Linear sequencing for machine layouts by a modified simulated annealing

Machine sequencing is an essential step towards the physical layout of machines as it determines the relative positions of machines in a layout. Linear machine sequencing is most popular due to its efficient flow structure and its ability to arrange machines in various flow layouts. For example, in a conveyor or an AGV system, the layout can be a straight line, a U-shape line, a serpentine line, or a loop. This paper addresses the problem of determining a common linear machine sequence (also known as a linear flowline) for multi-products with different operation sequences. Each machine type has a limited number of duplicates available for use. The objective is to minimize the total flow distance travelled by the products on this linear flowline. The flows of products are allowed in the forward direction, either in-sequence or by-pass (i.e. no backtrack movements are allowed). To solve this problem, we first construct a feasible flow network that satisfies all operation sequences and then transform it into a linear machine sequence. To improve the solution, a modified simulated annealing is utilized. The new algorithm was tested on several examples in the literature.