A location-routing problem for the conversion to the “click-and-mortar” retailing: The static case

The static conversion from brick-and-mortar retailing to the hybrid click-and-mortar business model is studied from the perspective of distribution logistics. Retailers run warehouses and brick-and-mortar stores to meet the demand of their walk-in customers. When they decide to operate on the Web as an e-tailer, also click-and-mortar stores are needed which can serve both walk-in and online customers. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a quality of service (QoS) guarantee for online customers is timely delivery of their orders. We describe and solve a static location-routing based problem for companies that embrace the clicks-and-bricks strategy in their retail operations. An augmented Lagrangian relaxation method embedded in a subgradient optimization procedure generates lower bounds, whereas a heuristic method finds feasible solutions. The performance of the Lagrangian-based solution method is tested on a number of randomly generated test problems.     

A large-scale application of the partial coverage uncapacitated facility location problem

The traditional, uncapacitated facility location problem (UFLP) seeks to determine a set of warehouses to open such that all retail stores are serviced by a warehouse and the sum of the fixed costs of opening and operating the warehouses and the variable costs of supplying the retail stores from the opened warehouses is minimized. In this paper, we discuss the partial coverage uncapacitated facility location problem (PCUFLP) as a generalization of the uncapacitated facility location problem in which not all the retail stores must be satisfied by a warehouse. Erlenkotter's dual-ascent algorithm, DUALOC, will be used to solve optimally large (1600 stores and 13?000 candidate warehouses) real-world implemented PCUFLP applications in less than two minutes on a 500?MHz PC. Furthermore, a simple analysis of the problem input data will indicate why and when efficient solutions to large PCUFLPs can be expected.     

考虑传统双渠道和BOPS双渠道的消费者和零售商决策研究

本论文在全渠道零售的BOPS模式下,考虑允许退货研究消费者渠道选择问题。首先研究传统双渠道和实施BOPS的双渠道下的消费者和零售商决策。然后加入退货设定,对二者的决策进行重新研究和对比分析。研究发现:不考虑退货的情况下,引入BOPS模式能够提升实体店对零售商及消费者的吸引力;退货情况下,引入BOPS使消费者更愿意选择线下购买和销售,但不一定总能带来销售总量的增加;实施BOPS时,退货允许让零售商更愿意在实体店销售,同时消费者的购买渠道选择也变得复杂。     

Tabu search heuristics for the order batching problem in manual order picking systems

In a manual order picking system, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders be combined into (more substantial) picking orders that are limited in size. The order batching problem considered in this paper deals with the question of how a given set of customer orders should be combined into picking orders such that the total length of all picker tours necessary for all of the requested items to be collected is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first is a (classic) tabu search (TS), and the second is the attribute-based hill climber (ABHC). In a series of extensive numerical experiments, these approaches are benchmarked against other solution methods put forward in the current literature. It is demonstrated that the proposed methods are superior to the existing methods and provide solutions which may allow distribution warehouses to operate more efficiently.     

Sales effort free riding and coordination with price match and channel rebate

This paper studies sales effort coordination for a supply chain with one manufacturer and two retail channels, where an online retailer offers a lower price and free-rides a brick-and-mortar retailer’s sales effort. The free riding effect reduces brick-and-mortar retailer’s desired effort level, and thus hurts the manufacturer’s profit and the overall supply chain performance. To achieve sales effort coordination, we designed a contract with price match and selective compensation rebate. We also examined other contracts, including the target rebate contract and the wholesale price discount contract, both with price match. The numerical analysis shows that the selective rebate outperforms other contracts in coordinating the brick-and-mortar retailer’s sales effort and improving supply chain efficiency.     

基于物料周转率与需求相关性的储位分配优化策略与算法

优化储位分配策略是加快订单拣选速度和提高仓储效率的重要前提。在实际出入库操作中,物料可能具有一定的需求相关性,如螺钉与螺母。若这些需求相关度较高的物料被安排于距离较远的货位,将大大影响其拣选出库的效率。因此,本研究考虑不同储位分配方案的影响,提出将基于物料周转率的存储策略(COI)与物料需求相关度相结合的存储策略,使得周转频率高和相关度大的物料在仓库中的位置接近,且存储于更近仓库出入口的巷道货位。由于模型的计算规模随着参数增长呈指数式增长,本研究开发出一种近似算法,并通过实验证明,相较于商业软件,本算法可更为有效得获取问题的最优或近似解。最后通过实例分析,给出不同COI系数与物料需求度偏好下该仓库的可行储位分配方案     

A fast simulated annealing method for batching precedence-constrained customer orders in a warehouse

Batching customer orders in a warehouse can result in considerable savings in order pickers’ travel distances. Many picker-to-parts warehouses have precedence constraints in picking a customer order. In this paper a joint order-batching and picker routing method is introduced to solve this combined precedence-constrained routing and order-batching problem. It consists of two sub-algorithms: an optimal A^∗-algorithm for the routing; and a simulated annealing algorithm for the batching which estimates the savings gained from batching more than two customer orders to avoid unnecessary routing. For batches of three customer orders, the introduced algorithm produces results with an error of less than 1.2% compared to the optimal solution. It also compares well to other heuristics from literature. A data set from a large Finnish order picking warehouse is rerouted and rebatched resulting in savings of over 5000 kilometres or 16% in travel distance in 3 months compared to the current method.     

A hybrid of adaptive large neighborhood search and tabu search for the order-batching problem

Given a set of customer orders and a routing policy, the goal of the order-batching problem?(OBP) is to group customer orders to picking orders (batches) such that the total length of all tours through a rectangular warehouse is minimized. Because order picking is considered the most labor-intensive process in warehousing, effectively batching customer orders can result in considerable savings. The OBP is NP-hard if the number of orders per batch is greater than two, and the exact solution methods proposed in the literature are not able to consistently solve larger instances. To address larger instances, we develop a metaheuristic hybrid based on adaptive large neighborhood search and tabu search, called ALNS/TS. In numerical studies, we conduct an extensive comparison of ALNS/TS to all previously published OBP methods that have used standard benchmark sets to investigate their performance. ALNS/TS outperforms all comparison methods with respect to both average solution quality and run-time. Compared to the state-of-the-art, ALNS/TS shows the clearest advantages on the larger instances of the existing benchmark sets, which assume a higher number of customer orders and higher capacities of the picking device. Finally, ALNS/TS is able to solve newly generated large-scale instances with up to 600 customer orders and six articles per customer order with reasonable run-times and convincing scaling behavior and robustness.     

Routing order pickers in a warehouse with a middle aisle

This paper considers a parallel aisle warehouse, where order pickers can change aisles at the ends of every aisle and also at a cross aisle halfway along the aisles. An algorithm is presented that can find shortest order picking tours in this type of warehouses. The algorithm is applicable in warehouse situations with up to three aisle changing possibilities. Average tour length is compared for warehouses with and without a middle aisle. It appears that in many cases the average order picking time can be decreased significantly by adding a middle aisle to the layout.     

Retail store scheduling for profit

In spite of its tremendous economic significance, the problem of sales staff schedule optimization for retail stores has received relatively scant attention. Current approaches typically attempt to minimize payroll costs by closely fitting a staffing curve derived from exogenous sales forecasts, oblivious to the ability of additional staff to (sometimes) positively impact sales. In contrast, this paper frames the retail scheduling problem in terms of operating profit maximization, explicitly recognizing the dual role of sales employees as sources of revenues as well as generators of operating costs. We introduce a flexible stochastic model of retail store sales, estimated from store-specific historical data, that can account for the impact of all known sales drivers, including the number of scheduled staff, and provide an accurate sales forecast at a high intra-day resolution. We also present solution techniques based on mixed-integer (MIP) and constraint programming (CP) to efficiently solve the complex mixed integer non-linear scheduling (MINLP) problem with a profit-maximization objective. The proposed approach allows solving full weekly schedules to optimality, or near-optimality with a very small gap. On a case-study with a medium-sized retail chain, this integrated forecasting–scheduling methodology yields significant projected net profit increases on the order of 2–3% compared to baseline schedules.     

考虑完全拆分的拣选分批与拣选路径集成优化模型

在电商海量订单背景下,在线订单拣选作业难度加大,因此设计了基于订单完全拆分的拣选分批与拣选路径综合优化模型解决此问题.模型共分两阶段.第一阶段,基于种子算法,设计考虑订单完成度、等待时间与拣选路径的拣选分批模型;第二阶段以拣选单流为单队列,设计多拣选员并行服务的拣选系统.行走策略为基于返回型和遍历型的综合策略,拣选路径优化模型采用模拟退火算法求解.算例分析表明,与传统的不拆分拣选分批模型相比,构建的综合优化模型能够显著提高拣选系统效率.拣选员为4人时,模型能够使总服务时间减少58.79%,订单完成率提高10.09%.     

Data warehouse clustering on the web

In collaborative e-commerce environments, interoperation is a prerequisite for data warehouses that are physically scattered along the value chain. Adopting system and information quality as success variables, we argue that what is required for data warehouse refreshment in this context is inherently more complex than the materialized view maintenance problem and we offer an approach that addresses refreshment in a federation of data warehouses. Defining a special kind of materialized views, we propose an open multi-agent architecture for their incremental maintenance while considering referential integrity constraints on source data.     

蔬菜B2C直销中基于批配送模式的拣货方案序贯求解方法

针对蔬果类商品B2C直销模式下拣货与配送环节拣货量大、订单个性化强、时间性强及批配送等特点,基于相似订单成组拣货这一现实需求,引入成组作业思想,建立最小化拣货成本和配送成本之和的成批成组拣货序列优化模型;针对该模型多阶段决策、多决策变量及NP-难等特点,以降低求解维度和减少求解时间为目标,基于逆序决策思想,提出序贯求解方法,并给出了客户成批聚类、批次内相似订单成组及成批成组拣货序列优化求解算法;通过应用实例验证本文模型和算法的可行性和有效性。研究结果表明,本文方法得到的方案比成组拣货与配送独立决策,以及批配送但非成组方法大大缩减了拣货时间,为蔬果类商品网上直销企业生成拣货作业计划提供理论指导。     

The impact of order batching and picking area zoning on order picking system performance

This paper proposes an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. The model includes the sorting process needed to sort the batch again by order. Service times at pick zones are assumed to follow general distributions. The first and second moments of service times at zones and the visiting probability of a batch of orders to a pick zone are derived. Based on this information, the mean throughput time of an arbitrary order in the order picking system is obtained. Results from a real application and simulation show that this approximation model provides acceptable accuracy for practical purposes. Furthermore, the proposed method is simple and fast and can be easily applied in the design and selection process of order picking systems.     

Product allocation to different types of distribution center in retail logistics networks

We consider the problem of assigning stockkeeping units to distribution centers (DCs) belonging to different DC types of a retail network, e.g., central, regional, and local DCs. The problem is motivated by the real situation of a retail company and solved by an MIP solution approach. The MIP model reflects the interdependencies between inbound transportation, outbound transportation and instore logistics as well as capital tied up in inventories and differences in picking costs between the warehouses. A novel solution approach is developed and applied to a real-life case of a leading European grocery retail chain. The application of the new approach results in cost savings of 6% of total operational costs compared to the present assignment. These savings amount to several million euros per year. In-depth analyses of the results and sensitivity analyses provide insights into the solution structure and the major related issues.     

The warehouse-inventory-transportation problem for supply chains

Warehouses play a vital role in mitigating variations in supply and demand, and in providing value-added services in a supply chain. However, our observation of supply chain practice reveals that warehousing decisions are not included when developing a distribution plan for the supply chain. This lack of integration has resulted in a substantial variation in workload (42–220%) at our industry partner’s warehouse costing them millions of dollars. To address this real-world challenge, we introduce the warehouse-inventory-transportation problem (WITP) of determining an optimal distribution plan from vendors to customers via one or more warehouses in order to minimize the total distribution cost. We present a nonlinear integer programming model for the WITP considering supply chains with multiple vendors, stores, products, and time-periods, and one warehouse. The model also considers worker congestion at the warehouse that could affect worker productivity. A heuristic based on iterative local search is developed to solve industry-sized problems with up to 500 stores and 1000 products. Our experiments indicate that the distribution plans obtained via the WITP, as compared to a sequential approach, result in a substantial reduction in workload variance at the warehouse, while considerably reducing the total distribution cost. These plans, however, are sensitive to aisle configuration and technology at the warehouse, and the level and productivity of temporary workers.     

Exact results for the order picking time distribution under return routing

This paper derives exact expressions for the Laplace-Stieltjes transform of the order picking time in single- and 2-block warehouses. We consider manual warehouses that deploy return routing and assume that order sizes follow a Poisson distribution. The results in this paper apply to a wide range of storage policies, including but not restricted to class-based and random storage. Furthermore, we compare the performance of the storage policies and warehouse lay-outs by using numerical inversion of the Laplace-Stieltjes transforms.     

Ein Modell zur Planung und Kontrolle des Einsatzes von Verkaufspersonal

Zusammenfassung Einzelhandelsbetriebe sind Dienstleistungsunternehmen, die zur Erfüllung ihrer Aufgaben Verkaufskräfte benötigen. Obwohl durch Einführung neuer Vertriebsformen und Verkaufssysteme (z. B. Selbstbedienung) bestimmte Tätigkeiten z. T. erheblich eingeschränkt bzw. verlagert werden konnten, wird Verkaufen im Einzelhandel immer eine Dienstleistung bleiben, die personalaufwendig und daher kostspielig ist. Das Problem eines rationellen Personaleinsatzes hat der Einzelhandel mit fast allen Dienstleistungsunternehmen gemeinsam, wo im Gegensatz zur Industrie (Produktion auf Vorrat) Leistungen erst erbracht werden können, wenn sie vom Kunden abgefordert werden. Dieser Tatsache wird im Einzelhandel bis heute nicht genügend Rechnung getragen. Man hat sich auf diesem Gebiet bisher überwiegend auf das Gefühl verlassen und intuitiv bestimmt, wieviel Personal für die Bedienung der Kunden bereitzustehen hat. Ein wirksames und in der Praxis bewährtes Planungs- und Kontrollsystem gibt es bislang nicht. Das im folgenden zu beschreibende Modell versucht hier einen Schritt weiterzukommen. Ein darauf beruhendes Planungssystem wurde bei einem bekannten Unternehmen der Damen- und Herrenoberbekleidungsbranche installiert. Wegen der Ähnlichkeit mit Instandhaltungs- und Lagerhaltungsproblemen werden insbesondere Methoden aus diesen Bereichen verwendet.

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Summary Retail stores are service firms needing sales personnel to perform their specific function. Although certain routine operations were in part considerably reduced or shifted through introduction of new distribution patterns and retail systems (e.g. self-service), selling to the consumer will always remain a labor intensive and thus expensive service. The problem of rational manpower utilization is common to the retail trade and almost the entire service trade where — contrary to manufacturing industries which stockpile products — performance is possible only at the time the customer requires it. So far, the retail trade has not sufficiently taken into account that fact, but rather relied on feel and intuition when deciding how much sales personnel to schedule. To date, there is no efficient planning and control system which also passed the test of application in practice. The model described in the following represents an attempt to advance one more step. A personnel planning system based on this model was implemented by a well-known West German ladies and gentlemen apparel chain store. In view of the similarity of problems, methods applied in the maintenance and warehousing fields were used here, too.

     

Multi-period price promotions in a single-supplier, multi-retailer supply chain under asymmetric demand information

This paper considers a two-stage supply chain in which a supplier serves a set of stores in a retail chain. We consider a two-stage Stackelberg game in which the supplier must set price discounts for each period of a finite planning horizon under uncertainty in retail-store demand. As a mechanism to stimulate sales, the supplier offers periodic off-invoice price discounts to the retail chain. Based on the price discounts offered by the supplier, and after store demand uncertainty is resolved, the retail chain determines individual store order quantities in each period. Because the supplier offers store-specific prices, the retailer may ship inventory between stores, a practice known as diverting. We demonstrate that, despite the resulting bullwhip effect and associated costs, a carefully designed price promotion scheme can improve the supplier’s profit when compared to the case of everyday low pricing (EDLP). We model this problem as a stochastic bilevel optimization problem with a bilinear objective at each level and with linear constraints. We provide an exact solution method based on a Reformulation-Linearization Technique (RLT). In addition, we compare our solution approach with a widely used heuristic and another exact solution method developed by Al-Khayyal (Eur. J. Oper. Res. 60(3):306–314, 1992) in order to benchmark its quality.     

A travel time estimation model for a high-level picker-to-part system with class-based storage policies

Most previous related studies on warehouse configurations and operations only investigated single-level storage rack systems where the height of storage racks and the vertical movement of the picking operations are both not considered. However, in order to utilize the space efficiently, high-level storage systems are often used in warehouses in practice. This paper presents a travel time estimation model for a high-level picker-to-part system with the considerations of class-based storage policy and various routing policies. The results indicate that the proposed model appears to be sufficiently accurate for practical purposes. Furthermore, the effects of storage and routing policies on the travel time and the optimal warehouse layout are discussed in the paper.