外文原文（出自JOURNAL OF CONSTRUCTION ENGINEEING AND MANAGEMENT MARCH/APRIL/115-121）LOCATION OPTIMIZATION FOR A GROUP OF TOWER CRANESABSTRACT: A computerized model to optimize location of a group of tower cranes is presented. Location criteria are balanced workload, minimum likelihood of conflicts with each other, and high efficiency of operations. Three submodels are also presented. First, the initial location model classifies tasks into groups and identifies feasible location for each crane according to geometric closeness. Second, the former task groups are adjusted to yield smooth workloads and minimal conflicts. Finally, a single-tower-crane optimization model is applied crane by crane to search for optimal location in terms of minimal hook transportation time. Experimental results and the steps necessary for implementation of the model are discussed.INTRODUCTIONOn large construction projects several cranes generally undertake transportation tasks, particularly when a single crane cannot provide overall coverage of all demand and supply points, and/or when its capacity is exceeded by the needs of a tight construction schedule. Many factors influence tower crane location. In the interests of safety and efficient operation, cranes should be located as far apart as possible to avoid interference and collisions, on the condition that all planned tasks can be performed. However, this ideal situation is often difficult to achieve in practice; constrained work space and limitations of crane capacity make it inevitable that crane areas overlap. Subsequently, interference and collisions can occur even if crane jibs work at different levels. Crane position(s) tend to be determined through trial and error, based on site topography/shape and overall coverage of tasks. The alternatives for crane location can be complex, so managers remain confronted by multiple choices and little quantitative reference.Crane location models have evolved over the past 20 years. Warszawski (1973) established a time-distance formula by which quantitative evaluation of location was possible. Furusaka and Gray (1984) presented a dynamic programming model with the objective function being hire cost, but without consideration of location. Gray and Little (1985) optimized crane location in irregular-shaped buildings while Wijesundera and Harris (1986) designed a simulation model to reconstruct operation times and equipment cycles when handling concrete. Farrell and Hover (1989) developed a database with a graphical interface to assist in crane selection and location. Choi and Harris (1991) introduced another model to optimize single tower crane location by calculating total transportation times incurred. Emsley (1992) proposed several improvements to the Choi and Harris model. Apart from these algorithmic approaches, rule-based systems have also evolved to assist decisions on crane numbers and types as well as their site layout。 AssumptionsSite managers were interviewed to identify their concerns and observe current approaches to the task at hand. Further, operations were observed on 14 sites where cranes were intensively used (four in China, six in England, and four in Scotland). Time studies were carried out on four sites for six weeks, two sites for two weeks each, and two for one week each. Findings suggested inter alia that full coverage of working area, balanced workload with no interference, and ground conditions are major considerations in determining group location. Therefore, efforts were concentrated on these factors (except ground conditions because site managers can specify feasible location areas). The following four assumptions were applied to model development (detailed later):1. Geometric layout of all supply (S) and demand (D) points, together with the type and number of cranes, are predetermined.2. For each S-D pair, demand levels for transportation are known, e.g., total number of lifts, number of lifts for each batch, maximum load, unloading delays, and so on.3. The duration of construction is broadly similar over the working areas.4. The material transported between an S-D pair is handled by one crane only.MODEL DESCRIPTIONThree steps are involved in determining optimal positions for a crane group. First, a location generation model produces an approximate task group for each crane. This is then adjusted by a task assignment model. Finally, an optimization model is applied to each tower in turn to find an exact crane location for each task group.Initial Location Generation ModelLift Capacity and Feasible AreaCrane lift capacity is determined from a radius-load curve where the greater the load, the smaller the cranes operating radius. Assuming a load at supply point (S) with the weight w, its corresponding crane radius is r. A crane is therefore unable to lift a load unless it is located within a circle with radius rFig. 1(a). To deliver a load from (S) to deman