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

Incorporating machine reliability issue and backlogging into the EMQ model - Part I: Random breakdown occurring in backorder filling time

This study is concerned with determination of the optimal replenishment policy for economic manufacturing quantity (EMQ) model with backlogging and machine reliability issue. Classic EMQ model does not consider nonconforming items generated during a production cycle, nor does it deal with the machine breakdown situation. It is noted that in manufacturing system when back-ordering is permitted, a random machine failure can take place in either backorder filling time or in on-hand inventory piling period. The first phase of this study examines the aforementioned practical issues by incorporating rework process of defective items, scrap and random machine failure taking place specifically in backorder satisfying time into the EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall production-inventory costs. Mathematical modelling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. Theorem on conditional convexity of total cost function is proposed and proved. The optimal lot size for such a real-life imperfect manufacturing system is derived. A numerical example is given to demonstrate its practical usage

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

Optimal batch quantity models for a lean production system with rework and scrap

In an imperfect manufacturing process, the defective items are produced with finished goods. Rework process is necessary to convert those defectives into finished goods. As the system is not perfect, some scrap is produced during this process of rework. In this research, inventory models for a single-stage production process are developed where defective items are produced and reworked, where scrap is produced, detected and discarded during the rework. Two policies of rework processes are considered (a) First policy: rework is done within the cycle, and (b) Second policy: rework is done after N cycles of normal production. Also, three types of scrap production and detection methods are considered for each policy, such as (i) scrap is detected before rework, (ii) scrap is detected during rework and (iii) scrap is detected after rework. Based on these inventory situations, the total cost functions for a single-stage imperfect manufacturing system are developed to find the optimum operational policy. Some numerical examples are provided to validate the model and a sensitivity analysis is carried out with respect to different parameters used to develop the model

A production inventory model with exponential demand rate and reverse logistics

The objective of this paper is to develop an integrated production inventory model for reworkable items with exponential demand rate. This is a three-layer supply chain model with perspectives of supplier, producer and retailer. Supplier delivers raw material to the producer and finished goods to the retailer. We consider perfect and imperfect quality products, product reliability and reworking of imperfect items. After screening, defective items reworked at a cost just after the regular manufacturing schedule. At the beginning, the manufacturing system starts produce perfect items, after some time the manufacturing system can undergo into “out-of-control” situation from “in-control” situation, which is controlled by reverse logistic technique. This paper deliberates the effects of business strategies like optimum order size of raw material, exponential demand rate, production rate is demand dependent, idle times and reverse logistics for an integrated marketing system. Mathematica is used to develop the optimal solution of production rate and raw material order for maximum expected average profit. A numerical example and sensitivity analysis is illustrated to validate the model

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

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

A Fuzzy Economic Order Quantity (EOQ) Model with Consideration of Quality Items, Inspection Errors and Sales Return

In this paper, we develop an economic order quantity model with imperfect quality, inspection errors and sales returns, where upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a lessen price, prior to receiving the next shipment. The screening process to remove the defective items may involve two types of errors. In this article we extend the Khan et al. (2011) model by considering demand and defective rate in fuzzy sense and also sales return in our model. The objective is to determine the optimal order lot size to maximize the total profit. We use the signed distance, a ranking method for fuzzy numbers, to find the approximate of total profit per unit time in the fuzzy sense. The impact of fuzziness of fraction of defectives and demand rate on optimal solution is showed by numerical example