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Abstract
This paper discusses the scheduling problem for two factory cranes that move along a single track, which is one of the most important equipment in manufacturing shop. Each crane is assigned a sequence of pickups and deliveries at specified locations and the two cranes must be operated so as to avoid interference with each other. In order to minimize the makespan, we define the bottleneck crane, which takes the maximum time to complete a given set of tasks. And a mixed-integer programming model which considers various constraints related to the operations of cranes is formulated. However, this problem is NP-hard, therefore we propose a heuristic algorithm to solve this problem. Finally, a numerical experiment on a specific manufacturing plant is used to illustrate the efficiency from computational point of view.
... A GA was also used to study the quay crane scheduling problem [20][21][22]28] and its extended problems, such as berth allocation and quay crane assignment problem [23] , quay crane assignment and scheduling problem [25] , quay crane scheduling problem with draft and trim constraints [29] , and integrated quay crane and yard truck scheduling problem [31] . Other problems using GAs include the scheduling problems of multiple vehicles/cranes along a common lane [24,26,27,30] and the yard crane scheduling problem with a noninterference constraint in a container terminal [32] . The results of the previously mentioned studies show that GAs manage to provide practical solutions and significant time savings for scheduling problems. ...
Nowadays, more automated or robotic twin-crane systems (RTCSs) are employed in ports and factories to improve material handling efficiency. In a twin-crane system, cranes must travel with a minimum safety distance between them to prevent interference. The crane trajectory prediction is critical to interference handling and crane scheduling. Current trajectory predictions lack accuracy because many details are simplified. To enhance accuracy and lessen the trajectory prediction time, a trajectory prediction approach with details (crane acceleration/deceleration, different crane velocities when loading/unloading, and trolley movement) is proposed in this paper. Simulations on different details and their combinations are conducted on a container terminal case study. According to the simulation results, the accuracy of the trajectory prediction can be improved by 20%. The proposed trajectory prediction approach is helpful for building a digital twin of RTCSs and enhancing crane scheduling.
... In the workshop, parts must be transported to the precedence machine before the successor machines in the manufacturing plant (Ge et al., 2012). Therefore, the task order is assumed to be fixed, and crane scheduling only needs to allocate tasks to cranes. ...
In multi-crane systems, interference between cranes frequently occurs, and a significant amount of energy is wasted to avoid these interferences. Energy-efficient multi-crane scheduling and employing the required number of cranes are critical for saving energy. The energy consumption of a crane varies during operation; thus, it is important to accurately and effectively evaluate the operational energy consumption of a crane for different working phases. Digital twins (DTs) have various advantages such as virtual reality interaction, real-time mapping, and dynamic performance evaluation. Therefore, a DT-driven energy-efficient multi-crane scheduling and crane number selection approach is proposed in this study. The crane scheduling problem was described and modeled by considering energy consumption. Subsequently, a DT framework was established. Under this framework, a multi-crane system based on simulation was built in a virtual space. After inputting tasks into the virtual multi-crane system, a solution was generated based on the crane scheduling rules, interference detection, and avoidance methods. Then, the energy consumption of the program was evaluated. Finally, a case study was considered to illustrate the advantages of the proposed method.
... Finally, we discuss the overlap between different crane scheduling applications and the potential of transferring results from one area to another in Section 5.4 . (2011) [ 2D , 2 , ends , sm | M , mv XY , pos, r i | w j T j ] Prod DP Bierwirth and Meisel (2009) [1D, sm|mv X , r c , prec, pos| C max ] Quay BBH [1D, area|| C max ] Rail DP [1D, area|| C max ] Rail DP [1D, area, pass|| C max ] Quay DP Boysen, Briskorn, and Emde (2015) [1D, 2, ends|mv X | C max ] ASRS DEC, DP Briskorn and Angeloudis (2016) [1D, 2, ends|M, mv X , chains| C max ] Yard DP Briskorn and Angeloudis (2016) [1D, 2, ends, pass|M, mv X , chains| C max ] Yard DP Carlo and Vis (2012) [1D, 2, front|M, mv X , chains| C max ] ASRS H Carlo and Martínez-Acevedo (2015) [1D, 2, ends, sm|dual, mv X , pmtn| C max ] Yard B&B, H Chen et al. (2011) [1D, sm, pass|mv X , prec, pos| C max ] Quay H, TS Chen, Lee, and Goh (2014) [1D, sm|mv X , r c , δ c , prec, pos| C max ] Quay MILP Choo, Klabjan, and Simchi-Levi (2010) [1D, sm|mv X , r c , prec, pos| C max ] Quay BP Choe, Park, Ok, and Ryu (2007) [3D top , 2, ends|M, mv X , dy| T j ] Yard LS Choe, Yang, and Ryu (2012) [3D top , 2, ends|M, mv X , dy| T j , C max ] Yard GA Chung and Choy (2012) [1D, sm|mv X , r c , prec, pos| C max , C c ] Quay GA Chung and Chan (2013) [1D, sm|mv X , prec, pos| C max ] Quay GA Diabat and Theodorou (2014) [1D|| C max ] Quay GA Dell, Royset, and Zyngirdis (2009) [3D top , 2, ends, sm|M, mv X , dy, prec| ] Yard DEC Dohn and Clausen (2010) [1D, 2, ends, sm|M, mv X , pos, r i | ] Prod H Dorndorf and Schneider (2010) [ 1D , 3 , ends , sm,pass | mv X , dy , r i | , w i T i ] Yard DEC Emde and Boysen (2014) [1D, 2, front|mv X | C max ] Misc GA Emde and Boysen (2014) [1D, 2, front|mv X , chain| C max ] Misc DP Erdo gan, Battarra, and Laporte (2014) [1D, 2, ends|mv X | C max ] ASRS BB, AA Expósito-Izquierdo, González-Velarde, Melián-Batista, and Moreno-Vega (2013) [1D, sm|mv X , r c , prec, pos| C max ] Quay GA Fu, Diabat, and Tsai (2014) [ 1D || w i C i ] Quay GA Gharehgozli, Laporte, Yu, and de Koster (2015) [3D top , 2, ends, sm|dual, mv XYZ , prec, open| C max ] Yard LNS Ge, Wang, Jin, Ren, and Gao (2012) [1D, 2, ends|M, mv X , pos| C max ] Prod H Gellert and König (2011) [1D|R, mv X , pos| C max ] Misc H Guan, Yang, and Zhou (2013) [1D|mv X , pos| C max ] Quay DPH Guo, Cheng, and Wang (2014) [1D, sm|mv X , r c , prec, pos| C max ] Quay GEO Hakam, Solvang, and Hammervoll (2012) [1D, 2, sm|| C max ] Quay GA Hino et al. (2009) [ 2D , 2 , ends , pass | M, cmv XY , chain, pos |−] ASRS H Javanshir and Ganji (2010) [1D|| C max ] Yard GA Kaveshgar, Huynh, and Rahimian (2012) [1D, sm|mv X , r c , prec, pos| C max , C c ] Quay GA Kellner and Boysen (2015) [2D, pass |mv XY | C max ] Rail SA Kim and Park (2004) [1D, sm|mv X , r c , prec, pos| C max , C c ] Quay BB,GRASP Klaws et al. (2007) [3D top , 3, sm|mx XY , chain| C max ] Yard SIM Kung et al. (2012) [ 2D , 2 , ends , pass | M, cmv XY , chain, pos |−] ...
Nowadays, many industries rely on cranes for efficiently executing storage and retrieval operations of goods. Areas of application are, for instance, container logistics in seaports and warehousing operations in automated storage and retrieval systems. Therefore, it is not astounding that plenty scientific papers on crane scheduling in many different yet closely related logistics settings have accumulated. In many of these problems, crane interference occurs. A prominent example are non-crossing constraints where cranes share a common pathway and cannot overtake each other. In order to structure this vast field of research, this paper provides a classification scheme for crane scheduling problems with crane interference. We apply this scheme to classify the existing literature, to determined the status-quo of complexity results, and to identify future research needs.
In order to crack the NP-hard nuts of crane scheduling in workshop, a model for simulating crane scheduling in workshop is presented based on cellular automata in the paper. The crane scheduling system is composed of operation sites, cranes, materials and scheduling rules of operation tasks. In the simulation model, operation sites are considered as fixed grid nodes, the materials transported as mobile particles, and cranes as movable nodes. The properties of operation sites, cranes, materials are set especially from status in workshop. The self-organized evolution mechanism of the model is obtained from scheduling conditions in the shop. Simulation cases, from crane scheduling of slab continuous-cast shop in Panzhihua Iron and Steel Group Corporation, show that the model of crane scheduling based on cellular automata with local microscopic interaction mechanism and self-organization evolution dynamics is valid. The model is useful for simulating crane scheduling in manufacturing workshop.
Quay cranes (QC) are key resources at container terminals, and the efficiency of QC operations is vital for terminal productivity. The Quay Crane Scheduling Problem (QCSP) is to schedule the work activities for a set of cranes assigned to a single berthed vessel with the objective of minimizing the completion time of all container handling tasks. The problem is complicated by special characteristics of QC operations. Considering QC moving time and interference constraints, the concept of contiguous bay operations is proposed and a heuristic is developed to generate QC schedules with this feature. The heuristic is efficient and effective: it has polynomial computational complexity, and it produces schedules with a completion time objective bounded above by a small increment over the optimal completion time. Importantly, the heuristic guarantees that no quay cranes are idle due to interference. Numerical experiments demonstrate that the optimality gap is small for practical instances.
The demand for the maritime transportation has significantly increased over the past 20 years due to the rapid pace of globalization. Terminal managers confront the challenge in establishing the appropriate quay crane schedule to achieve the earliest departure time of ship and provide efficient service. In general, quay crane schedule problems include two main issues (1) the allocation of quay cranes to handle the discharging and loading operations, and (2) the service sequence of ship bays in a vessel of each quay crane. Traditionally, the terminal planners determine the quay crane schedule based on their experience and own judgment. In addition, the interference among cranes and the increased in ship size further magnify its difficulty dramatically. Accordingly, this paper proposed a modified genetic algorithm to deal with the problem. To test the optimization reliability of the proposed algorithm, a set of well known benchmarking problem is solved, and the results obtained are being compared with other well known existing algorithms. The comparison demonstrates that the proposed algorithm performs as good as many existing algorithms and obtains better solutions than the best known ones in certain instances. In addition, the computational time(s) required are significantly much lesser, allowing it to be more applicable in practical situation.
This paper discusses the quay crane scheduling problem at indented berth, an extension to the current quay crane scheduling problem in the field of container terminal operation. A mixed integer programming model by considering the unique features of the quay crane scheduling problem at indented berth is formulated. For solution, decomposition heuristic framework is developed and enhanced by Tabu search. To evaluate the performance of the proposed heuristic framework, a comprehensive numerical test is carried out and its results show the good quality of the proposed heuristic framework.
For two-operation crane scheduling problems we consider two basic procedures; namely, batching and meshing. A minimum-ordered partition forms the basis of the batching procedure. A mesh-ordered relation forms the basis of the meshing procedure. Under certain necessary conditions, these procedures yield optimal schedules. Examples are provided to illustrate each procedure. Four mixed procedures are defined and combined to form an efficient algorithm whose solution is no worse than 4/3 the optimal solution.
This paper studies a single crane scheduling problem motivated by batch annealing process in the iron and steel industry. Each coil stack placed on fixed base needs to go through two-stage processing: heating and cooling. During each stage, limited special machines (furnace and cooler) must be operated by crane, respectively. Our problem is to assign the shared machines and schedule a single crane for minimizing the last coil stack completion time (makespan). A mixed integer linear programming (MILP) model is formulated by considering both machine and crane positions. We show that the problem is NP-hard in the strong sense. Some optimal properties on the problem are derived. A two-phase algorithm is constructed for the problem. In the first phase, a fully polynomial time approximation scheme (FPTAS) is developed for the assignment subproblem. In the second phase, a heuristics is proposed for the scheduling subproblem. From an absolute performance point of view, we analyze the quality of the two-phase algorithm. We also consider special cases where some properties or algorithms are developed. In order to further verify the performance of the two-phase algorithm, we develop a lower bound on the optimal objective function. Computational experiments on the randomly generated problem instances show that the algorithm is close to the lower bound within a reasonable computation time.
Crane is widely used to move a heavy object from one place to another not only in manufacturing industry but also service industry. As an important resource in the train oilcan repairing, crane scheduling affects directly the productivity of the systems. In this paper, we study cyclic single crane scheduling problem with two parallel train oilcan repairing lines, where jobs are loaded into the line at one end and unloaded at the other end. The processing time at each workstation must be within a given range. There is no buffer between these stations. A crane is used to move jobs between the workstations in two parallel lines. The objective is to schedule the moves to minimize the production cycle. We proposed a time way diagram for two parallel lines and developed a mixed integer linear programming model. Then we extended the model to the scheduling problem with multi-station to eliminate the bottleneck in lines. Examples are given to demonstrate the effectiveness of the model.
In this paper, we study the cyclic scheduling problem for electroplating lines where products are loaded into the system at
one end and unloaded at the other end. The electroplating jobs must be processed within a given time window in each tank.
There is no buffer between tanks. Two hoists sharing a common track are used to move products between the tanks in the production
line. The objective is to minimize the production cycle time through scheduling hoist moves. A solution procedure is proposed
in this study. The production line is first divided into two non-overlapping zones with a hoist assigned to each zone. Then
a mixed integer linear programming model is developed for scheduling hoist moves. Computational results on a benchmark example
problem are given in the paper to demonstrate the application of the proposed method.
We consider the problem of on-line scheduling with non-crossing constraints. The objective is to minimize the latest completion time. We provide optimal competitive ratio heuristics for the online-list and online-time problems with unit processing times, and a 3-competitive heuristic for the general online-time problem.