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.

In this study, under the carbon cap-and-trade mechanism, the ordering cost presents a stepwise function for ordering quantity, and the optimal economic ordering quantity model aims to explore the manufacturer's total cost minimization in the finite planning horizon, in combination with the actual situation that the product will produce carbon emissions during transportation and storage. The economic order quantity (EOQ) model with stepwise ordering cost is applicable to the decision environment in which goods are utilized by sea, by rail or by air (e.g., the order cost is charged in addition to the basic fixed cost, the importer of raw materials will pay an additional freight related to delivery, such as the rent for the use of container numbers.). A heuristic algorithm is also proposed to analyze the relevant properties of the optimal solution of the model and to solve the optimal order times and quantities of the manufacturer under the constraint of carbon policy.We further compared the optimal order times with the case without carbon constraint and the order times corresponding to the manufacturer's realization of the minimum carbon emission, and obtained the conditions for the manufacturer to achieve low cost and low emission under the carbon policy.Finally, the theoretical results of the model are verified by numerical examples,and the influence of relevant parameters on the inventory strategy of manufacturers is discussed. The results show that under the carbon cap-and-trade policy, there is an optimal ordering strategy that minimizes the total cost of the manufacturer in the finite horizon. When the demand of the manufacturer is under finite horizon and the carbon policy is equal to the specific multiplier of orders, the manufacturer can achieve a win-win result of low cost and low emissions.

To respond to the adoption of carbon pricing regulations, researchers and industry are developing low carbon inventory models that can meet emission reduction targets while maintaining company profits. The challenge is getting tougher when the company is still facing problems related to imperfect product quality. This research solves this problem by developing an economic order quantity (EOQ) model by considering several sources of carbon emissions, as well as the influence of the defective rates, different demand rates, selling price and holding cost for defective products, and shortages backorder. The objective function of the formulated mathematical model is to minimize the total costs which include the emission costs. A numerical example is developed to illustrate the model based on the previous data set. Sensitivity analysis is also carried out to validate the model and to learn more about the system characteristics. The total emissions are calculated and the affecting factors are identified.

The study objects for determining whether or not a relationship exists between inventory management of the listed pharmaceutical firms at Amman Stock Exchange, and the profitability of these firms, and whether or not inventory management affects firm profitability. Only three pharmaceutical firms were found listed at Amman Stock Exchange by the end of 2020, and therefore, the annual data of the three firms along the period 2009-2019 were collected and used in the analysis and hypothesis testing. Inventory turnover and average inventory holding period were used as indicators for inventory management at a reciprocal form, whereas, return on assets was used as a measure of firm profitability. Using the Pearson correlation method, the analysis and hypothesis testing demonstrated that a significant positive relationship exists between inventory turnover and return on assets, and a negative significant relationship exists between average inventory holding period and return on assets. Moreover, using the ordinary least square method, the study shows that inventory management has a positive significant effect on firm profitability. More studies regarding inventory management and firm profitability relationships, are recommended to be performed on other manufacturing industries than pharmaceutical firms.

Inventory control of deteriorating items constitutes a large part of the world’s economy and covers various goods including any commodity, which loses its worth over time because of deterioration and/or obsolescence. Vendor managed inventory (VMI), which is a win-win strategy for both suppliers and buyers gains better results than traditional supply chain. In this research, we study an economic order quantity (EOQ) with shortage in form of partial backorder under VMI policy. The model is concerned with multi-item subject to multi-constraint including storage space, time period and budget constraints. Two metaheuristic algorithms, namely Simulated Annealing and Tabu Search, are used to find a near optimal solution for the proposed fuzzy nonlinear integer-programming problem with the objective of minimizing the total cost of the supply chain. Furthermore, the sensitivity analysis of the metaheuristic parameters is performed and five numerical examples containing different numbers of items are conducted in order to evaluate the performance of the algorithms.

In the recent decade, studying the economic order quantity (EOQ) models with imperfect quality has appealed to many researchers. Only few papers are published discussing EOQ models with imperfect items in a supply chain. In this paper, a two-echelon decentralized supply chain consisting of a manufacture and a supplier that both face just in time (JIT) inventory problem is considered. It is sought to find the optimal number of the shipments and the quantity of each shipment in a way that minimizes the both manufacturer’s and the supplier’s cost functions. To the authors’ best knowledge, this is the first paper that deals with imperfect items in a decentralized supply chain. Thereby, three different game theoretical solution approaches consisting of two non-cooperative games and a cooperative game are proposed. Comparing the results of three different scenarios with those of the centralized model, the conclusions are drawn to obtain the best approach.

Vendor Managed Inventory (VMI) is one of the effective techniques for managing the inventory in supply chain. VMI models have been proven to reduce the cost of inventory compared with traditional ones under some conditions such as constant demand and production expenditure. However, the modeling of the VMI problem has never been studied under some realistic assumptions such as price dependent demand. In this paper, three problem formulations are proposed. In the first problem formulation, we study a VMI problem with one buyer and one supplier when demand is considered to be a function of price and price elasticity to demand, and production cost is also a function of demand. The proposed model is formulated and solved in a form of geometric programming. For the second and the third models, we consider VMI problem with two buyers and two suppliers assuming that each buyer centre is relatively close to the other buyer centre. Each supplier has only one product which is different from the product of the other supplier. Two suppliers cooperate in customer relationship management and two buyers cooperate in supplier relationship management as well, so the suppliers send the orders of two buyers by one vehicle, simultaneously. For the third model, an additional assumption which is practically applicable and reasonable is considered. For all the proposed models, the optimal solution is compared with the traditional one. We demonstrate the implementation of our proposed models using some numerical examples.