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This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they do not purchase both items). This is the original aspect of the paper. We show the significance of the impact of optional demands on the system’s performance, which is the purpose of the paper. In this system, customers arrive, using the Markovian arrival process (MAP), to a demand for a single unit. The system is composed of a waiting hall with a limited capacity of F. The arriving customer observes the waiting hall is filled to capacity or the stock stage is zero, and they decide to leave the system. In the steady-state case, the joint probability distribution for the first commodity, the second commodity, and the number of customers in the system are computed using matrix geometric methods. We evaluate diverse system performance measures. Finally, we provide a numerical illustration of the optimal value for diverse parameters of the system, which highlights the results and implications of the article.

This article discusses a finite-source stock-dependent stochastic inventory system with multiple servers and a retrial facility. The system can store a maximum of S items, and the lifetime of each item is exponentially distributed. The primary customer arrives at the waiting hall from the finite source and receives service from multi-servers. The rate at which customers arrive depends on the current stock level. If the waiting hall is full during the primary customer’s arrival, he enters the finite orbit. Additionally, customers in the waiting hall may lose patience and enter the orbit. To replenish the stock, we follow the ( s ,  Q ) ordering policy. We calculate the joint probability distribution of the number of inventory items, busy servers, and number of customers in the waiting hall and orbit at a steady state. We conduct a comparative numerical analysis to determine the impact of heterogeneous and homogeneous service rates on various metrics, such as the average impatient customer rate, the fraction of successful retrials, and the average number of customers in the waiting hall and orbit.

This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution.

We present a general framework to study the design of spare parts logistics in the presence of three-dimensional (3-D) printing technology. We consider multiple parts facing stochastic demands and adopt procure/manufacture-to-stock versus print-on-demand to highlight the main difference of production modes featured in traditional manufacturing and 3-D printing. To minimize long-run average system cost, our model determines which parts to stock and which to print. We find that the optimal 3-D printer’s utilization increases as the additional unit cost of printing declines and the printing speed improves. The rate of increase, however, decays, demonstrating the well-known diminishing returns effect. We also find the optimal utilization to increase in part variety and decrease in part criticality, suggesting the value of 3-D technology in tolerating large part variety and the value of inventory for critical parts. By examining the percentage cost savings enabled by 3-D printing, we find that, although the reduction in printing cost continuously adds to the value of 3-D printing in a linear fashion, the impact of the improvement of printing speed exhibits S-shaped growth. We also derive various structural properties of the problem and devise an efficient algorithm to obtain near optimal solutions. Finally, our numerical study shows that the 3-D printer is, in general, lightly used under realistic parameter settings but results in significant cost savings, suggesting complementarity between stock and print in cost minimization. This paper was accepted by Victor Martínez-de-Albéniz, operations management.

Internet of things is a technology that allows communication between devices within a network. Since this technology depends on a network to communicate, the vulnerability of the exposed devices increased significantly. Furthermore, the use of internet protocol version 6 (IPv6) as the successor to internet protocol version 4 (IPv4) as a communication protocol constituted a significant problem for the network. Hence, this protocol was exploitable for flooding attacks in the IPv6 network. As a countermeasure against the flood, this study designed an IPv6 flood attack detection by using epsilon greedy optimized Q learning algorithm. According to the evaluation, the agent with epsilon 0.1 could reach 98% of accuracy and 11,550 rewards compared to the other agents. When compared to control models, the agent is also the most accurate compared to other algorithms followed by neural network (NN), K-nearest neighbors (KNN), decision tree (DT), naive Bayes (NB), and support vector machine (SVM). Besides that, the agent used more than 99% of a single central processing unit (CPU). Hence, the agent will not hinder internet of things (IoT) devices with multiple processors. Thus, we concluded that the proposed agent has high accuracy and feasibility in a single board computer (SBC).

In recent years, as a result of environmental legislation and an increasing interest in economics, many producers have been forced to implement the PTB (Products Tack Back) program. In this paper, we employ the basic (R, Q) model to control a single-item single-echelon inventory system with return flow. Based on the assumption that the return and the demand are independent Poisson processes, we derive a simple approximate algorithm to determine the optimal control parameters. The numerical examples show that the presented algorithm is more tractable than the exact algorithm and more accurate than other approximate algorithms, such as normal approximation.

In this study, we consider a perishable inventory system that has an (s, Q) ordering policy, along with a finite waiting hall. The single server, which provides an item to the customer after completing the required service performance for that item, only begins serving after N customers have arrived. Impatient demand is assumed in that the customers waiting to be served lose patience and leave the system if the server’s idle time overextends or if the arriving customers find the system to be full and will not enter the system. This article analyzes the impatient demands caused by the N-policy server to an inventory system. In the steadystate, we obtain the joint probability distribution of the level of inventory and the number of customers in the system. We analyze some measures of system performance and get the total expected cost rate in the steadystate. We present a beneficial cost function and confer the numerical illustration that describes the impact of impatient customers caused by N-policy on the inventory system’s total expected cost rate.

This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation.

We consider a single-item continuous-review ( r , q ) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review ( S , T ) systems with constant lead times. The electronic companion is available at https://doi.org/10.1287/opre.2017.1623 .

In this study, a continuous review (s,Q) inventory system with a service facility is examined. There is only one server and a limited number of customers waiting rooms in this facility. The demands arrive to the queueing-inventory system according to the Poisson process. Every customer needs a single product with a service period that is unpredictable and distributed arbitrarily. An external supplier replenishes the inventory, and the lead time for the reorder is predicated on an independent exponential distribution. Demands that arise during a stock out period must wait in the waiting area, and when the ordered items arrive, they are served using the first-come-first-serve queueing discipline. With the help of the imbedded Markov chain technique, we are able to compute the joint probability distribution of the number of customers in the system and the number of items in inventory at post-departure epoch. With the remaining service time of a customer in service as the supplementary variable, we are able to relate the system length distributions at post-departure and random epochs in order to determine the joint probability distribution at random epoch. The analysis of waiting time of an accepted customer in the queue is also examined. Several stationary system performance measures are computed and the total expected cost is determined under an appropriate cost structure to determine the optimal values for waiting space (N), reorder level (s), and order quantity (Q). In order to explain the important performance indicators of the system, some numerical findings are given for a variety of model parameters.