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A robotic mobile fulfillment system (RMFS) performs the order fulfillment process by bringing inventory to workers at pick-pack-and-ship warehouses. In the RMFS, robots lift and carry shelving units, called inventory pods, from storage locations to picking stations where workers pick items off the pods and put them into shipping cartons. The robots then return the pods to the storage area and transport other pods. In this article, we consider an item assignment problem in the RMFS in order to maximize the sum of similarity values of items in each pod. We especially focus on a reoptimization heuristic to address the situation where the similarity values are altered so that a good assignment solution can be obtained quickly with the changed similarity values. A constructive heuristic algorithm for the item assignment problem is developed, and then, a reoptimization heuristic is proposed based on the constructive heuristic algorithm. Then, computational results for several instances of the problem with 10–500 items are presented. We further analyze the case for which an item type can be placed into two pods. Note to Practitioners—This article proposes an efficient heuristic algorithm for assigning items to pods in a robotic mobile fulfillment system (RMFS) so that items ordered together frequently are put into the same pod. Computational results with 10–500 items show that the gaps from upper bounds are very small on average. For cases where the similarity values between items change or their estimation is not accurate due to the fluctuations in demand, a reoptimization heuristic algorithm that alters the original assignment is developed. The experimental results show that the reoptimization algorithm is robust when perturbation levels are approximately 40%–50% of the original similarity values with much less computation times. We believe that this research work can be very helpful for operating the RMFS efficiently. [ABSTRACT FROM AUTHOR]

Routing service considering uncertainty is at the core of intelligent transportation systems and has attracted increasing attention. Existing stochastic shortest path models require the exact probability distributions of travel times and usually assume that they are independent. However, the distributions are often unavailable or inaccurate due to insufficient data, and correlation of travel times over different links has been observed. This paper presents a robust shortest path (RSP) model that only requires partial distribution information of travel times, including the support set, mean, variance, and correlation matrix. We introduce a concept of robust mean-excess travel time to hedge against the risk from both the uncertainty of the random travel times and the uncertainty in their distributions. To solve the RSP problem, an equivalent dual formulation is derived and used to design tight lower and upper bound approximation methods, which adopt the scenario approach and semi-definite programming approach, respectively. To solve large problems, we further propose an efficient primal approximation method, which only needs to solve two deterministic shortest path problems and a mean-standard deviation shortest path problem, and analyze its approximation performance. Experiments validate the tightness of the proposed bounds and demonstrate the impact of uncertainty on the relative benefit and cost of robust paths. [ABSTRACT FROM PUBLISHER]