Common Replenishment Cycle Research Articles

Common replenishment cycle order policies for multiple products with capacity expansion opportunities and quantity discounts

Many companies face the challenge of maintaining hundreds, if not thousands, of items in inventory, where each product draws from a common resource (e.g., warehouse space). The introduction of this common resource constraint complicates the traditional lot-sizing problem due to the interdependencies of the lot sizes. This challenge intensifies when the firm can adjust the capacity of the common resource and with the presence of quantity discounts, which may encourage the company to increase lot sizes. This paper develops efficient solutions for a constrained, multi-product lot-sizing problem with a common replenishment cycle, all-units quantity discounts, and a flexible common resource capacity. Historically, the common replenishment cycle (similar to the popular periodic review inventory system) excels in convenience but tends to lag behind in cost effectiveness. We extend the traditional common replenishment cycle approach through the introduction of a refinement policy that allows for more flexibility in the lot-sizing decisions. This modification allows companies to leverage quantity discounts for certain items without detrimental increases to the required common resource capacity (by increasing the cycle length). Via numerical examples and sensitivity analysis, we identify situations where the common replenishment cycle approach with refinement policy outperforms the alternative independent cycles approach in both convenience and cost. Good candidate companies include (1) a growing retailer, (2) a factory with limited storage space, (3) a retailer without secondary warehouse space, (4) a company purchasing bulky items, and (5) a firm located in an expensive city with premium storage space costs.

A series-parallel inventory-redundancy green allocation system using a max-min approach via the interior point method

PurposeThe purpose of this study is to develop a novel and practical series-parallel inventory-redundancy allocation system in a green supply chain including a single manufacturer and multiple retailers operating in several positions without any conflict of interests. The manufacturer first produces multi-product and then dispatches them to the retailers at different wholesale prices based on a common replenishment cycle policy. In contrast, the retailers sell the purchased products to customers at different retail prices. In this way, the manufacturer encounters a redundancy allocation problem (RAP), in which the solution subsequently enhances system production reliability. Furthermore, to emphasize on global warming and human health concerns, this paper pays attention both the tax cost of industrial greenhouse gas (GHG) emissions of all produced products and the limitation for total GHG emissions.Design/methodology/approachThe manufacturer intends not only to maximize the total net profit but also to minimize the mean time to failure of his production system using a RAP. To achieve these objectives, the max-min approach associated with the solution method known as the interior point method is utilized to maximize the minimum (the worst) value of the objective functions. Finally, numerical experiments are presented to further demonstrate the applicability of the proposed methodology. Sensitivity analysis on the green supply chain approach is also performed to obtain more insight.FindingsThe computational results showed that increasing the number of products and retailers might lead into a substantial increase in the total net profit. This indicated that the manufacturer would feel adding a new retailer to the green supply chain strongly. Moreover, an increase in the number of machines provides significant improvement in the reliability of the production system. Furthermore, the results of the performed sensitivity analysis on the green approach indicated that increasing the number of machines has a substantial impact on both the total net profit and the total tax cost. In addition, not only the proposed green supply chain was more efficient than the supply chain without green but also the proposed green supply chain was very sensitive to the tax cost of GHG emission rather than the number of machines.Originality/valueIn summary, the motivations are as follows: the development of a bi-objective series-parallel inventory-RAP in a green supply chain; proposing a hybrid inventory-RAP; and considering the interior point solution method. The novel method comes from both theoretical and experimental techniques. The paper also has industrial applications. The advantage of using the proposed approach is to generate additional opportunities and cost effectiveness for businesses and companies that operate utilizing the green supply chain under an inventory model.

A vendor-managed inventory system considering the redundancy allocation problem and carbon emissions

This paper presents a novel and practical multi-product Vendor-Managed Inventory (VMI) system reliability in a green supply chain including a single manufacturer and multiple retailers operating in distinct markets without any conflicts of interest. The manufacturer produces several products and dispatches them to the retailers at different wholesale prices under a common replenishment cycle policy. In contrast, the retailers sell the purchased products to customers at different retail prices. On the other hand, the manufacture encounters a Redundancy Allocation Problem (RAP), which is a useful method of enhancing system production reliability. Furthermore, to emphasize global warming and human health concerns as well as to create a green supply chain, this paper considers the tax cost of industrial carbon emissions of all products produced and a limitation on total carbon emissions. Meanwhile, the manufacturer desires to maximize the total production system reliability by adding machines to the production system regarding constraints such as available budget, space and the total tax cost. Therefore, the manufacturer desires to maximize the total net profit as well as the mean time to failure of its production system using a redundancy allocation problem. With this aim, the max–min approach by utilizing GAMS/BARON software is utilized to maximize the minimum (the worst) value of the objective functions. Finally, numerical experiments are presented to demonstrate the applicability of the proposed methodology. Sensitivity analysis on the green approach is conducted to provide more insights as well.

The economic lot-size scheduling problem with equally sized batch shipment policy and stochastic demands

This study investigates economic lot–size scheduling problem (ELSP) comprising stochastic demand and equally sized batch shipment policy in a one–supplier multi–buyer integrated inventory model. All buyers have agreed on a joint replenishment policy with a common replenishment cycle (CRC). Equally sized batch shipment scheduling policy for each product in one CRC is applied to the whole system. The objective is to determine the optimal common replenishment cycle and the numbers of batch–shipment for each product, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure that the solution of ELSP involving equally sized batch shipment and stochastic demand model with the CRC policy obtained by the RCD and RT methods reaches the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods. [Received 5 March 2013; Revised 25 September 2013; Revised 3 December 2013; Accepted 11 December 2013]

Common replenishment cycle with mixed batch shipment policy for a single-vendor multi-buyer integrated system

This study addresses a single-vendor multi-buyer integrated system with a common replenishment cycle and a mixed batch shipment policy. The objective is to determine the common replenishment cycle, number of shipments and the structure of the mixed batch shipment which minimises the integrated total cost per unit time. The isolation model is constructed first, and then the isolation model is integrated into the integration model. The minimum total cost model is transformed into a maximum replenishment cycle model to optimise the structure of the mixed batch shipment. Moreover, two new concepts are introduced, namely domination curve and critical replenishment cycle. A new method, the replenishment cycle division method, is then developed to derive the optimal solutions to the subject problem. Examples are presented to illustrate the procedures involved in the replenishment cycle division method.

An Optimal Mixed Batch Shipment Policy for Multiple Items in a Single-Supplier Multiple-Retailer Integrated System

This study addresses mixed batch shipment policy with common replenishment cycle for multiple items in a single-supplier multiple-retailer integrated system. The supplier produces multiple items on a single facility under a common replenishment cycle and delivers products to retailer utilizing a mixed batch shipment policy. The objective is to determine the optimal replenishment cycle, the number of shipments, and the structure of mixed shipment, all of which minimize the integrated total cost per unit time. The single-item isolation model is constructed first, and the single-item isolation model is then integrated into the single-item integration model. Moreover, the single-item integration model is integrated into the multi-item integration model. The minimum total cost model is transformed into a maximum replenishment cycle model to optimize the structure of the mixed batch shipment. The replenishment cycle division method is then developed to obtain the optimal solutions to the subject problem. Examples are presented to illustrate the procedures involved in the replenishment cycle division method.

An integrated production and inventory model for a system comprising an assembly supply chain and a distribution network

This study investigates the production and inventory problem for a system comprising an assembly supply chain and a distribution network. A uniform lot size is produced uninterruptedly with a single setup at each production stage. Equal-sized batch shipment policy is applied to the whole system and the number of batches can be varied. All retailers have agreed on a joint replenishment policy with a common replenishment cycle. The objective is to determine the optimal common replenishment cycle, the number of batches of each production stage and retailer, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure the solutions obtained by the RCD and RT methods reaching the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods.

A vendor managed inventory supply chain with deteriorating raw materials and products

Abstract Fast deteriorating raw materials such as raw milk, fruit and vegetables are commonly used to produce slowly deteriorating finished products such as milk powders, cheeses, and pastas. This paper studies a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system-wide inventories of its fast deteriorating raw material and its slowly deteriorating product. The decision variables are a common replenishment cycle of the product and the replenishment frequency of the raw material. We assume the deteriorating rates are known constants and every retailer's demand is deterministic. We develop an integrated model to calculate the total inventory and deterioration cost for such a system. We prove the convexity of the cost functions, and based on this a golden search algorithm is developed to find the optimal solution of the model. Our numerical results show that the deteriorating rate of the product may increase the total cost by more than 40% compared to the zero-deteriorating rate, while the deteriorating raw material has less impact on the total cost (commonly less than 5% in our numerical examples). This indicates that more attention should be paid to the product than the raw material. Further, an increase in the number of retailers can make the replenishment frequency of the raw material increase significantly but the common replenishment cycle of the product decreases a little. This indicates that adding a new retailer would not be felt strongly by the other retailers but would be felt by the supplier of the raw material.

Simultaneous determination of multiproduct batch and full truckload shipment schedules

A fundamental premise of the well-known economic lot-scheduling problem (ELSP) is that the finished products are consumed at continuous rates, i.e. their respective cycle inventories are depleted on the basis of unit transactions. In today's supply chains, however, employing complex distribution networks, finished goods inventories from manufacturing plants are usually shipped in bulk to succeeding stages along the distribution process. Moreover, existing transport economies often tend to favor full truckload (TL), rather that partial or less than truckload (LTL) shipments, for economical movement of such goods. The scenario examined here, however, involves a set of products, for which individual TL shipments are uneconomical. As a remedy, we construct a model for taking advantage of TL rates by combining LTL quantities of the items into a full load. We adopt the common cycle approach for the ELSP, in conjunction with a common replenishment cycle, as a coordination mechanism that is simple to analyze and implement. This is integrated with a periodic full truckload shipping schedule. Such effective coordination of production and shipment schedules is likely to result in a more streamlined supply chain. The concepts developed are illustrated through a simple numerical example.

Optimal joint replenishment decisions for a central factory with multiple satellite factories

This study investigates the joint replenishment decisions for a central factory and its satellite factories on a Just in Time (JIT) basis. A joint replenishment program involves combining different materials/components from several satellite factories to form a large shipment delivered to the central factory, which provides an opportunity to take advantage of the strong economies of scale present in the freight cost. The program requires closely coordinating the inventory control across satellite factories of multiple materials/components. A decision model with a solution procedure is provided to find the optimal common replenishment cycle time of a group of materials/components for the central factory and the optimal production cycle time as well as the number of shipments per production cycle for each satellite factory. Based on the presented solution procedure, a decision support system has been implemented on a personal computer for the proposed decision. Numerical experiments were conducted to illustrate the application of the model.

Coordinated vs. independent inventory replenishment policies for a vendor and multiple buyers

Through a series of simulation experiments we show that classical lot sizing models do not adequately describe a situation where a single vendor produces and supplies a product to multiple industrial customers, buying in discrete lots. We suggest a common replenishment cycle based, coordinated inventory control model and show that this approach is superior to independent optimization.