiently solvable with a dynamic programming approach. However, this method is rarely applicable in practice for two reasons. First, the problem generally occurs in a real-time environment where the input data are revealed over time. Second, computing devices are in most cases not available in forklifts or gravity conveyors for decision-making. Online approaches that can easily be applied by human operators are therefore sought in practice. With this in mind, we first propose some intuitive approaches and analyse their performance through an extensive experimental study. The results show that these approaches are quite inefficient as they average between 14.7 and 59.3% above the optimum. A less intuitive but still simple approach is then designed that consistently produces good results with an average gap of 6.1% to the ...