The present work intends to optimize a hybrid delayed differentiation multiproduct economic production quantity-EPQ model with the scrap and end-products multi-shipment policy. Since the requirements of multi-goods have a standard part in common, our fabrication planning adopts a two-phase delayed differentiation strategy to make the standard components first and produce the finished multi-goods in the second phase. Implementing a partial subcontracting option (with the additional expense) for the standard parts helps us to expedite the required uptime in the first phase. A screening process identifies the faulty items that need to be removed to ensure the in-house production quality. A multi-shipment plan delivers the finished lot of end-products to clients in fixed time intervals. This study optimizes the overall operating expenses of this intra-supply chain system, including fabrication, delivery, and client stock holding, through our proposed modeling, formulation, and optimization procedure. In addition, this study gives a numerical demonstration of the obtained results’ applicability and usefulness to managerial decision-making.

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.

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

A hybrid batch fabrication plan involving an outsourcing option is often established to deal with the in-house capacity constraint and/or meet timely demand with a reduced cycle time. Besides, the occurrences of unpredictable equipment malfunction and imperfect product quality should also be effectively managed during in-house fabrication to meet the production schedule and the required quality level. To address these concerns, we examine a hybrid economic production quantity (EPQ) problem with an unreliable machine and quality reassurance; wherein, an outside provider helps supply a portion of the batch at a requested timing and desirable quality, but at the price of a higher than in-house unit cost. Corrective action is performed immediately when a Poisson-distributed breakdown occurs. Once the equipment repairing task completes, the interrupted lot’s fabrication resumes. Random nonconforming products are identified, and the re-workable items among them are separated from the scraps. A rework task follows the regular process in each cycle at an extra cost. A portion of reworked items fails and are scrapped. A model portraying the problem’s characteristics is built, and an optimization methodology is utilized to find the optimal runtime solution to the problem. A numerical example reveals our result’s applicability, and specific managerial implications are suggested.

This study explores the optimal fabrication runtime for a buyer-vendor incorporated system featuring repairable items, stochastic breakdown, accelerated rate, and multi-delivery strategy. Operating in today’s competitive global market, transnational production firms make every effort to meet client requirements in terms of the due date and quality goods. Further, they also must handle all inevitable events incurred in the manufacturing process, such as unanticipated equipment breakdowns and defective products, with caution to avoid production schedule delay and cost overrun. To examine such a vendor-buyer incorporated system, we build a model to characterize the aforementioned features in the system. The function of total system cost is derived through formulation and analyses. The optimization method and a recursive algorithm are employed to help in deriving the optimal (i.e., cost minimization) fabrication runtime for our problem. An example numerically illustrates how our model, method, and algorithm work. It also reveals the capability of our model in analyzing the impact of each and/or joint feature(s) (e.g., the breakdown, accelerated rate, rework, multi-delivery strategy) on the system’s utilization, optimal runtime, total expenses, and individual cost contributor to assist in managerial decision making, and hence, enabling the firm to gain competitive advantage.

This study develops a postponement model for the multi-item replenishment decision featuring commonality, an overtime strategy, and product quality reassurance. A single machine is used to meet the steady demand for multiple products wherein product commonality exists among these end products. The proposed postponement model assumes that all pertinent common parts are fabricated in Stage 1 and the finished products are sequentially fabricated in Stage 2. Random nonconformance rates are associated with both fabrication stages, the repairable nonconforming common parts are separated from scrap, and reworking in each cycle helps ensure product quality for each completed batch. An overtime strategy is used to reduce the lengthy fabrication and rework times for common parts. Mathematical analyses and derivation allow us to obtain the total system costs. The optimization method helps find the optimal replenishment decision. We provide a numerical illustration to show (1) how our model works; (2) the individual impact of the system features (e.g., the overtime factor, commonality in terms of the common part completion rate and its relative value, and the issues pertaining to scrap/rework) on the optimal decision, utilization, and the total system cost; and (3) the collective influence of system features on the highlighted problem. This proposed decision-support model helps production managers achieve the operating goals of lowering total system expenses and cutting the length of the production cycle.

This research constructs a mathematical scheme to explore replenishment-shipment decisions for a multiproduct producer-client coordinated finite production rate (FPR) model with the postponement, rework, and subcontracting plan. The considered multiple goods have a common component, and a batch FPR fabrication with postponement is planned to meet the annual multiproduct requirements. The first fabricating phase makes only the standard components needed for a batch and subcontracts a proportion of them (with additional cost) to expedite the process. In contrast, the second fabricating phase produces the finished multiple merchandise in sequence. The in-house rework processes with extra expense help retain the desirable quality. Each merchandise’s finished batch is transported to the clients in equal-sized numerous shipments. This study derives the optimal batch cycle length and transporting frequency by minimizing the overall fabricating-shipment expenses (including clients’ holding costs). This work offers a numerical example demonstrating various crucial system features influenced by the factors of subcontracting, postponement, rework, and transportation policies to facilitate managerial decision making in industries.

This study presents a multiproduct fabrication cost-minimization model featuring external providers, commonality, rework, and postponement in the supply chain environment. Customers’ requirements simultaneously emphasize quality, variety, and fast response time in current markets. To satisfy customer needs, most manufacturers in various industries (e.g., clothing, household goods, automotive, etc.) plan their multiproduct fabrication by incorporating a postponement strategy, rework process, and an outsourcing option. Motivated by the viewpoints above, this study offers a decision support system to address customers’ external expectations while optimizing internal operating expenses and machine utilization. We propose a single-machine, two-stage delayed differentiation system under a rotation cycle policy. All needed common parts are made in stage one, and stage two fabricates different end products. An external provider is hired to supply partially needed common parts to shorten uptime. The defective items are inevitably produced in both stages. They are categorized and reworked to maintain the desired product quality. Finally, we derive an optimal cost-minimization rotation cycle for our model and use a numerical example to investigate the collective and individual influences of reworking, postponement, and outsourcing to external providers on the multiproduct fabrication problem. In summary, this study can offer an optimization solution for production planning in various modern industries.

This research explores the collective impact of overtime, random breakdown, discontinuous issuing rule, and scrap on batch production planning in a supply-chain environment. In today’s global business environment, manufacturing firms encounter numerous operational challenges. Externally, they must promptly satisfy the customers’ various requests, while internally, they must cautiously manage several inevitable issues in the fabrication process. These issues might be concerned with scrap, random breakdown, etc. Resolving such issues is crucial for meeting the due dates of customers’ orders, adhering to the expected manufacturing schedules, product quality, and minimizing the total fabrication-transportation-inventory costs. The study develops a model to characterize the system’s features mentioned above and assist the manufacturers with batch fabrication planning. The model proposes a solution process with an algorithm seeking an optimal runtime for the system. Additionally, it gives a numerical illustration depicting the collective and individual impacts of these special features on the operating policy and other performance indices. This model and the research findings can facilitate manufacturers’ decision-making for green batch fabrication and enhance competitive advantage.