This paper presents a framework for reverse logistics aimed at managing reusable items within supplier-buyer relationships to promote sustainability and reduce environmental impact. In this model, the supplier produces and inspects items, shipping only perfect items to buyers, while recycling or disposing of imperfect ones. Returned items from consumers are categorized as either reusable or damaged at a collection center. The concept of a circular economy encourages the return and refilling of reusable items, while damaged items are recycled. Additionally, the model incorporates carbon emissions considerations across production, storage, transportation, and landfilling, emphasizing the importance of environmental factors. To evaluate the sustainability and economic efficiency of the supply chain network, both Stackelberg and Nash equilibrium strategies are employed. The paper provides a mathematical framework based on lemmas to analyze the impact of the network and promote sustainable supply chain practices. In this cycle, consumers use the items and eventually discard them. To support a zero-waste policy, the supplier labels the bottles with barcodes to identify used items upon collection. The supplier has two different rates at which they purchase used bottles from consumers. Refilled bottles are sent back for reuse, while damaged bottles are either repurposed as raw materials or disposed of. The research paper aims to develop a mathematical model that determines the buyer's cycle time and the number of deliveries from the supplier to the buyer, ensuring that the buyer's demand is met without shortages.

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.

Tehran, as one of the most populated capital cities worldwide, is categorized in the group of highly polluted cities in terms of the geographical location as well as increased number of industries, vehicles, domestic fuel consumption, intra-city trips, increased manufacturing units, and in general excessive increase in the consumption of fossil energies. City logistics models can be effectively helpful for solving the complicated problems of this city. In the present study, a queuing theory-based bi-objective mathematical model is presented, which aims to optimize the environmental and economic costs in city logistics operations. It also tries to reduce the response time in the network. The first objective is associated with all beneficiaries and the second one is applicable for perishable and necessary goods. The proposed model makes decisions on urban distribution centers location problem. Subsequently, as a case study, the fruit and vegetable distribution network of Tehran city is investigated and redesigned via the proposed modelling. The results of the implementation of the model through traditional and augmented ε-constraint methods indicate the efficiency of the proposed model in redesigning the given network.

The concept of green inventory systems is very important for economic growth and development in the era of sustainable development. There is a special need for green inventory systems to identify and manage perishable products since spoilage and deterioration can lead to significant losses of items, which negatively affect the satisfaction of consumers. As perishable products decay continuously (such as vegetables, fruits, milk, juices, frozen foods, baked foods), their demand is adversely affected as well as customers' purchasing decisions. The more realistic assumption is a price-sensitive demand. As well as deterioration rates, perishable products have an expiration date-dependent deterioration rate. Further, inventory holding, and the deterioration of perishables contribute significantly to carbon emissions when operating the inventory system. A carbon tax policy is more flexible and effective when it comes to reducing carbon emissions due to its environmental conscious nature. We develop two sustainable inventory procedures for perishable items based on a practical scenario in which the buyer has a limited storeroom. So, to achieve sustainability goals, a model for inventory management for perishable products based on expiration dates is presented in this paper. We distinguish between two inventory schemes: (i) one that allows shortages and fractional backlogs, and (ii) one that does not allow shortage. In both schemes, both the decay rate and demand function show an upward trend against storage time. Since the decay rate increases with storage time, it is assumed that the cost of storing items is linearly related to storage time. numerical examples along with a real-life case study are presented to validate the inventory schemes after several decision-making findings have been derived.