This paper presents a mathematical model for an INVENTORY control system in which customers’ demands and suppliers’ service time are considered as stochastic parameters. The proposed problem is solved through queuing theory for a single item. In this case, transitional probabilities are calculated in steady state. Afterward, the model is extended to the case of multi-item INVENTORY systems. Then, to deal with the complexity of this problem, a new heuristic algorithm is developed. Finally, the presented bi-level INVENTORY-queuing model is implemented as a case study in Electroestil Company.

This paper considers the comparison of two (s, S) PRODUCTION INVENTORY systems with retrials of unsatisfied customers. The time for producing and adding each item to the INVENTORY is exponentially distributed with rate b. However, a PRODUCTION rate ab higher than b is used at the beginning of the PRODUCTION. The higher PRODUCTION rate will reduce customers’ loss when INVENTORY level approaches zero. The demand from customers is according to a Poisson process. Service times are exponentially distributed.Upon arrival, the customers enter into a buffer of finite capacity. An arriving customer, who finds the buffer full, moves to an orbit. They can retry from there and interretrial times are exponentially distributed. The two models differ in the capacity of the buffer. The aim is to find the minimum value of total cost by varying different parameters and compare the efficiency of the models. The optimum value of a corresponding to minimum total cost is an important evaluation. Matrix analytic method is used to find an algorithmic solution to the problem. We also provide several numerical or graphical illustrations.

There is a great need to improve the classical INVENTORY models so that they can address real-world problems more properly. The presence of multiple products and a variety of INVENTORY items have complicated the INVENTORY control process, so companies need to classify INVENTORY items to reduce costs. On the other hand, the supplier selection problem is important, as there may be several suppliers with different options in the market. Also, several factors impact the demand for products and cause uncertainty for this parameter. This research develops a multi-product EPQ model that simultaneously classifies products, selects the best possible supplier for each group, and determines the replenishment policy under uncertainty in demand. To solve the proposed model, we present a simulation-optimization approach. This approach uses genetic and simulated annealing metaheuristic algorithms to solve the problem. Also, there is a simulation module that helps the algorithm to evaluate the fitness function. The parameters of algorithms are tuned by employing the Taguchi method. The results are analyzed for three categories of examples. Finally, the sensitivity of the objective function to the input parameters is also analyzed. We found that the system's total cost is highly sensitive to products unit holding cost.

In this paper a dual-channel supply chain with one retailer and one manufacturer is considered. The manufacturer produces in a lot to supply an integer number of the retailer’ s order and ships his product to the retailer in equal-sized batches. The manufacturer has also an online channel to meet the demand directly. It is assumed that two members have integrated PRODUCTION-INVENTORY system to minimize the total cost. A procedure is developed to find the optimal solution based on the convexity of the total cost. A numerical example is provided to clarify the characteristics of the model. The results show that the optimal number of the shipments from the manufacturer to the retailer is very sensitive to the holding cost of the manufacturer. When the manufacturer's holding cost is less than that of the retailer, most of the INVENTORY is held in the manufacturer and is delivered to the retailer in low quantities with more shipments. It was also obtained that if the dual-channel supply chain reshapes to single one, the total cost of the supply chain would be minimized and the maximum value of total cost of the supply chain would occur when the demand is distributed equally between the two channels.

This paper investigates a multistage PRODUCTION-INVENTORY model for deteriorating items, including raw materials and finished goods, based on collaborative preservation technology investment. The major purpose is to determine the optimal materials supply, PRODUCTION delivery, replenishment, and investment policies for the retailer and manufacturer in which the joint total pro, t of the integrated system is maximized. Mathematical programming analysis is employed to ascertain the optimal solutions for the retailer and manufacturer. Furthermore, several numerical examples are presented to demonstrate solution process and verify the concavity of the proposed model. Sensitivity analyses with respect to major parameters are also performed. The numerical results show that market demand, fixed shipping cost, PRODUCTION rate, manufacturer's sales price, and holding cost of , finished good may affect the optimal number of shipments. In addition, when collaborative preservation technology investment becomes an option, the effect of the deterioration rate on the shipping and ordering quantity will be reduced through investment in improving deterioration of raw material or , nished good. Finally, the increase in the amount of raw materials used to produce a , nished product implies that the amount of , nished goods produced by the original material is reduced,therefore, the collaborative preservation technology investment is increased.