Facing current client expectations for high quality, timely order response, and multiple shipments of various needed merchandise, today’s producers must simultaneously satisfy external requirements and operate internally with minimum overall expenses and capacity constrained. Aiming to help present-day producers achieve the operational goals mentioned above, this work develops a decisional scheme to determine the best manufacturing-delivery policy for a multi-item economic production quantity (EPQ) system with multi-shipment, quality assurance, overtime, postponement, and external source. Combining a production postponement strategy in our multi-item batch fabricating procedures intends to first make all required standard/common parts for various client-needed merchandise and make finished goods in the 2nd phase. Two fabricating-uptime-shortening strategies are adopted: contracting out a proportion of the standard part’s batch and overtime-making of finished goods. We include screening and rework tasks in fabricating procedures to help us remove the identified scraps and correct the repairable faulty items. The quality-assured finished batches are divided into multiple equal-amount shipments transported to meet client requests. The overall manufacturing-transportation relevant expenses, including quality and uptime-expedited costs, are mathematically modeled and minimized using optimization methodology to help derive the best manufacturing-delivery operating policy. Moreover, we offer an illustration to validate the results and our research scheme’s capability numerically. This work mainly contributes to the literature by presenting a practical decision-making model. It enables the producers to expose numerous crucial problem-related managerial insights to facilitate producers in deciding the most appropriate manufacturing-delivery policy to meet clients’ multi-criteria demands.

This study examines the joint impact of outsourcing, overtime, multi-delivery, rework, and postponement on a multiproduct fabrication problem. A growing/clear trend in today’s customer requirements turned into rapid response and desired quality of multi-merchandises and multiple fixed-amount deliveries in equal-interval time. To satisfy customers’ expectations, current manufacturing firms must effectively design/plan their multiproduct production scheme with minimum fabrication-inventory-shipping expenses and under confined capacity. Motivated by assisting manufacturing firms in making the right production decision, this study develops a decision-support delayed-differentiation model considering multi-shipment, rework, and dual uptime-reducing strategies (namely, overtime and outsourcing). Our delayed-differentiation model comprises stage one, which makes all common/standard parts of multi-end-merchandises, and stage two, which produces multiple end merchandise. For cutting making times, the study proposes subcontracting a portion of the common/standard part’s lot size and adopting overtime-making end merchandise in stage two. The screening and reworking tasks identify and repair faulty items to ensure customers’ desired quality. The finished lots of end merchandise are divided into a few equal-amount shipments and distributed to customers in equal-interval time. We employ mathematical derivation and optimization methodology to derive the annual expected fabrication- inventory-shipping expense and the cost-minimized production-shipping policy. A numerical demonstration is presented to exhibit our research scheme’s applicability and exposes the studied problem’s critical managerial insights, which help the management make beneficial decisions.

Production management operating in recent competitive marketplaces must satisfy the client desired quality and shorter order lead-time and avoid internal fabricating disruption caused by inevitable defects and stochastic equipment failures. Achieving these operational tasks without undesirable quality goods, missing due dates, and fabrication interruption help the management minimize operating expenditures. Motivated by assisting manufacturing firms in the situations mentioned this study explores a manufacturing system that features quality reassurances through reworking or removal of defectives, correction of probabilistic failures, and partial overtime and outsourcing options for reducing uptime. This study finds the function of system operating expenditures through model building, mathematical formulations, optimization approaches, and algorithm proposition, shows its convexity, and derives the optimal batch time for the studied manufacturing model. Finally, this study offers numerical illustrations to confirm our work’s applicability and disclose its capability to provide various profound crucial system information that helps the management make strategic operating decisions.

Internal supply chains exist in many global enterprises, where manufacturing tasks and sales jobs operate separately, but the management needs to integrate their financial performance reports. In addition, the fabrication planning must meet specific operational goals, such as meeting external clients’ requirements on quality and short order due dates, avoiding internal fabricating interruptions due to inevitable equipment breakdowns, and minimizing overall manufacturing and stock holding costs. Motivated by helping multinational corporations deal with the issues mentioned earlier, this study aims to optimize a finite production rate (FPR)-based supplier-retailer cooperative problem with multi-shipment, rework, subcontracting, probabilistic failure, and expedited rate. Wherein using an outsourcer and expedited-rate help shorten the needed batch producing time significantly; the rework of defects and corrective action on unanticipated breakdown assist in up-keeping the quality and avoiding fabricating delay. We develop an FPR-based model to cautiously represent the considered manufacturing features and activities involved in transporting end products and retailers’ stock holding. Model’s formulating and investigating assists us in gaining the function of operating costs. In addition, optimization procedures with a proposed algorithm help us verify its convexity and decide the model’s best fabricating runtime solution. Finally, we validate how this study works and what important information our model can disclose using a numerical example to facilitate management’s decision-making to end our work.

Manufacturers today need to optimize their fabrication runtime decision by meeting short customer order due dates externally and managing the potentially unreliable machines and manufacturing processes internally. Outsourcing and overtime are commonly utilized strategies to expedite fabricating time. Additionally, detailed analyses and necessary actions on inevitable product defects (i.e., removal of scraps) and equipment breakdowns (such as machine repairing) are prerequisites to fabrication runtime planning. Motivated by assisting today’s manufacturers decide the best batch runtime plan under the situations mentioned above, this study applies mathematical modeling to a hybrid fabrication problem that incorporates partial overtime and outsourcing, inevitable product defects, and a Poisson-distributed breakdown. We develop a model to accurately represent the problem’s characteristics. Formulations and detailed model analyses allow us to find the cost function first. Differential equations and algorithms help us confirm the gain function’s convexity and find the best runtime decision. Lastly, we use numerical illustrations to show our study’s applicability by revealing in-depth crucial managerial information of the studied problem.

The study examines the combined effect of rework, multiple shipments, postponement, and overtime producing common-component on a multiproduct vendor-client incorporated system. Clients’ product demand trend turns to diversity, quality, and rapid response in the current supply-chain environment. Under such a stiff competitive environment, today’s manufacturers must effectively plan their multi-item fabrication to boost utilization and product quality, minimize total relevant costs, and meet short given order lead time. By considering the commonality of the finished goods, required quality, and completion lead time, this study presents an exact model featuring rework of defects, multiple shipments, postponement, overtime producing the mutual component, and satisfying the market needs. Through the techniques of explicitly modeling, formulating, and system cost minimization, this study simultaneously derives the optimal cycle-time and shipping frequency for the studied problem. A numerical example helps show how our model works for any given parameter values and how the variation in single and multiple factors of the problem affects the crucial system performances (e.g., total uptimes, each relevant cost, utilization, total cost, etc.) A wide variety of today’s industries (e.g., automotive, household goods, etc.) and their related supply chains can utilize our decisional model to reveal in-depth managerial insights for planning their fabrication and shipments.

Transnational producers facing the present-day competitive global supply-chain environments need to pursue the most appropriate manufacturing scheme, quality screening task, and stock shipping plan to satisfy customer’s timely multi-item requirements under minimum overall product fabrication-delivery expenses. This study develops a producer-retailer incorporated multi-item two-stage economic production quantity- (EPQ-) based system with delayed differentiation, expedited-rate for common parts, multiple deliveries plan, and random scrap. It aims to assist current manufacturing firms in achieving the aforementioned operating goals. Mathematical methods help us build an analytical model to explicitly portray the studied problem’s features and derive its overall system expenses. Hessian matrix equations and optimization approaches help us prove convexity and derive the cost-minimized fabrication- delivery decision. This study gives a simulated example to illustrate the research outcome’s applicability and the proposed model’s capabilities numerically. Consequently, diverse crucial information becomes obtainable to the manufacturers to facilitate various operating decision makings as follows: (i) the cost-minimized fabrication-delivery policy; (ii) the behavior of system’s overall expenses and operating policy regarding mean scrap rate, and different relationships between common part’s values and completion-rate; (iii) the system’s detailed cost components; (iv) the system’s overall expenses, utilization, and common part’s uptime concerning different common part’s expedited rates; and (v) the collective effects of critical system features on the overall expenses, uptime, and optimal cycle length, etc.

Production planners today must simultaneously face with the time and quality demands of various goods externally and meet limited capacity internally. This study presents a two-stage delayed- differentiation multiproduct model that considers the outsourcing options for common parts, overtime strategy for end products, and quality reassurance to assist in making fabrication runtime decisions that are cost-effective. Stage one produces all necessary common intermediate components for end products. To reduce stage one’s utilization/uptime, this study adopts a partial outsourcing option. Stage two uses an overtime strategy to fabricate end products that further shorten the uptime. The production processes in both phases are assumed to be imperfect. This study employs the reworking/scrapping of random faulty items to reassure product quality. The researchers build a model to depict the proposed problem’s characteristics and used the mathematical modeling, analysis, and optimization approach to determine the best rotation cycle length that minimizes the system’s expenses. Further, in this study, the researchers provide sensitivity analyses and a numerical illustration, which validate the result’s applicability and exhibit its capability. This result contributes to practical multiproduct-fabrication by (1) deriving the optimal manufacturing policy for a delayed-differentiation multiproduct system with dual uptime reduction policies and quality reassurance; and (2) offering a decisional model that allows production planners to explore the collective/separate effect of a quality-ensured and dual uptime reduction strategy on a problem’s operating policy and crucial system performance indicators, which assists in cost-effective decision-making.

Variety, quality, and rapid response are becoming a trend in customer requirements in the contemporary competitive markets. Thus, an increasing number of manufacturers are frequently seeking alternatives such as redesigning their fabrication scheme and outsourcing strategy to meet the client’s expectations effectively with minimum operating costs and limited in-house capacity. Inspired by the potential benefits of delay differentiation, outsourcing, and quality assurance policies in the multi-item production planning, this study explores a single-machine two-stage multi-item batch fabrication problem considering the abovementioned features. Stage one is the fabrication of all the required common parts, and stage two is manufacturing the end products. A predetermined portion of common parts is supplied by an external contractor to reduce the uptime of stage one. Both stages have imperfect in-house production processes. The defective items produced are identified, and they are either reworked or removed to ensure the quality of the finished batch. We develop a model to depict the problem explicitly. Modeling, formulation, derivation, and optimization methods assist us in deriving a cost-minimized cycle time solution. Moreover, the proposed model can analyze and expose the diverse features of the problem to help managerial decision-making. An example of this is the individual/ collective influence of postponement, outsourcing, and quality reassurance policies on the optimal cycle time solution, utilization, uptime of each stage, total system cost, and individual cost contributors.

This study explores the quality control system featuring visual inspection and grade judgment for detecting distortion defects in spectacle lens fabrication. Spectacle lenses must be precisely curved to help accommodate nearsightedness and farsightedness. The curved shape allows the lens to have different curvatures in different areas during grinding. The spectacle lens will be prone to optical distortion when the curvature changes abnormally. Accordingly, this study proposes an automatic distortion flaw inspection system for spectacle lenses to substitute professional inspectors who rely on empirical judgment. We first apply the digital imaging of a concentric circle pattern through a testing lens to create an image of that lens. Second, the centroid–radii model is employed to stand for the shape property of each concentric circle in the image. Third, by finding the deviations of the centroid radii for detecting distortion flaws through a small variation control method, we obtain a different image showing the detected distortion regions. Four, based on the distortion amounts and locations, we establish the fuzzy membership functions and inference rulesets to measure distortion severity. Finally, the GA-ANFIS model is applied to determine the quality levels of distortion severity for the detected distortion flaws. Trial outcomes reveal that the proposed automatic inspection system can help practitioners in spectacle lens fabrication, for it attains a high 94% correct classification rate of quality grades in distortion severity, 81.09% distortion flaw detection rate, and 10.94% fake alert rate, in distortion inspection of spectacle lenses.