Spatial scheduling algorithm minimising makespan at block assembly shop in shipbuilding

Spatial scheduling pursues optimal sequencing and dynamic spatial layouts that satisfy traditional restrictions in resource capacity and due dates. In shipbuilding, block spatial scheduling can be regarded as arranging some polygonal objects within rectangular work plates in an optimal sequence. This problem is important because of its impact on shipbuilding productivity and it is a NP-hard problem due to the complex constraints. In this paper, detailed analysis and mathematical description are made on block shape and block intersection. Based on the investigations of the characteristics of block shapes, the corresponding processing techniques and typical constraints, a mathematical model for block spatial scheduling is developed. Subsequently, a block spatial scheduling greedy algorithm with the objective of minimising makespan is presented using several proposed spatial scheduling strategies. The algorithm is implemented by developing a block spatial scheduling system at a block assembly shop, through which visual scheduling results of daily block layouts and the progress charts for all blocks can be obtained. Moreover, several main spatial scheduling performance indicators are proposed for comparing the proposed greedy algorithm with the existing grid algorithm and manual methods. A case study is made with real data from a shipyard, and the result shows that better performance and higher efficiency can be achieved in a short computational time.