American Institute of Mathematical Sciences

The blending operation is a key process in alumina production. The real-time optimization (RTO) of finding an optimal raw material proportioning is crucially important for achieving the desired quality of the product. However, the presence of uncertainty is unavoidable in a real process, leading to much difficulty for making decision in real-time. This paper presents a novel robust real-time optimization (RRTO) method for alumina blending operation, where no prior knowledge of uncertainties is needed to be utilized. The robust solution obtained is applied to the real plant and the two-stage operation is repeated. When compared with the previous intelligent optimization (IRTO) method, the proposed two-stage optimization method can better address the uncertainty nature of the real plant and the computational cost is much lower. From practical industrial experiments, the results obtained show that the proposed optimization method can guarantee that the desired quality of the product quality is achieved in the presence of uncertainty on the plant behavior and the qualities of the raw materials. This outcome suggests that the proposed two-stage optimization method is a practically significant approach for the control of alumina blending operation.

In this paper, we discuss the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval values, the gain of returns is interval value as well. A new multiperiod mean semi-absolute deviation interval portfolio selection model with the transaction costs, borrowing constraints, threshold constraints and diversification degree of portfolio has been proposed, where the return and risk are characterized by the interval mean and interval semi-absolute deviation of return, respectively. The diversification degree of portfolio is measured by the presented possibilistic entropy. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on interval theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of differently desired number of assets and different preference coefficients are provided by numerical examples to illustrate the efficiency of the proposed approach and the designed algorithm.

This paper addresses weapon selection and planning problems (WSPPs), which can be considered as an amalgamation of project portfolio and project scheduling problems. A multi-objective optimization model is proposed for WSPPs. The objectives include net present value (NPV) and effectiveness. To obtain the Pareto optimal set, a multi-objective evolutionary algorithm is presented for the problem. The basic procedure of NSGA-Ⅱ is employed. The problem-specific chromosome representation and decoding procedure, as well as genetic operators are redesigned for WSPPs. The dynamic nature of the planning environment is taken into account. Dynamic changes are modeled as the occurrences of countermeasures of specific weapon types. An adaptation process is proposed to tackle dynamic changes. Furthermore, we propose a flexibility measure to indicate a solution's ability to adapt in the presence of changes. The experimental results and analysis of a hypothetical case study are presented in this research.

In this paper, the valuation of an investment opportunity in a high-tech corporation using real option theory and modern capital budgeting is studied. Some key characteristics such as high-risk, multi-stage and technology life cycle of a high-tech project are considered in the proposed model. Since a real option is usually not tradable in the market, an actuarial approach is adopted in our study. We employ an irreversible regime-switching Markov chain to model the multi-stage and technology life cycle of the project in the high-tech industry. The valuation of captured real option can be formulated as the valuation of an American option with time-dependent strike price. For the purpose of practical implementation, a novel lattice-based method is developed to value the American option. Numerical examples are given to illustrate the proposed models and methods.

We consider a queueing system with two classes of customers, two heterogeneous servers, and discriminatory random order service (DROS) discipline. The two servers may have either the same or different DROS weights for each class. Customers of each class arrive according to a Poisson process and the service times of each class of customers are assumed to be exponentially distributed with service rate depending on both the customer's class and the servers. We provide stability and instability conditions for this two-class two-server queue with DROS discipline.

In order to reduce the average delay of secondary user (SU) packets and adapt to various levels of tolerance for transmission interruption, we propose a novel opportunistic channel access mechanism with admission threshold and probabilistic feedback in cognitive radio networks (CRNs). Considering the preemptive priority of primary user (PU) packets, as well as the sensing errors of missed detection and false alarm caused by SUs, we establish a type of priority queueing model in which two classes of customers may interfere with each other. Based on this queueing model, we evaluate numerically the proposed mechanism and then present the system performance optimization. By employing a matrix-geometric solution, we derive the expressions for some important performance measures. Then, by building a reward function, we investigate the strategies for both the Nash equilibrium and the social optimization. Finally, we provide a pricing policy for SU packets to coordinate these two strategies. With numerical experiments, we verify the effectiveness of the proposed opportunistic channel access mechanism and the rationality of the proposed pricing policy.

In this paper, we investigate a continuous-time mean-variance portfolio selection model with only risky assets and its optimal Sharpe ratio in a new way. We obtain closed-form expressions for the efficient investment strategy, the efficient frontier and the optimal Sharpe ratio. Using these results, we further prove that (ⅰ) the efficient frontier with only risky assets is significantly different from the one with inclusion of a risk-free asset and (ⅱ) inclusion of a risk-free asset strictly enhances the optimal Sharpe ratio. Also, we offer an explicit expression for the enhancement of the optimal Sharpe ratio. Finally, we test our theory results using an empirical analysis based on real data of Chinese equity market. Out-of-sample analyses shed light on advantages of our theoretical results established.

A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. It is derived from a discrete approximation of the generalized Ginzburg-Landau functional, and we are interested in understanding its global minimum solution and all local non-global points. The main difficulty for the model is due to its non-convexity. In part Ⅰ of the paper, we first characterize the global minimum solution set, whereas the study for local non-global optimal solutions is left for Part Ⅱ. We show that, the dual of the Lagrange dual of the double well potential problem is a linearly constrained convex minimization problem, which, under a designated nonlinear transformation, can be equivalently mapped to a portion of the original double well potential function containing the global minimum. In other words, solving the global minimum of the double well potential function is essentially a convex minimization problem, despite of its non-convex nature. Numerical examples are provided to illustrate the important features of the problem and the mapping in between.

In contrast to taking the dual approach for finding a global minimum solution of a double well potential function, in Part Ⅱ of the paper, we characterize the local minimizer, local maximizer, and global minimizer directly from the primal side. It is proven that, for a ''nonsingular" double well function, there exists at most one local, but non-global, minimizer and at most one local maximizer. Moreover, the local maximizer is ''surrounded" by local minimizers in the sense that the norm of the local maximizer is strictly less than that of any local minimizer. We also establish necessary and sufficient optimality conditions for the global minimizer, local non-global minimizer and local maximizer by studying a convex secular function over specific intervals. These conditions lead to three algorithms for identifying different types of critical points of a given double well function.

This paper considers single server retrial queues with setup time where the server is aware of the existence of retrying customers. In the basic model, the server is switched off immediately when the system becomes empty in order to save energy consumption. Arriving customers that see the server occupied join the orbit and repeat their attempt after some random time. The new feature of our models is that an arriving customer that sees the server off waits at the server and the server is turned on. The server needs some setup time to be active so as to serve the waiting customer. If the server completes a service and the orbit is not empty, it stays idle waiting for either a new or retrial customer. Under the assumption that the service time and the setup time are arbitrarily distributed, we obtain explicit expressions for the generating functions of the joint queue length. We also obtain recursive formulas for computing the moments of the queue length. We then consider an extended model where the server has a closedown time before being turned off for which an explicit solution is also obtained.

Nowadays, customers are the decisive part in the market. The retailers who are closest to final consumers in a supply chain begin to show their power and thereby dominate the supply chain. Thus, the research about a retailer-led supply chain continues to be a burning question in the recent trade press and academic literature. Our research adds fresh fuel to the fire by studying how one channel member' fairness concern affects the coordination of a two-stage supply chain with a dominant retailer and a supplier. We carry out our investigation in two cases which involve different degrees of trust between the channel members about the unit cost $c$ provided by the supplier. Our analysis shows that if the channel members have the same degree of trust on $c$-value, the dominant retailer can use a constant markup pricing contract to align the fair-minded supplier's interest with the channel's and coordinate the channel with a wholesale price higher than the supplier's marginal cost; but the coordination fails if the dominant retailer is the only one who cares about fairness, and he obtains a lower profit than nobody cares about fairness. If the dominant retailer and the supplier have different degrees of trust on $c$-value, the retailer can not coordinate the channel with a markup pricing contract when only the supplier has fairness concerns.

The paper introduces a class of vacation queues where the arrival and service processes are modulated by the same Markov process, hence they can be dependent. The main result of the paper is the probability generating function for the number of jobs in the system. The analysis follows a matrix-analytic approach. A step of the analysis requires the evaluation of the busy period of a quasi birth death process with arbitrary initial level. This element can be useful in the analysis of other queueing models as well. We also discuss several special cases of the general model. We show that these special settings lead to simplification of the solution.

Inspired by the inertial proximal algorithms for finding a zero of a maximal monotone operator, in this paper, we propose two inertial accelerated algorithms to solve the split feasibility problem. One is an inertial relaxed-CQ algorithm constructed by applying inertial technique to a relaxed-CQ algorithm, the other is a modified inertial relaxed-CQ algorithm which combines the KM method with the inertial relaxed-CQ algorithm. We prove their asymptotical convergence under some suitable conditions. Numerical results are reported to show the effectiveness of the proposed algorithms.

In this paper, we study the valuation of a single-name credit default swap and a $k$th-to-default basket swap under a correlated regime-switching hazard processes model. We assume that the defaults of all the names are driven by a Markov chain describing the macro-economic conditions and some shock events modelled by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of a CDS contract and the $k$th-to-default basket swap.

This paper studies a newsvendor problem with random supply capacity, where the retailer (newsvendor) is loss-averse and the shortage cost is considered. When the retailer orders, the quantity actually received is the minimum between the order quantity and supply capacity, and his objective is to choose an order quantity to maximize the expected utility. It is shown that under different conditions, the loss-averse retailer may order larger than, equal to or less than the risk-neutral one, which is different from the existing result in the case without considering shortage cost. Further, if the shortage cost is less than a critical value, then the loss-averse retailer's optimal order quantity is always less than the risk-neutral retailer's. The numerical experiments are conducted to demonstrate our theoretical results.

This study investigates a challenging problem of rescheduling a hybrid flow shop in the steelmaking-continuous casting (SCC) process, which is a major bottleneck in the production of iron and steel. In consideration of uncertain disturbance during SCC process, we develop a time-indexed formulation to model the SCC rescheduling problem. The performances of the rescheduling problem consider not only the efficiency measure, which includes the total weighted completion time and the total waiting time, but also the stability measure, which refers to the difference in the number of operations processed on different machines for the different stage in the original schedule and revised schedule. With these objectives, this study develops a Lagrangian heuristic algorithm to solve the SCC rescheduling problem. The algorithm could provide a realizable termination criterion without having information about the problem, such as the distance between the initial iterative point and the optimal point. This study relaxes machine capacity constraints to decompose the relaxed problem into charge-level subproblems that can be solved using a polynomial dynamic programming algorithm. A heuristic based on the solution of the relaxed problem is presented for obtaining a feasible reschedule. An improved efficient subgradient algorithm is introduced for solving Lagrangian dual problems. Numerical results for different events and problem scales show that the proposed approach can generate high-quality reschedules within acceptable computational times.

In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.

In this paper, we consider a discrete time Geo/Geo/1 repairable queueing system with a pseudo-fault, setup time, $N$-policy and multiple working vacations. We assume that the service interruption is caused by pseudo-fault or breakdown, and occurs only when the server is busy. If the pseudo-fault occurs, the server will enter into a vacation period instead of a busy period. At a breakdown instant, the repair period starts immediately and after repaired the server is assumed to be as good as new. Using a quasi birth-and-death chain, we establish a two-dimensional Markov chain. We obtain the distribution of the steady-state queue length by using a matrix-geometric solution method. Moreover, we analyze the considered queueing system and provide several performance indices of the system in steady-state. According to the queueing system, we first investigate the individual and social optimal behaviors of the customer. Then we propose a pricing policy to optimize the system socially, and study the Nash equilibrium and social optimization of the proposed strategy to determine the optimal expected parameters of the system. Finally, we present some numerical results to illustrate the effect of several parameters on the systems.

We propose a distributed MAC protocol for cognitive radio when primary network is IEEE 802.16e/m WiMAX. Our proposed MAC protocol is the Truncated Binary Exponential Backoff Algorithm where the backoff window size of algorithm is doubled at each collision, and the backoff counter is operated by frame basis in IEEE 802.16e/m and is freezed at a frame with no idle slots. We model our proposed MAC protocol as a 3-dimensional discrete-time Markov chain and obtain steady state probability of the Markov chain by using a censored Markov chain method. Based on this steady state probability, we obtain the throughput, packet loss probability and packet delay distribution of secondary users. Our numerical examples show that the initial contention window size can be determined according to the number of secondary users in order to obtain higher throughput for secondary users, and the maximum backoff window has a large impact on the secondary user's packet loss probability. Secondary users' packet delay distribution is much influenced by the initial contention window size and the number of secondary users.

In order to realize a smart grid, Advanced Metering Infrastructure (AMI) has started to be deployed. AMI automates meter reading operations and enables real-time monitoring of power usage. Monitoring power consumption data will be useful for power generation planning, power demand control, and peak shift. In addition to monitoring power consumption, in AMI networks, other types of communication (e.g., gas and water consumption, demand response for electricity, and inquiries to electric power companies) can be accommodated by using surplus bandwidth. An essential part of AMI is a set of electricity meters with communication functions, called smart meters, which transmit power consumption data to electric power companies periodically with fixed intervals. They have been installed in houses, factories, or buildings, and are expected to be equipped with electric vehicles in a future. We can also save energy by turning off smart meters when it is not necessary to communicate. In this paper, we present an analytical model to evaluate the performance of AMI taking the randomness of the number of smart meters into consideration, caused by the turn on/off of meters and mobility of meters across the AMI network coverage.

In this paper, we develop an integrated inventory model to determine the optimal lot size and production uptime while considering stochastic machine breakdown and multiple shipments for a single-buyer and single-vendor. Machine breakdown cannot be controlled by the production house. Thus, we assume it as stochastic, not constant. Moreover, we assume that the manufacturing process produces defective items. When a breakdown takes place, the production system follows a no resumption policy. Some defective products cannot be reworked and are discarded from the system. To prevent shortages, we consider safety stock. The model assumes that both batch quantity and the distance between two shipments are identical and that the transportation cost is paid by the buyer. We prove the convexity of the total cost function and derive the closed-form solutions for decision variables analytically. To obtain the optimal production uptime, we determine both the lower and upper bounds for the optimal production uptime using a bisection searching algorithm. To illustrate the applicability of the proposed model, we provided a numerical example and sensitivity analysis.

In this paper, we analyze the optimal control of a retrial queueing system with finite buffer K. At any decision epoch, if the buffer is full, the controller have to make two decisions: one is for the new arrivals, to decide whether they are allowed to join the orbit or not (admission control); the other one is for the repeated customers, to decide whether they are allowed to get back to the orbit or not (retrial control). The problems are constructed as a Markov decision process. We show that the optimal policy has a threshold-type structure and the thresholds are monotonic in operating parameters and various cost parameters. Furthermore, based on the structure of the optimal policy, we construct a performance evaluation model for computing efficiently the thresholds. The expression of the expected cost is given by solving the quasi-birth-and-death (QBD) process. Finally, we provide some numerical results to illustrate the impact of different parameters on the optimal policy and average cost.

This paper describes a two-echelon supply chain model with two manufacturers and one common retailer. Two types of complementary products are produced by two manufacturers, and the common retailer buys products separately using a reservation price and bundles them for sale. The demands of manufacturers and retailer are assumed to be stochastic in nature. When the retailer orders for products, any one of manufacturers agrees to allow those products, and the rest of the manufacturers have to provide the same amount. The profits of two manufacturers and the retailer are maximized by using Stackelberg game policy. By applying a game theoretical approach, several analytical solutions are obtained. For some cases, this model obtains quasi-closed-form solutions, for others, it finds closed-form solutions. Some numerical examples, sensitivity analysis, managerial insights, and graphical illustrations are given to illustrate the model.

Matrix eigenvalue problems play a significant role in many areas of computational science and engineering. In this paper, we propose a fast continuous method for the extreme eigenvalue problem. We first convert such a nonconvex optimization problem into a minimization problem with concave objective function and convex constraints based on the continuous methods developed by Golub and Liao. Then, we propose a continuous method for solving such a minimization problem. To accelerate the convergence of this method, a self-adaptive step length strategy is adopted. Under mild conditions, we prove the global convergence of this method. Some preliminary numerical results are presented to verify the effectiveness of the proposed method eventually.