Inventory control systems are supposed that the purchasing cost is paid at the time of delivery of product. But sometimes in order to motivate the customers to buy more, supplier lets customers to pay the purchasing cost under delay payment method as an incentive policy. In this paper a periodic inventory control model is considered in which the interval between two replenishments is a random variable. Indeed the economic order quantity model is developed under two policies including delayed payment and stochastic replenishment interval. It is proved that the profit function of retailer is concave and the main aim of this paper is to determine the maximum level of inventory such that the profit of retailer is maximized. In continue in order to show the applicability of the proposed model, several numerical examples and sensitivity analyses have been presented.

Joint optimal inventory control and preventive maintenance are interested in many research and has a potential impact on the performance of manufacturing systems. In addition, due to the uncertainty in demand, maintenance and inventory shortages are almost inevitable. Therefore, determining the optimal amount of buffer level, the time required to create additional storage space to address the loss, and the maintenance time is a concern for many manufacturers. Paper studied a single-machine production unit with incremental failure rates. The system begins with a h-sized inventory stored in period A and stops as soon as it reaches period m, whichever occurs earlier, and is subject to maintenance. The buffer inventory during this period. A mathematical model and a numerical approach are used to obtain optimal values of variables simultaneously to minimize the average total cost and satisfy the access constraint. The results show that, in the presented model, the total cost and decision variables are highly sensitive to the inventory holding cost but not also for the occurred scenario.

Improving participation in voluntary activities in Iran is important because increasing productivity among young people, given the country's young population, contributes to community sustainability. Therefore, a better understanding of volunteer motivation in Iranian youth is needed. The Volunteer Functions Inventory (VFI) for assessing volunteer motivations has good psychometric properties and is adapted to several languages, but no validated Iranian translation yet exists. The purpose of this study was to investigate the psychometric Characteristics of voluntary functions inventory in members of Iranian Red Crescent Society. Sample size was 595 members of Youth Organization of Iranian Red Crescent Society from 31 provinces and 175 cities of Iran that were selected by multi-stage cluster sampling method and responded to voluntary functions inventory. Data were collected using a demographic sample and voluntary functions inventory (VFI). Confirmatory factor analysis using principal components method was used for data analysis. The results of the present study showed that the voluntary functions inventory had validity and reliability. Also, the factor structure showed that 29 items and 6 factors well assess people's attitudes to volunteering, and the structure of this inventory was well-fitted and confirmed all goodness of fit models. The present study provides the use of the Iranian translation of the Voluntary Functions Inventory (6 scales and 29 items) to assess volunteer motivation among young Iranian volunteers.

In industrial and commercial settings, inventory systems often involve managing multiple products with diverse demand patterns, making the direct application of the single-item newsvendor model inefficient. To address this complexity, this study proposes an adaptation of the newsvendor model through demand aggregation, where related items are grouped into a product family. By aggregating demand and financial parameters, the traditional newsvendor approach can be extended to multi-item systems, simplifying the inventory management process. This method was tested in two different case studies—a coffee roaster company and a meatball producer—demonstrating its validity and applicability. The aggregated newsvendor model was found to enhance inventory accuracy and efficiency, reducing random error and improving operational performance. This approach offers a valuable extension of the newsvendor model, with potential for broader application across various industries.

The current paper deals with modeling a resilient, sustainable supply chain with an inventory management approach by the seller under the uncertainty of demand and system costs. The importance of inventory management by the seller in the sustainable supply chain has led them to consider a set of buyers and sellers whose goal is to minimize the total costs of ordering, shortage, maintenance, and use of the vehicle to make the right decisions to fulfill the orders. Due to the indeterminacy of the model parameters, the robust-fuzzy-probabilistic optimization method has been used. The calculation results with the invasive weed optimization algorithm and the Baron method show that with the increase in the uncertainty rate in the network, the amount of demand has increased. Therefore, the total ordering, maintenance, and shortage costs have increased. Also, with the increase of the stability coefficient of the model, the total cost of inventory management by the seller has increased, and a greater amount of customer demand has been estimated. On the other hand, with the increase in resilience, the amount of orders transferred to the buyer has decreased. Also, the calculation results show the high efficiency of the invasive weed optimization algorithm in solving the resilient, sustainable supply chain model with the seller's inventory management approach.

The current paper deals with modeling a resilient, sustainable supply chain with an inventory management approach by the seller under the uncertainty of demand and system costs. The importance of inventory management by the seller in the sustainable supply chain has led them to consider a set of buyers and sellers whose goal is to minimize the total costs of ordering, shortage, maintenance, and use of the vehicle to make the right decisions to fulfill the orders. Due to the indeterminacy of the model parameters, the robust-fuzzy-probabilistic optimization method has been used. The calculation results with the invasive weed optimization algorithm and the Baron method show that with the increase in the uncertainty rate in the network, the amount of demand has increased. Therefore, the total ordering, maintenance, and shortage costs have increased. Also, with the increase of the stability coefficient of the model, the total cost of inventory management by the seller has increased, and a greater amount of customer demand has been estimated. On the other hand, with the increase in resilience, the amount of orders transferred to the buyer has decreased. Also, the calculation results show the high efficiency of the invasive weed optimization algorithm in solving the resilient, sustainable supply chain model with the seller's inventory management approach.

Vendor management inventory (VMI), as one of the inventory management methods, reduces the cost of inventory in the chain, quick response to customers, increased service level, customer satisfaction, and improve collaboration between the members of the supply chain. In this study, a bi-level supply chain model with one manufacturer and one retailer under a vendor management inventory policy is investigated. The manufacturer produces a single product by the production capacity constraint at wholesale price and delivers the product to the retailer who then sells the product in the dispread market at retail price. The demand rate for the product in the retailer market is assumed to be a decreasing function of the price and an increasing function of the service level. The manufacturer determines its wholesale price, product’ s replenishment cycle time, and backorder quantity to maximize its profit. Retailer determines the optimal retail price and service level to maximize its profit. This problem formulated as a Stackelberg game model with consideration manufacture as a leader and retailer as a follower. To search the Stackelberg game equilibrium, a solution algorithm has been proposed. A numerical study has been conducted to demonstrate how the algorithm works and to understand the influences of decision variables and parameters. Also, in order to validate the proposed model, sensitivity analysis has been performed on some parameters.