Optimal common manufacturing cycle length for a multi-product inventory system with rework and an outside contractor

Facing global market’s rigid competition, today’s manufacturers need not only to satisfy the timely demands of multiproduct, but also to ensure quality of their goods. For the purpose of reducing fabrication cycle time so as to meet timely demands, outsourcing is always a helpful option in production planning. To address the aforementioned real issues, the present study derives the optimal common manufacturing cycle length for a multi-product inventory system, wherein a part of lot-size of each end product is supplied by an outside contractor, and in each cycle a rework process repairs random defects produced by the in-house process. The schedule of receipt time for outsourced items is practically assumed to be in the end of rework. A specific decision model is built to cautiously portray such a hybrid inventory problem. Through modeling, analysis, and derivation the expected annual system cost is obtained, and using optimization technique the optimal cycle length that minimizes system cost is gained. The proposed decision model not only can help find optimal solution to the problem, but also enables manufacturers to obtain diverse essential information, such as the critical outsourcing rate, individual manufacturing related cost for each end product, and influence or joint effects of variations in different system factor(s) on the problem. Without our in-depth exploration, the aforementioned information will still be unavailable to support managerial decision makings

Optimal production cycle time for multi-item FPR model with rework and multi-shipment policy

This paper determines the optimal common production cycle time for a multi-item finite production rate (FPR) model with rework and multi-shipment policy. The classic FPR model considers production planning for a single product with perfect quality production and a continuous issuing policy. However, in real life production environments, vendors often plan to produce multiple products in turn on a single machine in order to maximize the machine utilization. Also, due to various uncontrollable factors, generation of nonconforming items in any given production run is inevitable. It is also common for vendors to adopt multiple/periodic delivery policy for distributing their finished goods to customers. In this study, it is assumed that all nonconforming items can be reworked and repaired in the same cycle when regular production ends at additional cost per each reworked item. Our objective is to determine the optimal common production cycle time that minimizes the long-run average cost per unit time and to study the effect of rework on the optimal common cycle time for such a specific multi-item FPR model with rework and multi-shipment policy. Mathematical modeling is used, and the expected system cost for the proposed model is derived and proved to be convex. Finally, a closed-form optimal cycle time is obtained. A numerical example and sensitivity analysis is provided to show the practical use of our obtained results

Optimal production cycle time for multi-item FPR model with rework and multi-shipment policy

This paper determines the optimal common production cycle time for a multi-item finite production rate (FPR) model with rework and multi-shipment policy. The classic FPR model considers production planning for a single product with perfect quality production and a continuous issuing policy. However, in real life production environments, vendors often plan to produce multiple products in turn on a single machine in order to maximize the machine utilization. Also, due to various uncontrollable factors, generation of nonconforming items in any given production run is inevitable. It is also common for vendors to adopt multiple/periodic delivery policy for distributing their finished goods to customers. In this study, it is assumed that all nonconforming items can be reworked and repaired in the same cycle when regular production ends at additional cost per each reworked item. Our objective is to determine the optimal common production cycle time that minimizes the long-run average cost per unit time and to study the effect of rework on the optimal common cycle time for such a specific multi-item FPR model with rework and multi-shipment policy. Mathematical modeling is used, and the expected system cost for the proposed model is derived and proved to be convex. Finally, a closed-form optimal cycle time is obtained. A numerical example and sensitivity analysis is provided to show the practical use of our obtained results

Mathematical modelling for multiproduct EPQ problem featuring delayed differentiation, expedited rate, and scrap

The client requirements of present-day markets emphasize product quality, variety, and rapid response. To gain competitive advantages in marketplaces and meet customer needs, manufacturers today seek the most economical and fastest fabrication schemes and strategies to produce their various goods, especially when commonality exists within these multiple end products. Inspired by the above viewpoints, this study uses a mathematical modelling approach for solving a multiproduct economic production quantity (EPQ) problem featuring scrap, delayed differentiation, and expedited rate on the fabrication of the common part. We build a two-stage multiproduct fabrication scheme. Stage one uses an accelerated rate to produce all necessary common parts for multi-item to shorten its uptime, while stage two fabricates finished products sequentially using a rotation cycle rule. Inevitable random scraps produced in both stages are identified and removed to achieve the anticipated quality. We determined the optimal cost-minimization operating cycle length and used a numerical example to show our model’s capability and to explore collective and individual impacts of scrap, expedited-rate, and postponement strategies on various performances of the studied problem (such as uptime of common part, utilization, rotation cycle time, total system cost, and individual cost contributor, etc.) Our model can offer an optimization solution and in-depth managerial insights for fabrication and operations planning in a wide variety of present-day industries, such as automotive, household goods, clothing, etc

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

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 – II: Using two-machine production scheme

This paper concerns a delayed differentiation multi-product finite production rate (FPR) model with scrap and multi-delivery policy using a two-machine production scheme. Conventional FPR model considers a single product, single-stage production with all products fabricated being of perfect quality, and product demand satisfied by a continuous inventory issuing policy. However, in real vendor-buyer integrated systems, most vendors would adopt a multi-product production plan to maximize machine utilization. They often use a periodic or multi-shipment policy to distribute their finished products. When planning to produce a cluster of multiple products that share a common intermediate part, the vendor would often evaluate a two-stage production scheme. The first stage manufactures only the common parts for all products and the second stage separately manufactures the end products. The aim is to shorten the replenishment cycle time and reduce overall production-inventory related costs. This study considers a two-machine production scheme and the two-stage production process with the objective of determining the optimal production cycle time and number of deliveries. A numerical example with sensitivity analysis is provided to demonstrate practical use of the obtained results as well as to compare the proposed production scheme to that of using a single machine in the multi-product two-stage FPR model

Integrating a cost-reduction shipment plan into a single-producer multi-retailer system with rework

This study integrates a cost-reduction shipment plan into a single-producer, multi-retailer system with rework process. In a recent article, Chiu et al. [1] have examined a single-producer, multi-retailer integrated inventory model with a rework process. For the purpose of reducing the inventory holding cost, this study combines an alternative n+1 product distribution policy into their model. Under the proposed shipment plan, an extra (initial) delivery of finished items takes place during the production uptime to meet the retailers’ product demands for the periods of the producer’s uptime and reworking time. Upon the completion of rework, multiple shipments will be delivered synchronously to m different retailers. The objectives are to find an optimal production-shipment policy that minimizes the expected system cost for such a supply chain system, and to demonstrate that the result of this study gives significant holding cost savings in comparison with Chiu et al.’s model [1]. With the help of mathematical modelling and Hessian matrix equations, the optimal operating policy for the proposed model is derived. Through a numerical example, we demonstrate our model gives significant savings in stock holding cost for both the producer and retailers

Revisiting "integrating a cost-reduction shipment plan into a single-producer multi-retailer system with rework" using an alternative approach

This study revisits a single-producer multi-retailer system with a cost-reduction shipment plan and rework [1] using an alternative approach. Unlike the conventional method that uses differential calculus on system cost function to prove its convexity and derive the optimal production-shipment policy, we proposed an algebraic solution procedure to the problem. Such a straightforward approach may enable the practitioners with little knowledge of calculus to understand real supply chain systems more easily

Incorporating machine reliability issue and backlogging into the EMQ model - Part II: Random breakdown occurring in inventory piling time

This paper presents the second part of a research which is concerned with incorporating machine reliability issues and backlogging into the economic manufacturing quantity (EMQ) model. It may be noted that in a production system when back-ordering is permitted, a random machine failure can take place in either backorder filling stage or in on-hand inventory piling time. The first part of the research investigates the effect of a machine failure occurring in backorder filling stage on the optimal lot-size; while this paper (the second part of the research) studies the effect of random breakdown happening in inventory piling time on the optimal batch size for such an imperfect EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall productioninventory costs. Mathematical modelling is used and the renewal reward theorem is employed to cope with the variable cycle length. Hessian matrix equations are utilized to prove convexity of the cost function. Then, the optimal lot size for such a real-life imperfect manufacturing system is derived. Practitioners and managers in the field can adopt these replenishment policies to establish their own robust production plan accordingly