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.

The study applies a postponement strategy to a multi-item fabrication-shipment decision making in a vendor-buyer coordinated environment with multi-delivery, quality reassurance, and overtime. To cope with the recent client demand trend asking for rapid response, quality, and diversified goods, today’s manufacturers require a multi-item production-shipping scheme to satisfy customers’ needs in cost-saving, quality, and timely matter. In our model, we first produce all needed mutual components and postpone manufacturing of finished goods in the second phase. To expedite mutual parts’ fabrication time, overtime is used. Product quality is reassured through screening the defeats and reworking repairable defectives in both fabrication phases. To decide the optimal fabrication-shipment policy, we build a math model and apply the cost minimization technique to the problem. Upon deriving the optimal policy, we utilize an example to demonstrate how our model works and its capability in exposing various previously inaccessible information to the problem. These detailed results can facilitate managerial decision-making and boost the performance of such a specific multi-item postponement fabrication-shipment system in cost-saving, product quality, and timely response.

Operating in today’s turbulent and competitive world marketplaces, manufacturers must find the best production scheme and delivery policy to meet timely client’s multiproduct requirements and minimize the total manufacturing-shipment expenses. This study proposes a two-stage delayed differentiation model for a multiproduct manufacturer-retailer coordinated supply chain featuring the adjustable-rate for making common parts and a multi-shipment policy for transporting finished goods. The aim is to help present-day manufacturers achieve their operational goals mentioned above. The mathematical techniques help us build a specific model to explicitly represent the problem and derive its overall operating expense. Then, the convexity of the total expense is verified by Hessian matrix equations. The differential calculus helps derive the cost-minimized fabrication-shipment decision. This study offers an example to demonstrate the applicability and capabilities of our proposed model numerically. The following crucial information has been made available to the managers to facilitate their operating decision makings: (1) the problem’s best fabrication-shipment policy; (2) the collective influence of various common part’s completion rates and values on the problem’s total expenses and optimal fabrication-shipment policy; (3) the impact of various adjustable-rates in stage one on utilization and stage one’s uptime; (4) the details of cost contributors to the problem; and (5) the collective impacts of critical features on the problem’s performance.

This study employs mathematical modeling to explore the effects of overtime option, rework, and discontinuous end-item issuing policy on the economic manufacturing quantity (EMQ) model. Conventional EMQ model assumed that all products fabricated are of good quality and are issued under continuous policy. In real world, however, nonconforming items are randomly produced, due to diverse unexpected factors in fabrication process. When finished items are to be distributed to outside locations, discontinuous multi-shipment policy is often used rather than continuous rule. In addition, with the intention of increasing short-term capacity or shortening replenishment cycle length to smooth the production planning, adopting overtime option can be an effective strategy. To cope with the aforementioned features in real production systems, this study incorporates overtime option, rework, and multi-shipment policy into the EMQ model and explores their joint effects on optimal lot size and number of shipments, and on other relevant system parameters. Mathematical modeling and Hessian matrix equations enable us to derive the optimal policies to the problem. Through the use of numerical example, the applicability of research result is exhibited and a variety of significant effects of these features on the proposed system are revealed.

This study uses an alternative fabrication scheme to study the effect of rework of nonconforming items and delayed differentiation on a multiproduct supply-chain system. Traditional economic production quantity model focuses on a single-product inventory system where all products made are assumed to be perfect quality and finished products are issued continuously. To increase machine utilization, lower quality costs in production, and reflect the real-world vendor-buyer integrated systems Chiu et al. (2016a) [Chiu, Y-S.P., Kuo, J-S., Chiu, S. W., Hsieh, Y-T. (2016a). Effect of delayed differentiation on a multiproduct vendor–buyer integrated inventory system with rework. Advances in Production Engineering & Management, 11(4), 333-344.] employed a single-machine two-stage production scheme to study the effects of rework and delayed differentiation on a multi-product supply-chain system. With the intention of further reducing fabrication cycle time, this study considers an alternative two-machine two-stage fabrication scheme to re-explore the problem in Chiu et al. (2016a). Machine one solely produces all common parts for multiple end products. Then, machine two fabricates the customized multiproduct using a common cycle time strategy. Through the use of mathematical modeling and analyses, the optimal production cycle length and distribution policy are derived. Numerical examples are provided to demonstrate practical usage of the research results, and show its significant benefit in reducing fabrication cycle time compared to that obtained from prior studies that used different schemes.