Determining crane areas for balancing workload among interfering and noninterfering cranes

Abstract

This article treats the problem of subdividing an area for storing containers such that the workload is evenly shared among the cranes operating the resulting subareas. We consider two crane sets: while noncrossing constraints between cranes of the same set need to be observed, cranes of different sets do not interfere. Such a problem setting is, for instance, relevant for scheduling the (un‐)loading of vessels by parallel quay cranes operating on opposing berths or in container yards with cross‐over cranes. We formalize the resulting optimization problem, prove computational complexity, and present exact and heuristic solution procedures. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Modelling and Metaheuristic for Gantry Crane Scheduling and Storage Space Allocation Problem in Railway Container Terminals

“…As the objectives of operation, containers are gathered by different scopes by the researchers. Lee et al [10] and Boysen et al [11] carried on the research of quay gantry crane scheduling problem with bays. The former adopted a mixed integer programming method to establish the mathematical model and took the noncrossing constraints into consideration.…”

“…Constraint (10) redefines the operation time of the th task on considering the stop position of the container train. Constraint (11) undertakes that the start time of a task is not earlier than the soonest available time of the gantry crane which is utilized to complete this task. Constraints (12) and (13) provide a definition to the decision variable .…”

Optimally scheduling interfering and non‐interfering cranes

“…Using heuristics, they solve instances with up to 40 jobs and seven cranes (in the case of Chen et al, ). To the best of the author's knowledge, the only two exact algorithms in this context were proposed by Beens and Ursavas () and Boysen, Emde, and Fliedner (). Beens and Ursavas () investigate a fairly complex problem that considers many side‐constraints particular to their specific application, for example, yard congestion and workload safety.…”

“…They develop a solution technique based on branch and price. Finally, Boysen et al () deal with a somewhat reduced problem, where each crane can only move within its assigned area, thus greatly simplifying traffic control to avoid collisions. Their goal is to determine these crane areas, aiming to minimize the makespan.…”

Scheduling twin robots on a line

“…The collision constraint is well‐known within the crane scheduling literature, and is referred to as a “spatial constraint” , “inter‐crane interference” , or more commonly “non‐crossing” constraint . However, these problems involve many other features such as workload allocation among the cranes, release times for the jobs, and sets of cranes that do not interact.…”