In recent years, various issues such as industrial waste and emissions of greenhouse gases have led to serious environmental pollution. Industrial managers nowadays need to regard cutting carbon emissions as one of their principal responsibilities in relation to the environment, as industry is a major source of carbon emissions. Two prominent regulatory approaches to reducing carbon emissions from operations are the carbon tax and the cap-and-trade system. The existing literature on inventory studies has often considered the market-expanding effects of greening efforts. Nevertheless, a number of additional factors exert influence on greening efforts, with the cost reduction effect representing a critical one. This paper develops an inventory system in which each time a lot of items is received, a proportion of items are found to be of imperfect quality; to identify these, the retailer carries out a 100% inspection of goods received. Following this inspection, the saleable items are added to the inventory in the warehouse in batches of equal size, rather than one by one, and the retailer allows backordering to meet demand. Carbon emissions are incurred at every stage, including ordering, purchasing, repairing, transporting, and holding, so advanced green technology is employed to reduce them. Imperfect products can be sold to a second-hand market or sent to a repair shop. The model discussed in this paper calculates, for both options, the most cost-effective lot size for orders, shortage quantity, scale of green investment and number of batches.

This research proposes a dynamic decision-making framework for a hybrid production system that incorporates manufacturing and remanufacturing procedures into a closed-loop supply chain network with merchandise substitution and shortages within traditional markets (TM) and electronic markets (EM). In particular, we develop models of profit maximization and equilibrium analysis by using calculus with dynamic programming under four business schemes, including a manufacturing-only model within TM/EM and a hybrid remanufacturing model within TM/EM. Dynamic decision-making planning was taken for brand-new and like-new decayed merchandise in hybrid production systems. The results demonstrate that solutions generated within EMs surpass those within TMs in terms of maximizing profits. Further, the hybrid remanufacturing model did not surpass the manufacturing-only model under a general setting, but had better performance under certain conditions, including intense competition, a smaller remanufacturing cost, a larger brand-new merchandise market size, and a smaller like-new merchandise market size.

The present paper develops a sustainable framework under a supply chain environment by considering a vendor and a buyer. The vendor governs the manufacturing process to serve the demand of the buyer. The manufacturing system is imperfect which ends up producing some fraction of defectives. For the sake of maintaining the goodwill of the organization, it is imperative to maintain the quality standards. Thus, the buyer employs the screening process to bifurcate the perfect items from the imperfect ones. The imperfect items secluded after screening are reverted back to the vendor, for which a warranty cost is incurred. Further, in an attempt to achieve sustainability the model considers the carbon-emissions costs during the transportation process. A one-time discrete investment is also considered for minimizing the setup cost of the vendor for subsequent cycles. The models are developed for the case of the individual decision and for the joint verdict of the players under consideration. Moreover, it has been proved that the integrated model performs proficiently over the individual model. The objective is to jointly optimize the costs sustained by the two players. Numerical analysis and sensitivity analysis is done for imparting the validity and robustness of the model.

In this paper, we consider the inventory model for perishable items with quadratic trapezoidal type demand rate, that is, the demand rate is a piecewise quadratic function under constant deterioration rate. The model consider allows for shortages and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The result is illustrated with numerical example. Finally, we discuss sensitivity analysis for the model.

In today’s era of higher competition in the business, there are many conditions such as offered concession in bulk purchasing, seasonality, higher ordering cost, etc., which force a retailer to purchase more quantities than needed or exceed the storage capacity. So in this situation the retailer has to purchase an extra warehouse named as rented warehouse to stock the extra quantity. In this paper an inventory model for deteriorating products with selling price dependent rate is developed. The occurring shortages are assumed to be partially backlogged and cycle time is also variable. The purpose of the development of this model is to compute the amount and time of order which can optimize the total average cost of the system. A solution procedure and numerical example are presented to illustrate the implementation of the proposed study. Sensitivity analysis concerning with distinct system parameters is also presented to demonstrate the model.

Deterioration of items is a phenomenon which cannot be neglected as it may provide absurd result. In high-tech business market, deterioration is not always constant but it is time dependent. This paper presents inventory model for time dependent deterioration and time dependent demand under shortages. The mathematical model is provided to optimize the cycle time by minimizing the total cost. Numerical results are discussed to validate the proposed model. The variation of the optimal solution for different parameters is discussed for some instances.

The outset of new technologies, systems and applications in manufacturing sector has no doubt lighten up our workload, yet the chance causes of variation in production system cannot be eliminated completely. Every produced/ordered lot may have some fraction of defectives which may vary from process to process. In addition the situation is more susceptible when the items are deteriorating in nature. However, the defective items can be secluded from the good quality lot through a careful inspection process. Thus, a screening process is obligatory in today’s technology driven industry which has the customer satisfaction as its only motto. Moreover, in order to survive in the current global markets, credit financing has been proven a very influential promotional tool to attract new customers and a good inducement policy for the retailers. Keeping this scenario in mind, the present paper investigates an inventory model for a retailer dealing with imperfect quality deteriorating items under permissible delay in payments. Shortages are allowed and fully backlogged. This model jointly optimizes the order quantity and shortages by maximizing the expected total profit. A mathematical model is developed to depict this scenario. Results have been validated with the help of numerical example. Comprehensive sensitivity analysis has also been presented.

This study deals with an economic order quantity model to find out the optimal selling price and optimal ordering quantity for the products which deteriorates over time. The demand for the products depends on available stock level and selling price of the products. The shortages are allowed, and it is assumed that the occurring shortages are partially backlogged. Depending on the rate of backlogging two models are presented in this study. The first model assumes a constant rate of backlogging, while in second model the backlogging rate is assumed to be dependent on waiting time. Numerical example and sensitivity analysis are presented to illustrate the results of the proposed model.

In this paper, we develop a two-warehouse imperfect production model under two cases: (i) model starts with shortages (ii) model ends with shortages. Most of the researchers proposed the models for perfect items but we develop for imperfect quality items, which is very realistic. Demand is taken as time dependent and dependent on the production. Holding cost in rented warehouse (RW) is greater than own warehouse (OW). Deterioration is taken as Weibull distribution in both OW and RW. Shortages are allowed and partially backlogged. The effect of learning on production cost is also considered. Learning from one cycle to other cycle, improve the efficiency of the organization. A numerical example including the sensitivity analysis is given to validate the results of the production-inventory model.

Keeping in view the concern about environmental protection, the study investigates effects of remanufacturing in an integrated production inventory model consisting of forward and reverse supply chain over infinite planning horizon. This article is developed for the deteriorating products with stock dependent demand under shortages. To make the model more realistic, flexibility of production system has been incorporated during forward manufacturing. We derive total cost function and using the results of calculus, optimum production policy is derived, which minimizes the total cost incurred. The results are discussed with a numerical example to illustrate the theory.