A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

This study focuses on the problem of sequencing requests for an end-of-aisle automated storage and retrieval system in which each retrieved load must be returned to its earlier storage location after a worker has picked some products from the load. At the picking station, a buffer is maintained to absorb any fluctuations in speed between the worker and the storage/retrieval machine. We show that, under conditions, the problem of optimally sequencing the requests in this system with a buffer size of m loads forms a special case of the multiple traveling salesmen problem in which each salesman visits the same number of cities. Several interesting structural properties for the problem are mathematically shown. In addition, a branch-and-cut method and heuristics are proposed. Experimental results show that the proposed simulated annealing-based heuristic performs well in all circumstances and significantly outperforms benchmark heuristics. For instances with negligible picking times for the worker, we show that this heuristic provides solutions that are, on average, within 1.8% from the optimal value.

The Branch and Cut Method for Solving Capacitated Vehicle Routing Problem (CVRP) Model of LPG Gas Distribution Routes

Capacitated Vehicle Routing Problem (CVRP) is a problem that discusses how to choose several routes that must be passed by a number of transport vehicles in the process of distributing goods that combine customer demand with regard to transport capacity. CVRP designs an optimal delivery route where each vehicle only takes one route, each vehicle has the same characteristics, each customer has a request and there is only one depot. In this paper, two CVRP models were formulated. Formulation of the first CVRP model without regard to vehicle loads and vehicles returned to the depot. The second CVRP model formulation takes into account the vehicle load and the vehicle does not return to the depot. Determination of LPG gas distribution routes is completed using the Branch and Cut method.

Separator-Based Pruned Dynamic Programming for Steiner Tree

Steiner tree is a classical NP-hard problem that has been extensively studied both theoretically and empirically. In theory, the fastest approach for inputs with a small number of terminals uses the dynamic programming, but in practice, stateof-the-art solvers are based on the branch-and-cut method. In this paper, we present a novel separator-based pruning technique for speeding up a theoretically fast DP algorithm. Our empirical evaluation shows that our pruned DP algorithm is quite effective against real-world instances admitting small separators, scales to more than a hundred terminals, and is competitive with a branch-and-cut solver.