Redesigning a warehouse network

To take advantage of economies of scale, a growing number of firms have begun to explore the possibility of integrating supply chain activities. The advent of such a possibility would necessitate the redesign of a warehouse network. Typically, a warehouse redesign problem involves the consolidation of regional warehouses into a fewer number of master stocking points and the subsequent phase-out of redundant or underutilized warehouses without deteriorating customer services. This paper develops a mixed-integer programming model to solve the warehouse redesign problem. The usefulness of the model was validated by its successful application to a real-world problem and by its sensitivity analyses when used with changing scenarios within a warehouse network configuration.     

Forward-reserve allocation in a warehouse with unit-load replenishments

Many companies configure their warehouse with a forward area and a reserve area. The former is used for efficient order-picking, the latter for replenishing the forward area. We consider a situation in which orders are picked during a certain time period, referred to as the picking period. Prior to the picking period there is sufficient time to replenish the forward area. Our objective is to determine which replenishments minimize the expected amount of labor during the picking period. Further, we present a second model with a constraint on the replenishment activity. We model the problem as a binary programming problem and present efficient heuristics that provide tight performance guarantees. We compare the heuristics with procedures that are popular in practice and show that significant labor-savings are possible.     

Timetabling of sorting slots in a logistic warehouse

We study a problem that occurs at the end of a logistic stream in a warehouse and which concerns the timetabling of the sorting slots that are used to accommodate the prepared orders before they are dispatched. We consider a set of orders to be prepared in a certain number of preparation shops over a given time horizon. Each order is associated with the truck that will transport it to the customer. A sorting slot is an accumulation area where processed orders wait to be loaded onto a truck. For a given truck a known number of sorting slots is needed from the time the first order for this truck begins to be prepared, right up until the truck’s scheduled departure time. Since several orders destined for different trucks are processed simultaneously, and since the number of sorting slots is limited, the timetabling of these resources is necessary to ensure that all orders can be processed over the considered time horizon. In this paper we describe the general industrial context of the problem and we formalize it. We state that some particular cases of the problem are polynomially solvable while the general problem is NP-complete. We then propose optimization methods for solving the problem.     

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.     

Travel time estimation and order batching in a 2-block warehouse

Order batching problem (OBP) is the problem of determining the number of orders to be picked together in one picking tour. Although various objectives may arise in practice, minimizing the average throughput time of a random order is a common concern. In this paper, we consider the OBP for a 2-block rectangular warehouse with the assumptions that orders arrive according to a Poisson process and the method used for routing the order-pickers is the well-known S-shape heuristic. We first elaborate on the first and second moment of the order-picker’s travel time. Then we use these moments to estimate the average throughput time of a random order. This enables us to estimate the optimal picking batch size. Results from simulation show that the method provides a high accuracy level. Furthermore, the method is rather simple and can be easily applied in practice.     

A transportation mode selection model for a consolidation warehouse system

Summary This paper presents a transportation mode selection model for a consolidation warehouse system. It determines the transportation mode to be used by each plant or warehouse (point of origin) to ship its order to the company's consolidation point or central warehouse. The model considers the tradeoff between the total cost of transporting items and the maximum time until a complete order has reached the consolidation point. It brings to bare the effect of each possible mode on (1) buyer transportation cost, and (2) related buyer inventory costs. An algorithm is provided to determine the most preferable shipping plan. A prototypical example is presented to illustrate the use of the algorithm.

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Zusammenfassung Es wird ein Liefersystem betrachtet, bei dem die bestellten Waren von verschiedenen Herstellern oder Lagerhäusern über eine gemeinsame Zentrale an den Kunden geliefert werden. Für den Transport der Waren von jedem Hersteller zur Zentrale sind verschiedene Transportarten wählbar, die unterschiedliche Transportkosten und Transportdauern verursachen. Die verschiedenen Transportdauern führen zu unterschiedlichen Lagerhaltungskosten beim Kunden. Es wird ein Modell angegeben, das die mit der gewählten Transportart verbundenen Transportkosten und Lagerhaltungskosten berücksichtigt. Ein Algorithmus zur Auswahl der günstigsten Transportart wird bereitgestellt. An einem kleinen Beispiel wird der Algorithmus erläutert.

     

Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments

This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. In this work, it is assumed that in each cycle, the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails. This portion becomes scrap and only the perfect finished items can be delivered to customers at the end of rework process. A profit function is derived to model the inventory problem and it is shown that the profit function is concave. Due to the complexity of the optimization problem, an algorithm is developed to determine the optimal values of manufacturing lot size and price such that the long-run average profit function is maximized. Furthermore, two special cases are identified and explained. Finally, a numerical example is given to illustrate the applicability of the proposed inventory model.     

Optimal model for warehouse location and retailer allocation

Warehouse location and retailer allocation is a high‐level strategic decision problem that is commonly encountered by logisticians and supply chain managers, especially during the supply chain design phase. Considering the product distribution cost and warehouse capital cost trade‐offs, this paper models the warehouse location and retailer allocation problem as a 0–1 integer programming problem and provides an efficient two‐stage set covering heuristic algorithm to solve large‐sized problems. Finally, concluding remarks and some recommendations for further research are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

An integrated model for warehouse and inventory planning

The purpose of this article is to evaluate the value of integrating tactical warehouse and inventory decisions. Therefore, a global warehouse and inventory model is presented and solved. In order to solve this mathematical model, two solution methodologies are developed which offer different level of integration of warehouse and inventory decisions. Computational tests are performed on a real world database using multiple scenarios differing by the warehouse capacity limits and the warehouse and inventory costs. Our observation is that the total cost of the inventory and warehouse systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehouse decisions.     

Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem

In this paper we present a lower bound for the capacitated warehouse location problem based upon the Lagrangean relaxation of a mixed-integer formulation of the problem, where we use subgradient optimisation in an attempt to maximise this lower bound. Problem reduction tests based upon this lower bound and the original problem are given. Incorporating this bound and the reduction tests into a tree search procedure enables us to solve problems involving up to 50 warehouses and 150 customers.     

Travel time analysis for general item location assignment in a rectangular warehouse

A travel time model with general item location assignment in a rectangular warehouse system is presented. We give the exact probability mass functions that characterise the tour of an order picker and derive the first and second moments associated with the tour. We apply the model to analysing order batching and storage allocation strategies in an order picking system. The order picking system is modelled as a queueing system with customer batching. The results are compared and validated via simulation. The effects of batching and batch size on the delay time are discussed with consideration to the picking and sorting times for each batch of orders.     

Does battery management matter? Performance evaluation and operating policies in a self-climbing robotic warehouse

Our research is motivated by battery management in a new self-climbing robotic (SCR) system. The SCR system fully depends on battery-powered robots for tote movements. Therefore, battery management plays an important role and considerably impacts the system performance. This paper investigates the decision of battery charging technology (fast charging versus slow charging) taking into account the battery degradation, the battery charging policy (priority charging policy and dedicated charging policy), and the optimal number of chargers in the system. The paper also optimizes battery management in the SCR system by establishing semi-open queuing networks (SOQNs). The analytical models are solved by the approximate mean value analysis and are validated by simulation models. We find several interesting managerial insights: (1) In the operational policies, although fast charging can decrease the throughput time, we find a new condition when slow charging outperforms fast charging in robotic warehouses. (2) The priority charging policy is more cost-effective than the dedicated charging policy. (3) We also find a decision tool to determine the optimal number of chargers to satisfy the maximum allowed throughput time with the minimum cost.     

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.     

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

Recently, Chiu et al. (2012) [1] present an alternative optimization procedure to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. This inventory model was proposed by Chiu et al. (2011) [2]. Both papers do not consider the determining of the number of shipments. This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al.  and .     

A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages

In this paper, we develop a deterministic inventory model with two warehouses (one is the existing storage known as own warehouse (OW) and the other is hired on rental basis known as rented warehouse (RW). The model allows different levels of item deterioration in both warehouses. The demand rate is supposed to be a linear (increasing) function of time and the replenishment rate is infinite. The stock is transferred from RW to OW in continuous release pattern and the associated transportation cost is taken into account. Shortages in OW are allowed and excess demand is backlogged. For the general model, we give the equations for the optimal policy and cost function and we discuss some special cases. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model.     

Vehicle routing in an automated warehouse: Analysis and optimization

This study concerns the design of an operating system for vehicles in an automated warehouse. The layout of the warehouse and the number and properties of the vehicles are given. The objective is to maximize the throughput. Using a partial enumeration technique, we simulate several alternatives for the control and interplay of the vehicles within a reasonable time horizon. A subproblem is solved by network flow techniques. The algorithm is implemented as part of an automatic control system, and it has led to a satisfactory performance.     

A model based evaluation of a commonly used rule of thumb for warehouse layout

A model is formulated to describe the cost effects of alternative warehouse layouts in a dedicated storage warehouse that utilizes dual address order picking cycles. The model is utilized to evaluate a common warehouse layout rule of thumb where stock levels are determined using economic order quantities, and stock locations are obtained using the cube per order index. A simple heuristic procedure is devised to utilize the cost model to obtain warehouse layouts with lower total inventory and order picking cost than those obtained using the rule of thumb. Four test problems are generated to assess the difficulty of obtaining improved warehouse layouts. It is shown that the heuristic procedure can achieve significantly improved warehouse layouts with minimal computational effort.     

Inventory model with deteriorating items,ramp-type demand and partially backlogged shortages for a two warehouse system

In this paper, we consider a two warehouse inventory model, an owned one (OW) and a rented one (RW). Inventory deteriorates in the two warehouses at different constant rates, demand rate is a general ramp-type function of time and shortages are partially backlogged at a constant rate. Existence and uniqueness of the optimal solution is discussed. An algorithm is developed to obtain the overall optimal replenishment policy, which would enable the manager to decide upon the feasibility of renting a warehouse. The dynamics of the model and application of the algorithm are demonstrated through numerical examples. Sensitivity analysis is conducted with respect to model parameters and some important observations are drawn.     

Separating Market Efficiency from Profitability and its Implications for Planning

This paper discusses the practical usefulness of separating market efficiency from profitability when assessing the comparative performance of private sector organizational units. The market efficiency of a unit reflects its ability to attract custom. The paper shows how data envelopment analysis can be used to assess market efficiency and it illustrates the usefulness of this measure in managing the public houses of a brewery.