Integrated zone picking and vehicle routing operations with restricted intermediate storage

The competitiveness of a retailer is highly dependent on an efficient distribution system. This is especially true for the supply of stores from distribution centers. Stores ask for high flexibility when it comes to their supply. This means that fast order processing is essential. Order processing affects different subsystems at the distribution center: orders are picked in multiple picking zones, transferred to intermediate storage, and delivered via dedicated tours. These processing steps are highly interdependent. The schedule for picking needs to be synchronized with the routing decisions to ensure availability of orders at the DC’s loading docks when their associated tours are scheduled. Concurrently, intermediate storage represents a bottleneck as capacity for order storage is limited. The simultaneous planning of picking and routing operations with restricted intermediate storage is therefore relevant for retail practice but has not so far been considered within an integrated planning approach. Our work addresses this task and discusses an integrated zone picking and vehicle routing problem with restricted intermediate storage. We present a comprehensive model formulation and introduce a general variable neighborhood search for simultaneous consideration of the given planning stages. We also present two alternative sequential approaches that are motivated by the prevailing planning situation in industry. Numerical experiments and a case study show the need for an integrated planning approach to obtain practicable results. Further, we identify the impact of the main problem characteristics on overall planning and provide valuable insights for the application of these findings in industry.

Minimizing setups and waste when printing labels of consumer goods

A real-world planning problem of a printing company is presented where different sorts of a consumer goods’ label are printed on a roll of paper with sufficient length. The printer utilizes a printing plate to always print several labels of same size and shape (but possibly different imprint) in parallel on adjacent lanes of the paper. It can be decided which sort is printed on which (lane of a) plate and how long the printer runs using a single plate. A sort can be assigned to several lanes of the same plate, but not to several plates. Designing a plate and installing it on the printer incurs fixed setup costs. If more labels are produced than actually needed, each surplus label is assumed to be “scrap”. Since demand for the different sorts may be heterogeneous and since the number of sorts is usually much higher than the number of lanes, the problem is to build “printing blocks”, i.e., to decide how many and which plates to design and how long to run the printer with a certain plate so that customer demand is satisfied with minimum costs for setups and scrap. This industrial application is modeled as an extension of a so-called job splitting problem which is solved exactly and by various decomposition heuristics, partly basing on dynamic programming. Numerical tests compare both approaches with further straightforward heuristics and demonstrate the benefits of decomposition and dynamic programming for large problem instances.

Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

The concept of partially renewable resources provides a general modeling framework that can be used for a wide range of different real-life applications. In this paper, we consider a resource-constrained project duration problem with partially renewable resources, where the temporal constraints between the activities are given by minimum and maximum time lags. We present a new branch-and-bound algorithm for this problem, which is based on a stepwise decomposition of the possible resource consumptions by the activities of the project. It is shown that the new approach results in a polynomially bounded depth of the enumeration tree, which is obtained by kind of a binary search. In a comprehensive experimental performance analysis, we compare our exact solution procedure with all branch-and-bound algorithms and state-of-the-art heuristics from the literature on different benchmark sets. The results of the performance study reveal that our branch-and-bound algorithm clearly outperforms all exact solution procedures. Furthermore, it is shown that our new approach dominates the state-of-the-art heuristics on well known benchmark instances.

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

This paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches

In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called potential-driven network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones (“looping”). The paper introduces a new mixed-integer nonlinear programming model and a new nonlinear programming model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations to practitioners about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models with respect to computational time, the number of solutions found, the number of instances solved and cost savings. Moreover, the paper extends the models for optimizing over multiple demand scenarios and is the first to include the practically relevant option that a particular pipeline may be looped several times.

An ALNS algorithm for the static dial-a-ride problem with ride and waiting time minimization

The paper investigates the static dial-a-ride problem with ride and waiting time minimization. This is a new problem setting of significant practical relevance because several ride-sharing providers launched in recent years in large European cities. In contrast to the standard dial-a-ride problem, these providers focus on the general public. Therefore, they are amongst others in competition with taxis and private cars, which makes a more customer-oriented objective necessary. We present an adaptive large neighbourhood search (ALNS) as well as a dynamic programming algorithm (DP), which are tested in comprehensive computational studies. Although the DP can only be used for a single tour and, due to the computational effort, as a restricted version or for small instances, the ALNS also works efficiently for larger instances. The results indicate that ride-sharing proposals may help to solve the trade-off between individual transport, profitability of the provider, and reduction of traffic and pollution.