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.

When making a batch production decision for a buyer-vendor coordination system, the management must simultaneously consider the operating expenses incurred in in-house manufacturing and inventory, finished goods’ shipping, and stock holding at the retailer end. Achieving the operational goals of desirable quality, minimal production disruption, and shortening fabrication time help minimize overall in-house operating costs and maximize customer satisfaction. This work builds an operating cost minimization model for buyer-vendor coordination batch system with scrap, breakdowns, overtime, multi-shipment, and an external source to assist the management in optimizing their production-delivery plan. Removing inevitable scrap items ensures product quality, and correction action on stochastic equipment breakdown prevents unacceptable production delays. Implementing partial overtime and adopting an external source expedites in-house manufacturing time. Model construction and cost analysis enable us to decide the operating expense function. Then, we verify the function’s convexity and decide our model’s best manufacturing runtime with the differential calculus and a proposed algorithm. Furthermore, the numerical demonstrations are used to exhibit our work’s applicability and show what kinds of crucial in-depth information can be disclosed and made accessible to the production planners for their decision-making.

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.

This study examines the collective impact of postponement, scrap, and subcontracting standard components on the multiproduct replenishing decisions. Rapid response, desirable quality, and various goods guide the client’s demands in today’s competitive market. Therefore, many manufacturing firms search for alternative fabrication and outsourcing strategies during the production planning stage to satisfy the client’s expectations, minimize fabrication-inventory costs, and smoothen machine utilization. To effectively help producers meet today's client's needs and enhance their competitive advantage, we develop a two-stage multiproduct replenishing system incorporating scraps, standard parts subcontracting, commonality, and delayed differentiation. To reduce the production uptime, stage one has a hybrid fabrication process for the common components (i.e., a partial outsourcing strategy), and stage two manufactures the finished multiproduct. In-house fabrication processes in both stages are imperfect; a screening process detects and removes scraps to maintain the finished batch quality. We determine the cost-minimized operating cycle. The findings reveal the collective impact of postponement, scrap, and external suppliers on this multi-product replenishment problem and can be used to facilitate production planning and decision-making.

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.

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.

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.

Production managers face the growing trend of rapid-response orders and inevitable production defects and failures; they must carefully measure these factors’ effects to minimize operating expenditures and operational disruption. Inspired by assisting producers decide the optimal runtime policy under these real situations, this work investigates the collective impact of rework, expedited-rate, external source, and machine failures on such a specific fabrication system. A partial outsourcing and expedited manufacturing rate are considered in the studied system to reduce the batch fabricating time. Additionally, defects rework and repair failure machines are implemented to retain the quality and avoid production disruption. Our research scheme consists of (1) developing a model for the mentioned manufacturing characteristics; and (2) analytical and optimization techniques for deciding the best batch runtime decision by minimizing the system’s overall expenses. Lastly, we provide numerical examples to demonstrate the model’s applicability and disclose important, in-depth characteristics that facilitate managerial decision-making.

Facing stiff competition in worldwide markets, capability of meeting timely demands of multiproduct and satisfying customer’s desired product quality are essential to present-day manufacturers. Motivated by achieving the aforementioned goals, this research intends to find most economic common cycle length for a multiproduct finite production rate (FPR)-based inventory system, wherein, imperfect production process with expedited fabrication rate and random scrap is assumed. Extra setup and unit costs are associated with the adjusted rate, and imperfect products are screened and scrapped. A mathematical model is cautiously constructed to examine and resolve the problem. A numerical illustration is employed to exhibit the applicability of the proposed method. Except finding the most economic common cycle time for the problem, core contribution of this study also is associated with the individual and combined impact(s) of important factors to the problem, and hence, enabling management of manufacturing firms to make efficient/cost-effective decision and gain competitive advantages.