Reexamining a single-producer multi-retailer integrated inventory model with rework using algebraic method

In this study, a single-producer multi-retailer integrated inventory model with rework is reexamined using mathematical modeling and an algebraic method. It is assumed that a product is manufactured through an imperfect production process, and the reworking of random defective items is done right after the regular process in each cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in each production cycle. The objective is to find the optimal production lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. The conventional approach uses differential calculus on system cost function to derive the optimal production- shipment policy (Chiu et al. [1]); in contrast, the proposed algebraic approach is a straightforward method that enables practitioners who may not have sufficient knowledge of calculus to understand and manage real-world systems more effectively

A delayed differentiation multi-product FPR model with scrap and a multi-delivery policy – I: Using single-machine production scheme

This study examines a delayed differentiation multi-product single-machine finite production rate (FPR) model with scrap and a multi-delivery policy. The classic FPR model considers a single product, single stage production with all items manufactured being of perfect quality and product demand satisfied by a continuous inventory issuing policy. However, in real-life production-shipment integrated systems, multi-product production is usually adopted by vendors to maximize machine utilization, and generation of scrap items appear to be inevitable with uncontrollable factors in production. Further, distribution of finished products is often done through a periodic or multi-delivery policy rather than a continuous issuing policy. It is also assumed that these multiple products share a common intermediate part. In this situation, the producer would often be interested in evaluating a two-stage production scheme with the first stage producing common parts for all products and the second stage separately fabricating the end products to lower overall production-inventory costs and shorten the replenishment cycle time. Redesigning a multi-product FPR system to delay product differentiation to the final stage of production has proved to be an effective supply chain strategy from an inventory-reduction standpoint. Using mathematical modelling, we derive the optimal replenishment cycle time and delivery policy. A numerical example is provided to demonstrate its practical usage and compare our result to that obtained from the traditional single-stage multi-product FPR model

Solving for an Optimal Batch Size for a Single Machine Using the Closed-form Equations to Minimize Inventory Cost

Batch sizing strategy in the manufacturing system has significant impacts on the production performance. In the previous research studies, researchers proposed complicated techniques such as optimization models, simulation, queuing theory, and complex algorithms to solve for the optimal batch size. Using those techniques are difficult for plant managers to calculate for the optimal batch size. Therefore, the closed-form optimal batch size equations are proposed to minimize inventory cost of 2 models. The first model is illustrated when the inventory cost is associated with holding cost but without setup cost. The second model is illustrated when inventory cost is associated with both holding cost and setup cost. Besides the optimal batch size calculation, the value of λ, which is the shadow price of the available setup time, is also solved for sensitivity analysis purpose. Application of the closed-form equation is provided with various parameters applied to different products. The results show that the proposed closed-form equations approach performs well and verifies the effectiveness of the approach

Optimal and predefined policies for the static lot sizing problem in a two stage recovery system

Analyzing static lot sizing problems has always attracted a considerable interest in scientific literature. A commonly applied methodology to solve the trade-off between setup and holding costs is to order the Economic Order Quantity (EOQ) whenever the corresponding inventory is depleted. Yet, this simple proceeding can only be applied as long as there is only a single source of supply. Recovery systems, however, obtain in general two sources of supply, remanufacturing product returns and fabricating new products. Therefore, a more sophisticated approach needs to be taken into account for this kind of problem setting. This contribution focusses on extending the current knowledge in this field of research by showing that non-equal remanufacturing batches propose a significant cost reduction for some parameter classes. Furthermore, a more general optimization approach is introduced that allows to evaluate the solution quality of the preset policy structures

On the alignment of lot sizing decisions in a remanufacturing system in the presence of random yield

In the area of reverse logistics, remanufacturing has been proven to be a valu- able option for product recovery. In many industries, each step of the products’ recovery is carried out in lot sizes which leads to the assumption that for each of the different recovery steps some kind of fixed costs prevail. Furthermore, holding costs can be observed for all recovery states of the returned product. Although several authors study how the different lot sizes in a remanufacturing system shall be determined, they do not consider the specificity of the remanufacturing process itself. Thus, the disassembly operations which are always neglected in former analyses are included in this contribution as a specific recovery step. In addition, the assumption of deterministic yields (number of reworkable compo- nents obtained by disassembly) is extended in this work to study the system behavior in a stochastic environment. Three different heuristic approaches are presented for this environment that differ in their degree of sophistication. The least sophisticated method ignores yield randomness and uses the expected yield fraction as certainty equivalent. As a numerical experiment shows, this method already yields fairly good results in most of the investigated problem instances in comparison to the other heuristics which incorporate yield uncertainties. How- ever, there exist instances for which the performance loss between the least and the most sophisticated heuristic amounts to more than 6%.reverse logistics, remanufacturing, lot sizing, disassembly, random yield

An economic manufacturing quantity model for a two-stage assembly system with imperfect processes and variable production rate

[[abstract]]This article considers a two-stage assembly system with imperfect processes. The former is an automatic stage in which the required components are manufactured. The latter is a manual stage which deals with taking the components to assemble the end product. In addition, the component processes are independent of each other, and the assembly rate is variable. Shortage is allowed, and the unsatisfied demand is completely backlogged. Then, we formulate the proposed problem as a cost minimization model where the assembly rate and the production run time of each component process are decision variables. An algorithm for the computations of the optimal solutions under the constraint of assembly rate is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙