An Exact Model for the order picker routing problem in warehouses

This paper is dealing with the order picker routing problem within a multi-block warehouse layout with several aisles. In the literature, exact algorithms only exist for small warehouses with few cross aisles (typically two or three), while for larger warehouse configurations a series of heuristic and meta-heuristic methods are available. We present a novel pre-processing algorithm for graph reduction by eliminating the extra corner vertices and aisles from the graph of warehouse locations and aisles. This allows us to solve this routing problem with a general TSP solver while significantly reducing running times. The presented method allows us to solve adequately big (more realistic) instances exactly. The algorithm is implemented and evaluated experimentally on a set of problem instances from the literature. The computational results illustrate that the proposed model outperforms existing formulations in terms of simplicity, size, and calculation time. Our mathematical model gives an optimum solution for all the instances, while the network size could be reduced by almost 73% on average

The order picking problem under a scattered storage policy

When warehouses are operated according to a scattered storage policy, each Stock Keeping Unit(SKU) is stored at multiple locations inside the warehouse. Such a configuration allows for improved picking efficiency, as now an SKU can be picked from the location that is most compatible with the other SKU’s in the picking batch. Seizing these benefits, however, comes at the cost of additional decisions to be made while planning the picking operations. Next to determining the sequence in which SKU’s will be retrieved from the warehouse, the location at which each SKU needs to be extracted has to be chosen by the planner. In this paper, we model the order picking problem under a scattered storage policy as a Generalized Travelling Salesperson Problem (GTSP). In this problem, the vertices of the underlying graph are partitioned into clusters from which exactly one vertex should be visited in each cluster. In our order picking application, each cluster contains all product locations of a single SKU on the order list. The aim is to design a pick tour that visits all product locations of the SKU’s on the pick list (i.e., visit each cluster exactly once) and minimizes the total travel distance. We present an ILP formulation of the problem and a variable neighbourhood heuristic, embedded in a guided local search framework. The performance of both methods is tested extensively by means of computational experiments on benchmark instances from the literature

An Exact Model for the order picker routing problem in warehouses

This paper is dealing with the order picker routing problem within a multi-block warehouse layout with several aisles. In the literature, exact algorithms only exist for small warehouses with few cross aisles (typically two or three), while for larger warehouse configurations a series of heuristic and meta-heuristic methods are available. We present a novel pre-processing algorithm for graph reduction by eliminating the extra corner vertices and aisles from the graph of warehouse locations and aisles. This allows us to solve this routing problem with a general TSP solver while significantly reducing running times. The presented method allows us to solve adequately big (more realistic) instances exactly. The algorithm is implemented and evaluated experimentally on a set of problem instances from the literature. The computational results illustrate that the proposed model outperforms existing formulations in terms of simplicity, size, and calculation time. Our mathematical model gives an optimum solution for all the instances, while the network size could be reduced by almost 73% on average

A Multi-objective Optimization Model for Robust Skip-Stop Scheduling with Earliness and Tardiness Penalties

Inefficient transport systems impose extra travel time for travelers, cause dissatisfaction and reduce service levels. In this study, the demand-oriented train scheduling problem is addressed using a robust skip-stop method under uncertain arrival rates during peak hours. This paper presents alternative mathematical models, including a two-stage scenario-based stochastic programming model and two robust optimization models, to minimize the total travel time of passengers and their waiting time at stations. The modeling framework accounts for the design and implementation of robust skip-stop schedules with earliness and tardiness penalties. As a case study, each of the developed models is implemented on line No. 5 of the Tehran metro, and the results are compared. To validate the skip-stop schedules, the values of the stochastic solution and the expected value of perfect information are calculated. In addition, a sensitivity analysis is conducted to test the performance of the model under different scenarios. According to the obtained results, having perfect information can reduce up to 16% of the value of the weighted objective function. The proposed skip-stop method has been shown to save about 5% in total travel time and 49% in weighted objective function, which is a summation of travel times and waiting times as against regular all-stop service. The value of stochastic solutions is about 21% of the value of the weighted objective function, which shows that the stochastic model demonstrates better performance than the deterministic model