E-commerce companies often use manual order-picking systems in their warehouses since these systems can provide the required flexibility and scalability. Manual systems have been widely studied, but the operating policies may require significant changes for e-commerce settings. First, to maintain consumers' loyalty, it is important to maintain delivery reliability even on the busiest days. When the number of order pickers in an area increases, however, more delays due to interactions may occur. For example, travel speed may need to be lowered when order pickers pass each other in narrow aisles. Second, many products sold through e-commerce are returned by consumers. Before these returned products can be sold again, they must be reintegrated in the stock. This paper presents hybrid genetic algorithms to determine routes for simultaneous pickup of products in response to consumers' orders and delivery of returned products to storage locations. Furthermore, interactions between the order pickers are considered in the routing decisions. The developed algorithms use specific warehouse problem characteristics. We identify the mix of pickups and deliveries to realise the highest savings in practice. It is shown that order-picker interactions can be a significant cause for delay and should be accounted for in the routing.

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We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms while controlling for uncertainty in the maintenance tasks and weather conditions. Since the maintenance provider is typically not the owner of a wind farm, it needs to adhere minimum service requirements that specify the required service. We consider three of such settings: 1) perform all maintenance tasks, 2) allow for a fraction of unscheduled tasks, and 3) incentivize to perform maintenance rather quickly. We provide a two-stage stochastic mixed integer programming model for the three SMFTPO settings, and solve it by means of Sample Average Approximation. In addition, we provide an overview of the, what we discovered, non-aligned modeling assumptions in the literature regarding operational decisions. By providing a series of special cases of the second-stage problem resembling the different modeling assumptions, we aim to establish a common consensus regarding the key modeling decisions to be taken in maintenance planning problems for offshore wind farms. We provide newly constructed, and publicly available, benchmark sets. We extensively compare the different SMFTPO settings and its special cases on those benchmark sets, and we show that the special case reformulations are very effective for solving the second-stage problems. In addition, we find that for particular cases, established modeling techniques result in overestimations and increased running times.

In “Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm,” Uit het Broek, Schrotenboer, Jargalsaikhan, Roodbergen, and Coelho present a generic branch-and-cut framework to solve routing problems with multiple depots on directed graphs. They present new valid inequalities that eliminate subtours, enforce tours to be linked to the same depot, and enforce bounds on the number of customers in a vehicle tour. This is embedded in a branch-and-cut scheme that also contains generalized and adapted versions of valid inequalities that are well known for related routing problems. The authors show that the new inequalities tighten root node relaxations considerably. In combination with a simple but effective upper-bound procedure, only requiring a MIP solver and a smart reduction of the problem size, the authors show that the overall framework solves instances of considerably larger size to optimality than have been reported in the literature.

We study a multi-commodity multi-period resource constrained pickup-and-delivery problem inspired by the short-term planning of maintenance services at offshore wind farms. In order to begin a maintenance service, different types of relatively scarce servicemen need to be delivered (transported) to the service locations. We develop resource-exceeding route (RER) inequalities, which are inspired by knapsack cover inequalities, in order to model the scarcity of servicemen. In addition to a traditional separation approach, we present a column-dependent constraints approach so as to include the RER inequalities in the mathematical formulation. An alternative pricing strategy is developed to correctly include the column-dependent constraints. The resulting approach is broadly applicable to any routing problem that involves a set of scarce resources. We present a branch-and-price-and-cut algorithm to compare both approaches that include RER inequalities. The branch-and-price-and-cut algorithm relies on efficiently solving a new variant of the Elementary Resource Constrained Shortest Path Problem, using a tailored pulse algorithm developed specifically to solve it. Computational experiments show that the RER inequalities significantly tighten the root node relaxations. The column-dependent constraints approach searches then the branch and bound tree more effectively and appears to be competitive with the traditional separation procedure. Both approaches are able to solve instances of up to 92 nodes over 21 periods to optimality.

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