We focus on a logistics service provider (LSP) that organizes the inbound logistics for an original equipment manufacturer (OEM) using just-in-time production. The LSP conducts periodic milk runs, that is, tours visiting a subset of suppliers on a fixed route to collect shipments bound for the OEM. Although the milk-run routes and rough schedules are fixed well in advance, the exact shipment due dates at the OEM become known only once the production sequence has been finalized. During daily operation, the given milk runs are executed such that shipments are picked up from the suppliers and delivered to the OEM ideally exactly just in time. However, the production sequence on the assembly lines at the OEM often changes on the day of execution, which alters shipment due dates at the OEM and makes it necessary to anticipate potential disturbances when assigning shipments to milk runs. We formulate a two-stage stochastic program, where, in the first stage, shipments are assigned to specific milk runs and, in the second stage, when alterations to the production sequence are revealed, arrival times are adjusted and shipments are express delivered if necessary. The assignment induces earliness-tardiness costs depending on the uncertain due date of each shipment at the OEM, and express deliveries induce fixed costs. Besides an extensive-form mixed-integer linear program, we develop a solution procedure based on the integer L-shaped method, enriched with valid inequalities and cuts derived from partial Benders decomposition and a subproblem relaxation. In a computational study on realistic test data, we show that the proposed L-shaped method solves 62 out of 70 instances to optimality. From a managerial perspective, we show that express deliveries are an effective way of mitigating uncertainty in the production sequence, as are overlapping milk-run routes, which are not yet widely used in practice but are relatively easy to implement.

This paper deals with a general open-shop scheduling problem where jobs have release and due dates, transferring between machines incurs a machine–pair-dependent delay, and any regular objective defined over job completion times is minimized. Such problems are widely encountered in practice, e.g., in industrial testing and maintenance processes and just-in-time logistics. Despite its relevance, exact solution methods from the literature have so far focused on the makespan objective or very specific special cases. We hence present the first exact method for the general open-shop scheduling problem with any regular minsum objective with respect to job completion times. Moreover, we demonstrate how branch-cut-and-price methods can be applied to the open shop. Finally, we also adapt the famous subset-row inequalities, originally proposed for the vehicle routing problem, to the open shop. Our computational study on both newly generated instances as well as those from the literature demonstrates good performance on a broad set of different objective functions, finding tight bounds even for the largest problems.

Furniture retailers increasingly engage in the circular economy because many old furniture pieces are suitable for recycling or even reuse, while customers greatly appreciate collection services, reducing friction when purchasing new items. However, this poses particular challenges from a logistics perspective. First, customers often replace old furniture with new; hence, sales can be increased by offering collection services along with delivery. Second, because of the bulky nature of the merchandise, careful planning of deliveries and pickups is necessary because the vehicle capacity is easily exceeded. In this context, we present a novel multi-depot simultaneous pickup and delivery problem with time windows that considers selective pickups and seeks to minimize the lost rewards from failed pickups. We adopt a state-of-the-art routing solver from the literature for this problem to design both a heuristic that integrates route and collection planning and a decomposition heuristic that routes first and plans pickups second. In a computational study on instances from the literature and based on realistic data, we show that strictly minimizing tour length, as is common practice, can lead to a substantial amount of missed pickups. Moreover, we investigate the effects of time window management and fleet composition on reverse logistics efficiency. Finally, we discuss the environmental trade-off inherent in, on the one hand, collecting recyclable furniture and, on the other hand, increased transportation effort.

Shop-floor space in urban areas is scarce and expensive. To avoid a time-consuming zigzag movement when replenishing densely arranged shelves, store-specific shipment buildups (SSSBs) mirror the store layout in the packing pattern of the carriers (e.g., roll cages) on which merchandise arrives in brick-and-mortar sales outlets. If a carrier is pre-sorted according to the layout of its designated store, then the sales personnel can follow a clear route through the store while replenishing the shelves. However, the time savings in the stores come at the price of additional effort in the retail warehouses having to assemble SSSBs. If picker-to-parts order picking is applied to assemble SSSBs, then it is the order pickers who must zigzag through the warehouse. In this paper, we develop and test the performance of novel storage location assignment (SLA) policies that consider order frequencies and store layouts when deciding on the storage positions of stock keeping units on the shelves of a picker-to-parts warehouse. We evaluate these novel policies both with the theoretical optimum if perfect information were available and with traditional SLA policies merely based on order frequencies. These computational tests show that our novel policies can greatly reduce the picking effort during the assembly of SSSBs in picker-to-parts warehouses.

Order picking, a widely studied process in warehousing, is experiencing a growing implementation of automation. Among all the market-ready technologies, autonomous mobile robots (AMRs) have been receiving attention from both academics and practitioners lately. By utilizing AMRs, human pickers are relieved of the task of transporting items, typically performed using picking carts, giving rise to the term Assisted Order Picking Systems (AOPSs). However, the resulting changes in human work processes and the associated potential injury risks for humans working in these systems have largely been unaddressed so far. Caution is required due to the increased frequency of picking actions in AOPSs, which have been shown to be closely associated with potential musculoskeletal disorders. To address this research gap, we model the human work process in AOPSs, emphasizing task allocation within a homogenous human team and routing based on the multiple traveling salesman problem. Additionally, we consider human fatigue and develop a task allocation method that synchronizes human duty cycles within the wave picking strategy. Initial results from illustrative experiments demonstrate the impact of fatigue on the order picking make span, albeit with the limitation of a simplified human-robot collaboration mechanism. Further issues related to model extensions and heuristic design are discussed in this paper and will be explored in future studies. (c) Copyright 2025 The Authors.

The use of mobile robots, particularly the Robotic Mobile Fulfilment System (RMFS), has increased in retail logistics. Especially in e-commerce, which is characterized by high demand fluctuations and diverse product ranges, RMFSs offer advantages. The existing literature suggests that the overall optimization of an RMFS is often challenging due to the system’s complexity and the unknown relationships involved. Therefore, this study extends the previous literature on RMFSs by analysing how the complex interactions between parameters affect the system’s performance. A Design of Experiment framework is used to determine the implicit effects on seven performance indicators. In combination with a sensitivity analysis consisting of various statistical analyses as part of predictive analytics, we confirm previous expectations and statistically demonstrate several heretofore unknown parameter interactions. These consist of two-way interactions of three parameters: The dispersion of stock keeping units (SKUs), average order size, and incoming orders per time interval. Our main contribution lies in identifying key efficiency factors for RMFS’s layouts, particularly highlighting the importance of station arrangement and the significant impact of SKU dispersion on system performance and resource utilization. Furthermore, our comparison of different layouts shows that those with fewer stations can optimize order picker utilization and achieve higher efficiency with fewer resources. Our findings confirm that SKU dispersion is the most influential factor affecting RMFS’s performance. We conclude that RMFS can be effectively applied to various scenarios by following our recommendations on SKU dispersion and layout design.

Drones have received growing attention in logistics recently. One possible application is deploying drones for auditing inventory in warehouses. With the use of drones, warehouses are able to increase inventory record accuracy and decrease labor costs. In this research, we introduce the stocktaking drone routing problem (STDRP), which consists of routing a fleet of drones through a warehouse for stocktaking purposes as well as deciding on the location of charging stations on the warehouse floor, which is necessary due to the limited battery capacity of the drones. Subsequently, we develop an adaptive large neighbourhood search-based heuristic (ALNS) with novel solution encoding and decoding approaches to solve the STDRP. In a numerical study, we show that ALNS can solve realistic instances in reasonable time. We also derive recommendations regarding the ideal size of the drone fleet, the charging infrastructure, and battery capacity. Finally, we investigate the interplay between the storage assignment policy (such as the popular ABC rule) and stocktaking efficiency using drones.

The surge of e-commerce has revolutionized distribution channels, escalating from simple single-channel frameworks to complex multi-channel and omni-channel networks. In particular developments in information technology and rising customer expectations have popularized the transition from multi- to omni-channel distribution, where the classic brick-and-mortar stores can also be part of the omni-channel distribution strategy. This evolution poses intricate challenges for manufacturers, especially in the integration and optimization of these channels. Thus, there is a strong need for an in-depth analysis of how manufacturers navigate the transition across diverse distribution channels to meet the varying needs of different customer segments. To this end, we investigate single-, multi-, and omni-channel distribution strategies for the case of a manufacturer selling both standard and customized products to different customer segments with varying preferences. A central contribution of this research is the creation of an integrated optimization model that resolves a location-routing problem, designing a complex and realistic supply chain configuration suitable for an omni-channel distribution system. This model strategically serves to fragmented customer demands through multiple shopping and delivery options. The outcomes of our study indicate that an omni-channel distribution system is a viable approach, capable of serving more customer segments while simultaneously minimizing logistics costs. In addition, we offer a detailed analysis of the cost implications of in-store pickup versus home-delivery options, providing a comprehensive evaluation of their respective impacts on total logistics costs and customer responsiveness.

This paper addresses the operational planning problem of assigning orders and pods (i.e., mobile shelves) to picking stations in a multi-level robotic mobile fulfillment system (RMFS), which deals with two issues: deciding on which picking station handles which order, and from which pods to pick the ordered items, considering the limited storage capacity of the pods. Due to the relatively poor space utilization of single-level RMFS warehouses, such systems are often spread over multiple floors in practice. Therefore, we explicitly consider multi-level warehouse layouts with isolated levels (or zones) where a pod can only be brought to a station if both of them are on the same level. We optimize the problem with regard to a multi-criteria objective function that consists of three workload-oriented objectives: we aim to balance the total workload among all pickers, minimize the total order-consolidation effort for the packers, and the pod movement effort for the mobile robots. After formalizing the planning problem as a multi-objective optimization problem, we provide two mixed-integer linear programming models. Additionally, we propose a matheuristic that reduces the model size to the desired granularity so that realistically sized problem instances can be solved within less than four minutes of computation time. Moreover, we derive some managerial insights, such as the impact of the number of warehouse levels and picking waves on the objective values. We find evidence that running the RMFS warehouse in a multi-level facility can substantially compromise the consolidation effort at packing stations since it leads to a higher number of split orders. Furthermore, splitting the planning horizon into multiple short waves can lead to a higher number of pod-to-station assignments and, thus, to a raised pod-movement workload for mobile robots.

We consider a routing problem where orders are transported just-in-time from several suppliers to an original equipment manufacturer (OEM). This implies that shipments cannot be picked up before their release date when they are ready at the supplier and should be delivered as close as possible to their due date to the OEM. Every shipment may have a distinct due date but all shipments loaded onto the same truck arrive at the same time. The performance of the transportation network is optimized by finding an allocation of shipments to trucks and routes for each truck that minimizes the total earliness-tardiness cost. These penalties are caused by deviations between the truck arrival times at the OEM and the due dates of the loaded shipments. To solve the problem, we introduce a metaheuristic approach based on large neighborhood search, which we combine with an efficient local search scheme that allows the eval-uation of neighborhood solutions in worst-case logarithmic time despite the nonlinear objective function. Our algorithm can find high-quality solutions to large instances with 200 shipments in less than 12 min-utes of CPU time. From a practical perspective, our computational tests indicate that a too small truck fleet or very limited time differences between release and due date can dramatically affect the punctual-ity of the deliveries.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Electric vehicle scheduling is concerned with assigning a fleet of electrically powered vehicles to a set of timetabled trips. Since the range of these vehicles is limited, charging breaks need to be scheduled in-between trips, which require detours and time. This paper presents a novel electric vehicle scheduling problem with multiple charging stations in an in-plant logistics setting with the objective of minimizing the required fleet size. Contrary to previous works, we consider constant, linear and non-linear battery charging functions, which, among other things, allows to model realistic non-linear lithium-ion battery charging. We present an integer programming model and an exact branch-and-check solution procedure, which is based on decomposing the problem into a master and a subproblem. The former is concerned with assigning vehicles to trips while relaxing the battery constraints. The latter schedules charging breaks and checks if the master problem's solution is feasible with regard to the non-relaxed battery constraints. Our computational tests show that solving the IP model with a standard solver (CPLEX) is inferior to the branch-and-check approach, which generally performs well even for practically relevant instance sizes. Furthermore, we derive some insights into the influence of the charging mode and max-imum battery capacity on the required fleet size. Lastly, we investigate the effects of the number of warehouses (with respective charging stations).(c) 2022 The Authors. Published by Elsevier B.V.

We address the operational planning problem of loading and scheduling outbound trucks at a dispatch warehouse shipping goods to several customers. This entails, first, assigning shipments to outbound trucks given the trailers' capacities and, second, scheduling the trucks' processing at the dock doors such that the amount of required resources at the terminal (e.g., dock doors and logistics workers) does not exceed the available levels. The trucks should be scheduled as late as possible within their time windows, but no later than the deadlines of the loaded shipments. Such planning problems arise, e.g., at dispatch warehouses of automotive parts manufacturers supplying parts to original equipment manufacturers in a just-in-time or even just-in-sequence manner. We formalize this operational problem and provide a time-indexed mixed-integer linear programming model. Moreover, we develop an exact branch-and-price algorithm, which is shown to perform very well, solving most realistically sized problem instances to optimality within a few minutes. In a numerical study, we also look into the interplay between the time window policy for trucks and just-in-time deliveries. Finally, we find evidence that too small a workforce or too few outbound dock doors in the dispatch warehouse can substantially compromise the punctuality of the deliveries.

We consider the problem of scheduling a set of direct deliveries between a depot and multiple customers using a given heterogeneous truck fleet. The trips have time windows and weights, and they should be completed as soon after release as possible (minimization of maximum weighted flow time). Moreover, some trips can optionally be combined in predefined milk runs (i.e., round trip tours), which need not be linear combinations of the constituent direct trips, accounting, e.g., for consolidation effects because the loading dock needs to be approached only once. This problem has applications, e.g., in just-in-time, humanitarian, and military logistics. We adapt a mixed-integer programming model from the literature to this problem and show that deciding feasibility is NP-complete in the strong sense on three levels: assigning trips to trucks, selecting milk runs, and scheduling trips on each individual truck. We also show that, despite this complexity, a state-of-the-art constraint programming solver and a problem-specific approach based on logic-based Benders decomposition can solve even large instances with up to 175 trips in many cases, while the mixed-integer programming model is essentially unsolvable using commercial optimization software. We also investigate the robustness of the maximum flow time objective in the face of unforeseen delays as well as the influence of milk runs.

Seeing the huge success of sharing platforms such as Uber, Lyft, and Airbnb, where owners of under-used assets are connected with users willing to pay for the use of these assets, it is not surprising that retailers aim to transfer the basic idea of the sharing economy to their last-mile deliveries. In crowdshipping, the under-used assets are transport capacities of private drivers and the users are the retailers aiming for additional and cost-efficient delivery capacities for their home deliveries. A major drawback of crowd shipping is that retailers can hardly guarantee their promised delivery services when subcontracting individuals. To avoid this problem, different retailers are establishing crowdshipping platforms offering a reward to the employees of their distribution centers for crowdshipping online orders on their way back from work. We investigate the resulting optimization problem for matching crowdshipping supply and demand in this context. We present an efficient exact solution procedure based on Benders decomposition, which maximizes the number of matched shipments while considering the employees' minimum expected earnings per time unit. This procedure is shown to solve instances of real-world size before a work shift is over and the shipments have to be loaded into the trunks of the employees' cars. Furthermore, we show the impact of crowdshipping on all main stakeholders and identify critical success factors. (c) 2021 Elsevier B.V. All rights reserved.

To relieve human order pickers from unproductive walking through a warehouse, parts-to-picker systems deliver demanded stock keeping units (SKUs) toward picking workstations. In a wide-spread parts-to-picker setup, a crane-operated automated storage and retrieval system (ASRS) delivers bins with demanded SKUs toward an end-of-aisle picking workstation and returns them back into the rack once the picks are completed. We consider the scheduling of the crane that operates subsequent dual commands. Each dual command combines a retrieval request for another SKU bin demanded at the picking workstation with a storage request, where a bin that has already been processed and passed through the bin buffer is returned to its dedicated storage position in the ASRS. This system setup in general and the resulting crane scheduling problem in particular have been an active field of research for more than 30 years. We add the following contributions to this stream of research: We finally prove that the crane scheduling problem is strongly NP-hard. Furthermore, we show that, although only a single vehicle (namely, the crane) is applied, the problem is equivalent to the traditional vehicle routing problem (VRP). This opens the rich arsenal of very efficient VRP solvers, which substantially outperform existing tailor-made algorithms from the literature.

The uploaded ".zip"-file contains 6 folders corresponding to the 6 experiments in our working paper "Multi-shuttle crane scheduling in automated storage and retrieval systems". Each of these folders contains a "results.csv" file with the data from the experiments. All but the last two columns contain information about the solved instance, the second to last column contains the objective value and the last column the runtime. Then each folder contains ".txt"-files or several folders with ".txt"-files. Each files contains one instance. Each instance begins with the name of the file in which it is located. Then follows an empty line, a line with the word "VEHICLE" and a new line "NUMBER OF CAPACITY EMPTYING REQUIREMENTS HIGHEST SPEED LONGEST DISTANCE MAXIMUM DISTANCE". It follows a line containing the following integers: the number of vehicles, the capacity of all vehicles, the number of empty slots, the total number of requests, the speed in x dimension, the speed in y dimension, and an upper limit for the maximum distance between the I/O point and each slot. Next follows a line with the text "CUSTOMER" and then a line with the text "CUSTOMER NUMBER". XCOORD. YCOORD." This is followed by lines each containing a relevant slot. Each entry begins with a number that counts the entries, followed by the x-coordinate and then the y-coordinate. The first entry has the number 0 and is the I/O point. Then the customer locations follow, and then we start the restart the numbering at 1 for the following requests.

Truck scheduling, which assigns a dock-door and a processing interval to each inbound and outbound truck, is an essential operational decision problem in cross-docking platforms and distribution centers. It has attracted considerable academic attention. Most studies, however, have neglected internal resources (e.g., workers or material handling equipment) and hence failed to address two major concerns of cross docking practitioners: (i) determining the number of resources needed, and (ii) scheduling the internal resources in an efficient way. This study sets out to examine the value of utilizing the internal resource requirements as the main performance metrics in truck scheduling. The problem considered in this paper is how to schedule a set of inbound trucks with time windows at a multidoor cross-docking platform, where the departure times of outbound trucks follow a given schedule. The goal is to identify a feasible truck schedule that can be executed with a minimum number of internal resources. For this setting, a mixed-integer programming model is proposed. Furthermore, a column generation-based solution procedure is developed. We show that by using the internal resource requirements as the main performance measure, the operational efficiency of the cross-docking platform can be significantly increased. It also helps to avoid large peak workloads and leads to level truck schedules with superior resource utilization levels. Computational experiments show that the proposed heuristic algorithm can obtain high-quality solutions for very large problem instances within a short computation time. Due to its tight lower bound, the solution procedure can even prove optimality for most problem instances. (c) 2021 Elsevier Ltd. All rights reserved.

Faced with high return rates, many e-commerce retailers are considering novel technical solutions to expedite the processing of returned items in their warehouses. One such solution consists of lane-guided transport (LGT) vehicles. These small, electric vehicles follow optical markers on the floor, picking up boxes of returned items at a depot and dropping them offat workstations, releasing the logistics workers to focus on the productive task of actually processing the items instead of carrying them through the warehouse. These types of systems are simple to set up from a technical perspective; however, the routes on the warehouse floor still need to be carefully planned. This gives rise to the following routing problem. Given a set of stations to be served from multiple depots by a fleet of LGT vehicles, which stations doing what type of work should be visited on what route? Only one route per depot is allowed, but multiple vehicles may use the same route. Moreover, since routes cannot be changed on short notice, we consider an infinite planning horizon where the demand rate of the stations depends on the type of work they are assigned to do (e.g., handling defective items or refurbishing). We develop a decomposition heuristic, which solves instances derived from industry data to near-optimality in less than a minute. We also show that the depot location is rather unimportant for the overall system performance, but that the depot count can have a significant influence. (C) 2020 Elsevier B.V. All rights reserved.

Service network design is an important optimization problem for intermodal freight transportation on a tactical level. It includes the decisions on choosing transportation modes and paths for commodities throughout the intermodal network. We present a stochastic service network design model with an integrated vehicle routing problem (SSND-VRP), which simultaneously covers transportation service choice and tour planning decisions for road transportation under consideration of uncertain transportation times. A sample average approximation approach is combined with an iterated local search in order to solve problem instances in a real-world case study for three intermodal road-rail networks in Central Europe. Results of the SSND-VRP are compared with its expected value model and a successive planning approach, demonstrating the possible cost reductions and the decrease in missed intermodal services that are achieved by the integrated stochastic model. In further parameter variation experiments we show that the attractiveness of rail transportation is highly sensitive to changes in intermodal costs, whereas the impact of delay reductions of the railway services is relatively low.