Cost reduction for setup and improvement of processes quality are the main target of this research along with free minimal repair warranty for an imperfect production System. This paper deals with the effect of setup cost reduction and process quality improvement on the optimal production cycle time for an imperfect production process with free product minimal repair warranty. Here the production system is subject to a random breakdown from an controlled system to an out-of-control state. Shortages are fully backlogged. The main target to minimize the total cost by simultaneously optimizing the production run time, setup cost, and process quality. A solution algorithm with some numerical experiments are provided such as the proposed model can illustrate briefly. Sensitivity analysis section is decorated for the optimal solution of the model with respect to major cost parameters of the system are carried out, and the implications of the analysis are discussed.Mathematics Subject Classification. 90B05, 90B06.

<abstract><p>Production of defective products is a very general phenomenon. But backorder and shortages occur due to this defective product, and it hampers the manufacturer's reputation along with customer satisfaction. That is why, these outsourced products supply, a portion of required products for in-line production. This study develops a flexible production model that reworks repairable defective products and outsources products to prevent backlogging. A percentage of total in-line production is defective products, which is random, and those defective products are repairable. A green investment helps the reworking process, which has a direct impact on the market demand for products. A classical optimization solves the profit maximization model, and a numerical method proves the global optimal solutions. Sensitivity analysis, managerial insights, and discussions provide the highlights and decision-making strategies for the applicability of this model.</p></abstract>

Remanufacturing is getting attention nowadays due to increasing waste and corresponding emissions. One of the important factors of remanufacturing is the quality of the remanufactured products. The collection and distribution of used products require proper management. Based on this situation, this study discusses a hybrid closed-loop supply chain management in cooperation with a hybrid production system. The vendor comes up with the policy of sharing remanufacturing responsibility by sharing the technology license with other supply chain players. The carbon cap restricts emissions from the entire hybrid production system of the vendor. Other factors of this proposed study are service by the retailer and quality, gift policy, and customer awareness by the vendor. This study examines the scenario under random market demand. Classical optimization provides the solution under the Stackelberg game policy where the vendor acts as leader and the retailer & third party act as followers. This paper considers two scenarios: Scenario A for a continuous distribution and Scenario B for no specific distribution. A comparison is drawn between various motivating factors-based policies to control supply chain management.

<abstract><p>Social activities, economic benefits, and environmental friendly approach are very much essential for a sustainable production system. This is widely observed during the Covid-19 pandemic situation. The demand for essential goods in the business sector is always changing due to different unavoidable situations. The proposed study introduces a variable demand for controlling the fluctuating demand. However, a reworking of produced imperfect products makes the production model more profitable. Partial outsourcing of the good quality products has made the production system more popular and profitable. Separate holding cost for the reworked and produced products are very helpful idea for the proposed model. Moreover, consumption of energy during various purpose are considered. Separate green investment make the model more sustainable and eco-friendly. The main focus of the model is to find the maximum profit through considering optimum value of lot size quantity, average selling price, and green investment. The classical optimization technique is utilized here for optimizing the solution theoretically. The use of concave 3D graphs, different examples, and sensitivity analyses are considered here. Furthermore, managerial insights from this study can be used for industry improvement.</p></abstract>

In this proposed research, clear prospects of a real life marketing scenario, by analyzing a price discount policy and variable demand, are derived. The proposed study presents a production model along with time-dependent and selling price related demand for decaying items. Items deteriorate over time, therefore, considering deterioration in this model makes it more acceptable to the present marketing situation. The concept of delay-in-payments is utilized in this inventory system. In this research, a retailer buys some products, enjoys constant credit-period offers which are provided by the supplier. This model depicts a price discount strategy which is based on purchasing cost to attract more consumers in any business industry. By using this strategy, any manufacturer or business may gain more profit in comparison to methods suggested by earlier literature. The average profit function of the inventory system is maximized analytically and also finds the selling-price per unit and duration of the inventory cycle optimally. A numerical example, along with a case study and their graphical representations, are incorporated to verify the optimality of this research very clearly. The findings of this research have maximized the average profit function more than the existing literature.