Order Quantity, Product Popularity, and The Location of Stock in a Warehouse

In the assignment of warehouse space to inventory items, the amount of space allocated to each item is traditionally determined on the basis of inventory or production cost considerations. Actual assignment of items to storage locations within the warehouse is then carried out independently, with the space requirements taken as given. Assuming an out-and-back order picking procedure and the simple economic order quantity inventory model, it is demonstrated that the quantity and location problems must be considered simultaneously in order to achieve a minimum total cost (order picking cost plus inventory cost). An iterative solution procedure, based on a gradient search, is developed and applied to a test problem.     

An integrated storage assignment method for manual order picking warehouses considering cost,workload and posture

This paper presents an integrated storage assignment method for low-level picker-to-parts order picking warehouses taking into account economic and ergonomic objectives. Three different pallet rack layouts are studied in this paper, namely (a) picking from full pallets on the floor, (b) picking from half-pallets on the floor, and (c) picking from half-pallets on the upper rank of the shelf. First, cost functions are developed to assess the total order picking performance impact of these different pallet rack layouts. Second, with regard to workload, the metabolic cost and energy expenditure rates for picking from the different rack layouts under study are derived. Third, for assessing the working posture during order picking, the Ovako Working Posture Analysing System index is used where the required data is collected using a motion capturing system. The developed models are combined to propose a heuristic storage assignment procedure that supports the decision of which item to store on which pallet. The developed storage assignment method is then applied to an industrial case study. The results of the paper support warehouse managers in assessing the order picking storage assignment from an ergonomics viewpoint and in estimating its impact on financial order picking performance.     

配送中心单品拣货模式及其效能分析

紧扣拣货作业的关键目标,介绍了8种低成本的单品拣货模式,并从生产力指标和人员配置两个方面对各种模式的效能进行了计算分析,能为配送中心拣货系统的设计和选择合适的单品拣货模式提供依据.     

双周期可变供货协议的运转优化模型:以漫友为例

关注一个双周期且存在单一供应商和多个经销商组成的供应链生产和库存的分配优化问题：第1个期间,供应商根据经销商的订单进行生产。从第2期间开始,通过引入一个双周期调整协议,供应商为经销商提供了一个可以在第2期间重新调整库存的机会,即每个经销商可以从供应商那里购买额外库存或销售回多余库存（转运实际发货、收货等交割可在经销商之间进行）。研究运用建立数学模型论证了双周期情况下一个供应商和多个经销商组成的纵向集中而横向分散型系统（半分散型系统）的生产、库存及价格最优均衡模型,接着通过实例数据分析,对完全集中型、半分散型和完全分散型系统转运优化效果进行比较,结果显示,完全集中型优化效果最好(最高13%),但实现难度大;而半分散型是否强于完全分散型系统,取决于调节协议中约定的批发价与生产成本之间的差距因素,差距越小,则半分散型系统的优化效果越强（最高3.39%）。     

A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system

Re-manufacturing is recycling by manufacturing as-good-as-new products from used products, often involving disassembly, cleaning, testing, part replacement/repair, and re-assembly operations. Production planning and inventory control is one of the most important research issues for re-manufacturing system, which are faced with a greater degree of uncertainty and complexity. This leads to a critical need for planning and control systems designed to deal with the added uncertainty and complexity. We formulate a stochastic dynamic programming based model to study the production planning, i.e. dynamic lot sizing problem, of re-manufacturing systems. In the model the demand and return amounts are stochastic over the finite planning horizon. The objective is to determine the quantities that have to be re-manufactured at each period in order to minimise the total cost, including re-manufacturing cost, holding cost for returns and re-manufactured products and backlog cost. The optimal production plan of the re-manufacturing system over a finite planning horizon can be obtained with the policy iteration method. In the end, a numerical example is performed to illustrate how the model is applied and to prove its feasibility.     

考虑冲突避免的多AGV路径规划研究

目的 提高物流企业“货到人”拣选系统在实际生产中的工作效率，避免自动导引小车(AGV)间的冲突死锁，研究大规模多AGV的无冲突路径规划和协同避障问题。方法 首先考虑AGV空载、负载情况和路径扩展成本，改进A^*算法，动态调整代价函数，优化路径扩展方式。其次，提出冲突检测及避免算法，对可能产生局部冲突的路径交叉点进行避障调度，通过预约锁格，实现局部冲突的检测，制定优先级避障策略，解决AGV动态行驶路径上产生的局部冲突和死锁，进而实现全局无冲突路径规划。结果 对多组不同任务量和不同AGV规模的场景进行仿真，实验结果表明，考虑冲突避免的改进A^*算法能有效实现100个任务、90个货架单位和7个拣选站场景下的多AGV动态路径规划，相较于传统A^*算法，其平均拣选时长缩短了52.61%。结论 该方法可实现大规模场景下的多AGV动态路径规划，在付出较小转弯代价的同时有效避免局部动态冲突，该方法可为相关企业实现多AGV协同调度提供新的思路和理论依据。     

Economic batch quantity in a multi-stage production system

A mathematical model has been developed in this paper for determining the total annual variable cost for a product which requires processing on a number of production stages. The demand for the product is assumed uniform over time and it is manufactured in equal lot sizes. In order to minimize the manufacturing cycle time of o production lot, the movement of the items between production stages is in sub-batches of equal sizes, As a result of manufacturing a production lot in sub-batches, the following additional costs are incurred: (1) additional cost of stock holding for process inventory; (2) cost of transporting sub-batches; (3) cost of multiple set-ups. A simple method is then adopted for minimizing the total annual variable cost of the multistage production system. An example has been solved to illustrate the method.     

基于改进遗传算法的自动拣选系统 拣选位分配建模与优化

针对某自动拣选系统建立了拣选位分配优化模型,以拣选时间模型作为适应度函数,并通过判断海明距离添加一个惩罚函数对遗传算法进行了改进,对算例进行仿真实验,可以得到货位排序优化后,总拣选时间明显降低了27.85%。结果表明,货物拣选位的分配对自动拣选系统的拣选效率有很大的影响。要想降低总拣选时间,提高自动拣选系统的拣选效率,不能只考虑个别种类货物的位置分配,要从全局的方向去考虑。该研究对配送中心如何提高自动拣选系统的效率提供了理论支持。     

Manufacturing lot-sizing,procurement and delivery schedules over a finite planning horizon

In this study, an integrated manufacturing system for technology-related companies whose products are experiencing continuous price decrease during the life cycle is studied for optimal procurement, production and delivery schedules over a finite planning horizon. The model considers the inventory cost both at manufacturing and at delivery from supplier. Since the price is continuously decreasing, a manufacturing firm delivers the finished goods in small quantities frequently. Frequent deliveries in small lots are effective to reduce the total cost of the supply chain. The key for high-tech industries is to reduce the inventory holding time since the component prices are continuously decreasing, and this can only be achieved by implementing an efficient supply chain. Therefore, the main purpose of this paper is to develop an integrated inventory model for high-tech industries in JIT environment under continuous price decrease over finite planning horizon while effectively and successfully accomplishing supply chain integration so that the total cost of the system is minimal. An efficient algorithm is developed to determine the optimal or near-optimal lot sizes for raw material procurement, and manufacturing batch under a finite planning horizon. Finally, the solution technique developed for the model is illustrated with numerical examples.     

Enhancing performance in order picking processes by dynamic storage systems

Increasing productivity and reducing labour cost in order picking processes are two major concerns for most warehouse managers. Particularly picker-to-parts order picking methods lead to low productivity as order pickers spend much of their time travelling along the aisles. To enhance order picking process performance, an increasing number of warehouses adopt the concept of dynamic storage where only those products needed for the current order batch are dynamically stored in the pick area, thereby reducing travel time. Other products are stored in a reserve area. We analyse the stability condition for a dynamic storage system with online order arrivals and develop a mathematical model to derive the maximum throughput a DSS can achieve and the minimum number of worker hours needed to obtain this throughput, for order picking systems with a single pick station. We discuss two applications of dynamic storage in order picking systems with multiple pick stations in series. In combination with simulation modelling, we are able to demonstrate that dynamic storage can increase throughput and reduce labour cost significantly.     

Using a multiple-GA method to solve the batch picking problem: considering travel distance and order due time

Warehousing involves all activities related to the movement of goods such as receiving, storage, order picking, accumulation, sorting and shipping within warehouses or distribution centres. Among these activities, order picking is the most costly process because its operations are labour-intensive and repetitive. In this paper, we propose a batch picking model that considers not only travel cost but also an earliness and tardiness penalty to fulfil the current complex and quick-response oriented environment. This model is solved using a multiple-GA method for generating optimal batch picking plans. The core of the multiple-GA method consists of the GA__BATCH and GA__TSP algorithms. The GA__BATCH algorithm finds the optimal batch picking plan by minimizing the sum of the travel cost and earliness and tardiness penalty. The GA__TSP algorithm searches for the most effective travel path for a batch by minimizing the travel distance. To exhibit the benefits of the proposed model a set of simulations and a sensitivity analysis are conducted using a number of datasets with different order characteristics and warehouse environments. The results from these experiments show that the proposed method outperforms benchmark models.     

An integrated model for inventory and production planning in a two-stage hybrid production system

A two-stage hybrid flow-shop production system is considered. The first stage is a process production system and the second stage is a job-shop production system. The two stages are separated by an intermediate warehouse to introduce flexibility (some independence) in the planning of production at both stages. The inventory level at the warehouse should be optimized to provide a trade-off between the cost of carrying the inventory of the semi-finished products, the minimum batch size requirement in the first stage, and the required service level at the second stage. An integrated model for planning the production in these hybrid flow-shop production systems types is developed. The objectives of optimizing the production and inventory costs at the two stages of the system, including the warehouse, while satisfying customer demands, are considered. An algorithm to solve the suggested model is described in detail, and a solution is provided for a real world case, which has inspired the study. A computational study to measure the performance of the approach was also carried out and the results are reported.     

The effects of pick density on order picking areas with narrow aisles

The cost and service performance of an order fulfillment center are determined partly by how workers are organized into an order picking system. One common approach is batch picking, in which workers circumnavigate a picking area with other workers, gathering items on a pick list. In some systems with high space utilization, narrow aisles prohibit workers from passing one another when in the same aisle, and this leads to congestion. We build analytical and simulation models of these systems to investigate their behavior under different levels of activity. Among other things, our results suggest that when the system is busier and pick density is high (that is, when workers stop often to make picks) congestion is less of a problem and workers are more productive.     

The use of bucket brigades in zone order picking systems

As the transactions through electronic commerce and TV home shopping increase, the warehouses often receive a large amount of small orders to be picked within tight time windows. One of the important warehousing activities is order picking, the process of retrieving a number of items from warehouse storage to meet a number of independent customer orders. This paper examines a new order picking method, bucket brigade order picking (BB picking). Bucket brigade is a way of coordinating workers who progressively perform a set of operations on a flow line. In the BB picking system, a worker performs operations on an order until the next worker downstream takes it over; then goes back to the previous worker upstream to take over a new order. We discuss distinct characteristics in order picking systems when bucket brigades are applied. We identify some efficiency losses under the BB picking and present a new BB picking protocol to improve the performance of order picking systems. The new BB picking is compared with the existing BB picking and zone picking through simulation experiments.     

Supply chain cell activities for a consumer goods company

The supply chain cell is a new cross-functional area in many industries in India. It involves the integration of production planning, dispatch order generation and logistics planning, apart from general logistics, which primarily includes distribution. This paper deals with the study conducted for a fast moving consumer goods company having 14 production locations and 22 branches/clearing and forwarding agents. There were 36 packing lines, with each line packing different varieties of stock-keeping units. In this company, supply chain cell activities were concentrated on the middle of the classical supply chain. An attempt has been made to integrate production logic with the logistics by considering the total cost concept. The total cost concept also includes non-quantifiable parameters, which have been incorporated by the use of the analytical hierarchy process. An optimization technique has been proposed simultaneously to support the planning logic developed. The supply chain cell helps to optimize the total supply chain cost as well as enabling it to supplement other benefits such as an improvement in inventory turnover and a reduction in the inventory carrying cost.     

Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

In this paper, we devise a framework for obtaining the optimal ordering policy in a single location, continuous-review inventory system with arbitrary inter-demand times. We show that it is optimal to order at demand arrival epochs only if the inter-demand time has a constant or decreasing failure rate. When the inter-demand time has an increasing failure rate, we show that the optimal policy is to delay the order. We then extend this policy to multi-echelon distribution systems consisting of one supplier and many retailers. Both decentralized and centralized systems are considered. We derive expressions and procedures for the evaluation of the total cost and the computation of optimal delay in all the considered settings. More importantly, we study the impact of our delay policy in all the settings. The numerical results indicate that for the single-location model, the optimal delay can significantly reduce the total cost. Results from the single-location model can be applied to the decentralized multi-echelon system, where the upstream supplier acts as a single-location system. The supplier order delay can also have a significant impact (either positive or negative) on the retailers' total cost as well as the system's total costs. Finally, the impact of supplier order delay is minimal in the centralized multi-echelon setting. We offer an intuitive explanation for this observation.     

Infinite horizon production planning with periodic demand: solvable cases and a general numerical approach

In this paper, we consider a single part-type pull manufacturing system, which controls its production rates in response to periodic demand. When tracking the demand results in a product surplus, an inventory storage cost is incurred. Likewise, if an overall shortage occurs then a backlog cost is paid. In addition, production costs accrue when the system is not idle. Given an infinite planning horizon, the objective is to determine the cyclic production rates in order to minimize the total cost. With the aid of the maximum principle, extremal behavior of the system is studied and the continuous-time production planning problem is reduced to a discrete problem with a limited number of switching points at which time the production rates change. Using this result, an efficient numerical algorithm is proposed, which will yield an approximation to the optimal solution within any desired level of accuracy. In addition, we determine the analytical solution to the problem for three special cases: (i) the system capacity is not limited and the inventory storage cost factor is equal to the backlog cost factor; (ii) the production cost is negligible; and (iii) the surplus and shortages costs are negligible.     

Coordination of joint pricing-production decisions in a supply chain

We consider the coordination of dynamic, joint pricing-production/ordering decisions in a decentralized supply chain where a manufacturer outsources her product distribution/retailing function to an independent distributor/retailer. The manufacturer produces and wholesales her product to the distributor who, after some further processing, sells the product to an external market. In a leader-follower setting with convex production/ordering cost functions, both parties make pricing and production/ordering decisions over a discrete, finite-time horizon (a selling season) to maximize their respective profits. For a given manufacturer's (the leader's) wholesale price schedule, we develop a simple forward algorithm to solve the distributor's problem optimally, and prove a planning horizon property of the solution. Our key result is to show the existence of a manufacturer's price schedule that induces distributor to adopt decisions in the decentralized setting to achieve the performance of a centralized supply chain. Based on this channel-optimal pricing policy we then develop an incentive scheme for the manufacturer to achieve channel coordination. A numerical example is provided to compare the performance of different policies and lo reinforce key managerial insights generated through analysis.     

Parallel-machine,multiple-product-type,continuous-time scheduling: decomposable cases

This paper considers a manufacturing system where multiple-product-types are produced on a set of parallel machines. The production quantity for each product-type in a planning horizon is predetermined. However, the planning horizon is not fixed, and a cost must be paid for each unit of time in the horizon. Inventory holding costs are incurred due to storing products in the buffer placed after each machine. In addition, a production cost is incurred if a machine is not idle. Our objective is to schedule the production so that inventory, production, and planning horizon costs are minimized. With the aid of the maximum principle, this continuous-time scheduling problem is studied, and the conditions such that the problem can be decomposed into a set of well-structured, discrete-time sub-problems are derived. Consequently, several solvable cases are identified, and their corresponding polynomial-time algorithms are suggested.     

多人拣选系统拥堵的马尔科夫建模与仿真研究

目的 为了降低拣选系统拥堵率提高应急物资的运输效率,文中提出一种基于马尔科夫的多人拥堵模型。方法 分别构建窄通道货位单件拣选和货位多件拣选情况下的马尔科夫状态转移矩阵,求解平稳分布,获得拣选概率与拥堵率的函数关系式,并通过仿真分析不同因素变化对拥堵率的影响。结果 研究发现在货位单件拣选情况下,拣选概率取值为0.3左右时,系统拥堵率达到峰值,之后随拣选概率的增大而减小;在货位多件拣选情况下,拣选概率与系统拥堵率呈正相关,系统拥堵率随着拣选概率的增加而增加。结论 在实际拣选作业中,为了降低系统拥堵率,货位单件拣选应尽量避免拣选概率在0.3左右;货位多件拣选应尽量降低拣选概率。