A robust optimization approach to address correlation uncertainty in stock keeping unit assignment in warehouses

A real life order picking system consisting of a set of unidirectional picking lines is inves- tigated. Batches of stock keeping units (SKUs) are processed in waves dened as a set of SKUs and their corresponding store requirements. Each wave is processed independently on one of the parallel picking lines as pickers walk in a clockwise direction picking stock. Once all the orders for a wave are completed a new mutually exclusive set of SKUs are brought to the picking line for a new wave. SKUs which dier only in size classication, for example small, medium and large shirts, are grouped together into distributions (DBNs) and must be picked in the same wave. The assignment of DBNs to available picking lines for a single day of picking is considered in this paper. Dierent assignments of DBNs to picking lines are evaluated using three measures, namely total walking distance, the number of resulting small cartons and work balance. Several approaches to assign DBNs to picking lines have been in- vestigated in literature. All of these approaches seek to minimise walking distance only and include mathematical formulations and greedy heuristics. Four dierent correlation measure are introduced in this paper to reduce the number of small cartons produced and reduce walking distance simultaneously. These correlation measures are used in a greedy insertion algorithm. The correlation measures were compared to historical assignments as well as a greedy approach which is known to address walking distances eectively. Using correlation measures to assign DBNs to picking lines reduces the total walking distance of pickers by 20% compared to the historical assignments. This is similar to the greedy approach which only considers walking distance as an objective, however, using correlations reduced the number of small cartons produced by the greedy approach. Key words : SKU assignment, order picking, assignment problems, combinatorial optimisation.

The worst-case performance of the Cube per Order Index slotting strategy is infinitely bad – A technical note

Trolley line picking is a special warehousing system particularly suited to fulfill high-volume demands for heavy stock keeping units (SKUs). In such a system, unit loads of SKUs are positioned along a given path passed by automated trolleys, i.e., carriers hanging from a monorail or automated guided vehicles. Once a trolley reaches a requested SKU, it automatically stops and announces the requested items on a display. This is the signal for an accompanying human picker to put the demanded items onto the trolley. In this way, picking continues until, at the end of the path, the current picking order is complete and the trolley moves onward to the shipping area. Meanwhile, the picker rushes back to meet the subsequent trolley associated with the next picking order. The picking performance of the trolley line system is mainly influenced by the picker’s unproductive walking from SKU to SKU during order processing and back to the next trolley when switching to the next order. In this paper, we investigate how the storage assignment of SKUs along the path and the order sequence influence picking performance. Specifically, we explore the positive effect of duplicating SKUs and storing them at multiple positions along the path. We formulate the interdependent storage assignment and order sequencing problems and introduce a decomposition heuristic. Our computational study investigates the solution performance of this procedure and shows that SKU duplication can considerably improve picking performance.

The Backboard Wiring Problem: A Placement Algorithm

This paper studies multiple-deep automated vehicle storage and retrieval systems (AVS/RSs) known for their high throughput performance and flexibility. Compared to a single-deep system, multiple-deep AVS/RS has a better space area utilisation. However, a relocation cycle occurs, reducing the throughput performance whenever another stock keeping unit (SKU) blocks a retrieving SKU. The SKU retrieval sequence is undetermined, meaning that the arrangement is unknown, and all SKUs have an equal probability of retrieval. In addition to the shuttle carrier, a satellite vehicle is attached to the shuttle carrier and is used to access storage locations in multiple depths. A discrete event simulation of multiple-deep AVS/RS with a tier captive shuttle carrier was developed. We focused on the dual-command cycle time assessment of nine different storage and relocation assignment strategy combinations in the simulation model. The results of a simulation study for (i) random, (ii) depth-first and (iii) nearest neighbour storage and relocation assignment strategy combinations are examined and benchmarked for five different AVS/RS case study configurations with the same number of storage locations. The results display that the fivefold- and sixfold-deep AVS/RSs outperform systems with fewer depths by utilising depth-first storage and nearest neighbour relocation assignment strategies.

The Quadratic Assignment Problem (QAP) and its corollary Quadratic Bottleneck Assignment Problem (QBAP) are reputed for being non-deterministic polynomial-time hard (NP-hard) problems. In aviation, they have been used to assign aircraft to gates. This paper, based on the case of Seattle/Tacoma International airport, proposes to illustrate how the QAP and QBAP models can be used to help measure the impact of runway reassignment decisions in terms of tarmac times. This study identifies the global optimal solution for the QAP as a Mixed Integer Linear Programming and the local optimal solution for the QBAP as a Mixed Integer Non-Linear Programming.

The commodity storage assignment problem (CSAP), which assigns stock-keeping units (SKUs) to a suitable location for matching the customer demand patterns, is crucial for improving the order picking efficiency. In this study, we jointly consider the SKUs classification and correlation, and propose a new scattered storage policy named scattered-correlation storage policy based on the commodity classification (SCSPCC) for mitigating CSAP in the robotic mobile fulfillment systems (RMFS). We call the new problem CSAP-SCSPCC. To address this problem, we construct a mixed-integer programming model, and propose a novel variable neighborhood search with self-adaption and simulated annealing acceptance mechanisms (SA-VNSSA). Besides, a heuristic algorithm is proposed to select the minimum number of shelves to evaluate the optimization effect of SA-VNSSA and SCSPCC in terms of the number of shelf transports. Extensive numerical experiments are conducted on small-, medium-, and large-scale instances, respectively. The results reveal that the proposed model and algorithms are reasonable and effective in solving CSAP-SCSPCC compared with the state-of-the-art methods. Specifically, SA-VNSSA outperforms the three state-of-the-art comparison algorithms [i.e., SA-1 (Muppani and Adil, 2008), SA-Pop (Assadi and Bagheri, 2016), and SA-2 (Zhang et al., 2019)] by more than 4.19% and 3.23% on average in medium- and larger-scale instances, respectively. The comparisons between SCSPCC and CDSAP (Mirzaei et al., 2021) and DCP (Zhang et al., 2019) show that the order picking efficiency is improved by our SCSPCC more than 6.31%. It is can be concluded that SCSPCC is efficient and robust to match the SKU storage pattern and customer demand patterns in e-commerce retail. Note to Practitioners—Robotic mobile fulfillment systems (RMFS) have been widely used in the warehouses of Amazon, Jingdong, Cainiao, and so on. Considering practical situations and requirements in commodity storage assignment problems (CSAP) is necessary for improving RMFS order picking efficiency. We proposed a new problem named CSAP-SCSPCC for RMFS. Particularly, SCSPCC is a novel scattered storage policy that can assign best-selling SKUs and general-selling SKUs to a suitable location based on the SKU correlation, respectively. Computational results with small-, medium-, and large-scale instances show that our proposed SA-VNSSA and SCSPCC are effective, robust, and practically applicable compared with two state-of-the-art approaches [i.e., CDSAP (Mirzaei et al., 2021) and DCP (Zhang et al., 2019)]. Compared with CDSAP (Mirzaei et al., 2021) and DCP (Zhang et al., 2019), SCSPCC can improve order picking efficiency by more than 6.31%. In summary, the methods proposed in our work can match the SKU storage mode and the customer demand patterns in a giant e-commerce retail warehouse. This research work can contribute to the improvement of RMFS picking efficiency. In the future, it is necessary to study multiple problems in RMFS jointly, including CSAP-SCSPCC, shelves storage assignment problems, and order batching, etc.

Most large distribution centers’ order picking processes are highly labor-intensive. Increasing the efficiency of order picking allows these facilities to move higher volumes of products. The application of data mining in distribution centers has the capability of generating efficiency improvements, mainly if these techniques are used to analyze the large amount of data generated by orders received by distribution centers and determine correlations in ordering patterns. This paper proposes a heuristic method to optimize the order picking distance based on frequent itemset grouping and nonuniform product weights. The proposed heuristic uses association rule mining (ARM) to create families of products based on the similarities between the stock keeping units (SKUs). SKUs with higher similarities are located near the rest of the members of the family. This heuristic is applied to a numerical case using data obtained from a real distribution center in the food retail industry. The experiment results show that data mining-driven developed layouts can reduce the traveling distance required to pick orders.

This paper considers heuristic approaches that can be used to assign stock keeping units (SKU) to individual slots in distribution center. Firstly, we propose two novel strategies, slot selection and frequent itemset grouping. The former is used to find the most suitable slot for a single SKU, while the latter is for sequencing SKUs in an appropriate order. Secondly, we develop several storage location assignment heuristics by applying the two strategies. Especially, the heuristics are designed to assign frequently ordered SKU to a slot close to I/O (input/output) point and SKUs frequently ordered together to slots close to each other. Consequently, the proposed heuristics are helpful to reduce the travel distance of order picker in distribution center. In this paper, travel distance of order picker is calculated based on a routing policy that enables order picker to move along a flexible route. For illustration, we applied the heuristics to real data collected from a large distribution center. The experiment results reveal that slot selection strategy is very helpful to reduce average travel distance of order picker, especially under greedy routing policy. Also, frequent itemset grouping strategy can provide additional reduction in average travel distance if it is applied together with slot selection strategy.

Warehouse operations typically aggregate identical stock keeping units (SKU) into the same storage bin for easier bookkeeping and organizing of goods. With the emergence of automatic identification and tracking technologies like RFID, free-form storage of goods becomes a viable alternative. We consider the strategy of storing identical copies of an SKU in a fragmented manner and evaluate the operational characteristics that benefit from fragmented storage. Fragmented storage of identical SKUs creates a greater number of feasible picklist opportunities - with greater choice, greater optimization follows. We present an abstract warehouse model to evaluate the location assignment problem in warehouse systems. Specifically, we investigate picking operations that retrieve multiple items during a warehouse pass. We provide an analytical result for operations using a 'hybrid-cost' cost metric, and a brute force analysis for operations using the more common 'maximum-cost' picking metric. We show that fragmentation is more favorable when the number of copies picked for each SKU is small.

The quadratic three-dimensional assignment problem (Q3AP) is a generalization of the well-known quadratic assignment problem (QAP). Unlike QAP which has been extensively studied by the combinatorial optimization community, few works have been devoted to the resolution of the Q3AP which is proved to be an NP-hard problem. In this paper, a particle swarm optimization algorithm hybridized with a tabu search is presented to solve the quadratic three-dimensional assignment problem.

Machine Learning in Warehouse Management: A Survey

The quadratic three-dimensional assignment problem: Exact and approximate solution methods

A new bounding procedure for the Quadratic Assignment Problem (QAP) is described which extends the Hungarian method for the Linear Assignment Problem (LAP) to QAPs, operating on the four dimensional cost array of the QAP objective function. The QAP is iteratively transformed in a series of equivalent QAPs leading to an increasing sequence of lower bounds for the original problem. To this end, two classes of operations which transform the four dimensional cost array are defined. These have the property that the values of the transformed objective function Z′ are the corresponding values of the “old” objective function Z, shifted by some amount C. In the case that all entries of the transformed cost array are nonnegative, then C is a lower bound for the initial QAP. If, moreover, there exists a feasible solution U to the QAP, such that its value in the transformed problem is zero, then C is the optimal value of Z and U is an optimal solution for the original QAP. The transformations are iteratively applied until no significant increase in constant C as above is found, resulting in the so called Dual Procedure (DP). Several strategies are listed for appropriately determining C, or equivalently, transforming the cost array. The goal is the modification of the elements in the cost array to obtain new equivalent problems that bring the QAP closer to solution. In some cases the QAP is actually solved, though solution is not guaranteed. The close relationship between the DP and the Linear Programming formulation of Adams and Johnson is presented. The DP attempts to solve Adams and Johnson's CLP, a continuous relaxation of a linearization of the QAP. This explains why the DP produces bounds close to the optimum values for CLP calculated by Johnson in her dissertation and by Resende, et al. in their Interior Point Algorithm for Linear Programming. The benefit of using DP within a branch-and-bound algorithm is described. Then, two versions of DP are tested on the Nugent test instances from size 5 to size 30, as well as several other test instances from QAPLIB. These compare favorably with earlier bounding methods.

Local search methods (LSM) are powerful metaheuristics known for efficiently exploring complex optimization landscapes. However, a key limitation is their “amnesiac” nature – they fail to utilize valuable data from past search iterations. This untapped data contains crucial information that can enhance the efficiency and outcomes of the search process. In this work, we propose a novel reinforcement learning (RL)-based move scoring mechanism to augment LSM, aiming to leverage historical data for improved adaptiveness and intelligence in the search process. We apply this hybrid method to the quadratic 3-dimensional assignment problem (Q3AP), a benchmark in combinatorial optimization that generalizes the quadratic assignment problem (QAP). Notably, few studies have focused on Q3AP, and to our knowledge, no prior work has integrated RL into its solution. Our experimental results demonstrate substantial improvements in both solution quality and execution time, particularly for larger and more complex problem instances. This performance gain is attributed to our unique iterative learning and scoring approach, which effectively guides the search process, balancing exploration and exploitation to escape local optima and find superior solutions.