On Improving an Integrated Inventory Model for a Single Vendor and Multiple Buyers with Ordering Cost Reduction

In this paper, we propose a new model for improving lot size as obtained on applying the model given in “An integrated inventory model for a single vendor and multiple buyers with ordering cost reduction” (Int. J. Production Economics 73 203-215) proposed by Woo, Hsu, and Wu (2001) and our model provides a lower or equal joint total relevant cost as compared to Woo, Hsu, and Wu’s model. And a numerical study based on the example used by Woo, Hsu, and Wu is presented

Open Location Management in Automated Warehousing Systems

A warehouse needs to have sufficient open locations to be able to deal with the change of item inventory levels, but due to ongoing storage and retrieval processes, open locations usually spread over storage areas. Unfavorable positions of open locations negatively impact the average load retrieval times. This paper presents a new method to manage these open locations such that the average system travel time for processing a block of storage and retrieval jobs in an automated warehousing system is minimized. We introduce the effective storage area (ESA), a well-defined part of the locations closest to the depot; where only a part of the open locations –the effective open locations-, together with all the products, are stored. We determine the optimal number of effective open locations and the ESA boundary minimizing the average travel time. Using the ESA policy, the travel time of a pair of storage and retrieval jobs can be reduced by more than 10% on average. Its performance depends hardly on the number or the sequence of retrievals. In fact, in case of only one retrieval, applying the policy leads already to beneficial results. Application is also easy; the ESA size can be changed dynamically during storage and retrieval operations. Keywords: Distribution science, warehousing; AS/RS; storage and retrieval; open locations

Nash Game Model for Optimizing Market Strategies, Configuration of Platform Products in a Vendor Managed Inventory (VMI) Supply Chain for a Product Family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising and retail price to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications

A Single Item Lot Sizing with Backorder and a Finite Replenishment Rate in MRP

There are the following characteristics in decision on lot size in material requirements planning (MRP) systems: multiple time periods, a finite time horizon, discrete demand, and time-varying costs etc. In MRP system there are several different types of lot size techniques, such as the economic order quantity (EOQ), lot-for-lot, periodic order quantity, Wagner-Whitin algorithm, Silver-Meal algorithm and part-period algorithm. Although these lot size approaches focus on controlling the cost of holding cost and order cost, none of them, with the exception of the Wagner-Whitin algorithm, assures an optimal or minimum cost solution for time-varying demand patterns and copes with quantity discount. And Zangwill(1966), Blackburn and Kunreuther (1974) et al extended the Wagner-Whitin algorithm by following demand to go unsatisfied during some period, provided it is satisfied eventually by production in some subsequent period. R. M. Hill (1997), Stanislaw Bylka, Ryszarda Rempala (2001) give dynamic programming formulation to decide lot sizing for a finite rate input process. But the Wagner-Whitin algorithm and its extensions commonly are criticized as being difficult to explain and compute because the algorithms are complicated dynamic programming algorithms. In this paper, we propose a series of inventory models in which backorder and a finite replenishment rate are considered according to the characteristics in MRP ordering and the optimal solutions can be obtained by using general-purpose linear program solver, like EXCEL, LINDO, etc

Optimal Zone Boundaries for Two-class-based Compact 3D AS/RS

Compact, multi-deep (3D), Automated Storage and Retrieval Systems (AS/RS) are becoming more common, due to new technologies, lower investment costs, time efficiency and compact size. Decision-making research on these systems is still in its infancy. We study a particular compact system with rotating conveyors for the depth movement and a Storage/Retrieval (S/R) machine for the horizontal and vertical movement of unit loads. W

Class-based Storage With a Finite Number of Items

ABC class-based storage is widely studied in literature and applied practice. It divides all stored items into a limited number of classes according to their demand rates (turnover per unit time). Classes of items with higher turnovers are stored in a region closer to the warehouse depot. In literature, it is commonly shown that the use of more storage classes leads to shorter travel time for storing and retrieving items. A basic assumption in this literature commonly is that the required storage space of items equals their average inventory levels, which is right if an infinite number of items are stored in each storage region. However, if a finite number of items are stored in the warehouse, more storage classes need more space to store the items: more classes lead to fewer items stored per class, which have less opportunity to share space with other items. This paper revisits ABC class-based storage by relaxing the common assumption that the total required storage space of all items is independent of the number of classes. We develop a travel time model and use it for optimizing the number and the boundaries of classes. Our numerical results illustrate that a small number of classes is optimal

Sequencing Heuristics for Storing and Retrieving Unit Loads in 3D Compact Automated Warehousing Systems

Sequencing unit load retrieval requests has been studied extensively in literature for conventional single-deep automated warehousing systems. A proper sequence can greatly reduce the makespan when carrying out a group of such requests. Although the sequencing problem is NP-hard some very good heuristics exist. Surprisingly the problem has not yet been investigated for compact (multi-deep) storage systems, which have greatly

Open Location Management in Automated Warehousing Systems

A warehouse needs to have sufficient open locations to be able to store incoming shipments of various sizes. In combination with ongoing load retrievals open locations gradually spread over the storage area. Unfavorable positions of open locations negatively impact the average load retrieval times. This paper presents a new method to manage these open locations such that the average system travel time for processing a block o

On the Suboptimality of Full Turnover-Based Storage

In the past thirty years the full turnover-based storage policy as described by Hausman et al. (1976, Management Science 22(6)) has been widely claimed to outperform the commonly used ABC class-based storage policy, in terms of the resulting average storage and retrieval machine travel time. In practice however, ABC storage is the dominant policy. Hausman et al. (1976) model the turnover-based policy under the unrealistic assumption of shared storage, i.e. the stor

Optimal Storage Rack Design for a 3D Compact AS/RS with Full Turnover-Based Storage

Compact, multi-deep (3D) automated storage and retrieval systems (AS/RS) are becoming increasingly popular for storing products with relatively low turnover on a compact area. An automated storage/retrieval crane takes care of movements in the horizontal and vertical direction in the rack, and a gravity conveying mechanism takes care of the depth movement. An important question is how to layout such systems to minimize the pr