In this paper, we describe and compare serial, parallel, and distributed solver implementations for large batches of Traveling Salesman Problems using the Lin-Kernighan Heuristic (LKH) and the Concorde exact TSP Solver. Parallel and distributed solver implementations are useful when many medium to large size TSP instances must be solved simultaneously. These implementations are found to be straightforward and highly efficient compared to serial implementations. Our results indicate that parallel computing using hyper-threading for solving 150- and 200-city TSPs can increase the overall utilization of computer resources up to 25 percent compared to single thread computing. The resulting speed-up/physical core ratios are as much as ten times better than a parallel and concurrent version of the LKH heuristic using SPC3 in the literature. We illustrate our approach with an application in the design of order picking warehouses.
The problem of improving the environmental performance of a supply chain without entailing excessive cost is becoming a frequent problem as
companies face an increasing pressure from governments and customers for reducing the environmental impact of their activities. As the environmental improvement of an operating supply chain implies not only technology upgrading decisions, but also decisions regarding the structure of the supply chain itself; deciding on what strategy to follow is a complex task. The aim of this work is to provide a bi- objective solution approach for finding such strategy so that both the environmental and financial goals are best met.
We introduce the visibility graph as a new way to estimate the length of a route traveled by order pickers in a warehouse. Heretofore it has been assumed that workers travel along a network of travel paths corresponding to centers of aisles, including along the right angles formed where picking aisles join cross aisles. A visibility graph forms travel paths that correspond to more direct and, we believe, more realistic \travel by sight.” We compare distance estimations of the visibility graph and the aisle-centers method for traditional and fishbone warehouse layouts. Our results suggest that the aisle-centers method overestimates the length of a picking tour by 10-20%, depending on the number of lines picked and the size of the warehouse. The visibility graph method also has implications for warehouse design: in an experiment comparing three traditional layouts, the distance model using a visibility graph chose a different layout in 12.5% of the cases.
Non-traditional layouts decrease the average travel distance for unit-load operations compared to traditional warehouse (i.e, straight rows with pick aisles and perpendicular cross aisles that reduce the travel distance between pick locations). Gue and Meller (2009) propose the fishbone layout that decreases average travel distance up to 20%. Ozturkoglu et. al. (2012) relax the assumption of Gue and Meller (2009) so that the pick aisles can take any angle, and achieve up to 22% improvement over traditional layout. Moreover, they prove that these designs are optimal for unit-load operations. However, the optimal warehouse designs for order picking operations are unknown. Here we describe an approach that optimizes layouts with up to 4% improvement over traditional layouts. For small pick list sizes, because of the higher importance of depot location in travel cost, near optimal layouts are creating a vertical cross aisles. As the pick list size increases these cross aisles become horizontal allowing better access between storage locations. We anticipate our approach to be a starting point for more detailed research for warehouse layout optimization. For example, analytical models can be created for the near-optimal layouts we present. Furthermore, layout optimization is a major target for retail industry, and a well-defined encoding and routing approach will be relevant for such optimizations.