Stochastic allocation of inspection capacity to competitive processes

Optimal allocation and control of limited inspection capacity for multiple production processes are considered. The production processes, which operate independently but share inspection capacity, are subject to random failures and are partially observed through inspection. This study proposes an approach of stochastic allocation, using a Markov decision process, to minimize expected total discounted cost over an infinite time horizon. Both an optimal model and a disaggregate approximation model are introduced. The study provides some structural results and establishes that the control policy is of a threshold type. Numerical experiments demonstrate a significantly decreased amount of computational time required for the disaggregate approach when compared to the optimal solution, while generating very good control policies. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 78–94, 2002; DOI 10.1002/nav.1049     

A new importance sampling Monte Carlo method for a flow network reliability problem

The exact evaluation of the probability that the maximum st‐flow is greater than or equal to a fixed demand in a stochastic flow network is an NP‐hard problem. This limitation leads one to consider Monte Carlo alternatives. In this paper, we propose a new importance sampling Monte Carlo method. It is based on a recursive use of the state space decomposition methodology of Doulliez and Jamoulle during the simulation process. We show theoretically that the resulting estimator belongs to the variance‐reduction family and we give an upper bound on its variance. As shown by experimental tests, the new sampling principle offers, in many cases, substantial speedups with respect to a previous importance sampling based on the same decomposition procedure and its best performances are obtained when highly reliable networks are analyzed. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 204–228, 2002; DOI 10.1002/nav.10004     

Life distribution analysis based on Lévy subordinators for degradation with random jumps

For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of nondecreasing Lévy processes. Based on the inverse Fourier transform, we derive a new closed‐form reliability function and probability density function for lifetime, represented by Lévy measures. The reliability function derived using the traditional convolution approach for common stochastic models such as gamma degradation process with random jumps, is revealed to be a special case of our general model. Numerical experiments are used to demonstrate that our model performs well for different applications, when compared with the traditional convolution method. More importantly, it is a general and useful tool for life distribution analysis of stochastic degradation with random jumps in multidimensional cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 483–492, 2015     

Inventory control under substitutable demand: A stochastic game application

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018     

Predictability of operational processes over finite horizon

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well‐known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Centralized inventory control in a two‐level distribution system with Poisson demand

This paper introduces a new replenishment policy for inventory control in a two‐level distribution system consisting of one central warehouse and an arbitrary number of nonidentical retailers. The new policy is designed to control the replenishment process at the central warehouse, using centralized information regarding the inventory positions and demand processes of all installations in the system. The retailers on the other hand are assumed to use continuous review (R, Q) policies. A technique for exact evaluation of the expected inventory holding and backorder costs for the system is presented. Numerical results indicate that there are cases when considerable savings can be made by using the new (α₀, Q₀) policy instead of a traditional echelon‐ or installation‐stock (R, Q) policy. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 798–822, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10040     

On the availability of R out of N repairable systems

An R out of N repairable system consisting of N components and operates if at least R components are functioning. Repairable means that failed components are repaired, and upon repair completion they are as good as new. We derive formulas for the expected up‐time, expected down‐time, and the availability of the system, using Markov renewal processes. We assume that either the repair times of the components are generally distributed and the components' lifetimes are exponential or vice versa. The analysis is done for systems with either cold or warm stand‐by. Numerical examples are given for several life time and repair time distributions. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 483–498, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10025     

On lifetimes in random environments

For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented. Some applications to the case of repairable components are finally provided. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 365–375, 1998     

Integrated scheduling of loading and transportation with tractors and semitrailers separated

Motivated by some practical applications, we study a new integrated loading and transportation scheduling problem. Given a set of jobs, a single crane is available to load jobs, one by one, onto semitrailers with a given capacity. Loaded semitrailers are assigned to tractors for transportation tasks. Subject to limited resources (crane, semitrailers, and tractors), the problem is to determine (1) an assignment of jobs to semitrailers for loading tasks, (2) a sequence for the crane to load jobs onto semitrailers, (3) an assignment of loaded semitrailers to tractors for transportation tasks, and (4) a transportation schedule of assigned tractors such that the completion time of the last transportation task is minimized. We first formulate the problem as a mixed integer linear programming model (MILPM) and prove that the problem is strongly NP‐hard. Then, optimality properties are provided which are useful in establishing an improved MILPM and designing solution algorithms. We develop a constructive heuristic, two LP‐based heuristics, and a recovering beam search heuristic to solve this problem. An improved procedure for solutions by heuristics is also presented. Furthermore, two branch‐and‐bound (B&B) algorithms with two different lower bounds are developed to solve the problem to optimality. Finally, computational experiments using both real data and randomly generated data demonstrate that our heuristics are highly efficient and effective. In terms of computational time and the number of instances solved to optimality in a time limit, the B&B algorithms are better than solving the MILPM. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 416–433, 2015     

Modeling and analysis of a mixed‐model assembly line with stochastic operation times

We consider a mixed‐model assembly line (MMAL) comprised a set of workstations and a conveyor. The workstations are arranged in a serial configuration. The conveyor moves at a constant speed along the workstations. Initial units belonging to different models are successively fed onto the conveyor, and they are moved by the conveyor to pass through the workstations to gradually generate final products. All assembling tasks are manually performed with operation times to be stochastic. An important performance measure of MMALs is overload times that refer to uncompleted operations for operators within their work zones. This paper establishes a method to analyze the expected overload times for MMALs with stochastic operation times. The operation processes of operators form discrete time nonhomogeneous Markov processes with continuous state spaces. For a given daily production schedule, the expected overload times involve in analyzing the Markov processes for finite horizon. Based on some important properties of the performance measure, we propose an efficient approach for calculating the expected overload times. Numerical computations show that the results are very satisfactory. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

An index policy for a stochastic scheduling model with improving/deteriorating jobs

We consider stochastic scheduling models which have the natural character that jobs improve while being processed, but deteriorate (and may possibly leave the system altogether) while processing is diverted elsewhere. Such restless bandit problems are shown to be indexable in the sense of Whittle. A numerical study which elucidates the strong performance of the resulting index policy is complemented by a theoretical study which demonstrates the optimality of the index policy under given conditions and which develops performance guarantees for the index heuristic more generally. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 706–721, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10036     

The quay crane scheduling problem with time windows

The quay crane scheduling problem consists of scheduling tasks for loading and unloading containers on cranes that are assigned to a vessel for its service. This article introduces a new approach for quay crane scheduling, where the availability of cranes at a vessel is restricted to certain time windows. The problem is of practical relevance, because container terminal operators frequently redeploy cranes among vessels to speed up the service of high‐priority vessels while serving low‐priority vessels casually. This article provides a mathematical formulation of the problem and a tree‐search‐based heuristic solution method. A computational investigation on a large set of test instances is used to evaluate the performance of the heuristic and to identify the impact of differently structured crane time windows on the achievable vessel handling time. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Suppression of enemy air defenses (SEAD) as an information duel

Blue strike aircraft enter region ? to attack Red targets. In Case 1, Blue conducts (preplanned) SEAD to establish air superiority. In the (reactive) SEAD scenario, which is Case 2, such superiority is already in place, but is jeopardized by prohibitive interference from Red, which threatens Blue's ability to conduct missions. We utilize both deterministic and stochastic models to explore optimal tactics for Red in such engagements. Policies are developed which will guide both Red's determination of the modes of operation of his engagement radar, and his choice of Blue opponent to target next. An index in the form of a simple transaction kill ratio plays a major role throughout. Published 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 723–742, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10046     

Discrete stochastic optimization using variants of the stochastic ruler method

We present two random search methods for solving discrete stochastic optimization problems. Both of these methods are variants of the stochastic ruler algorithm. They differ from our earlier modification of the stochastic ruler algorithm in that they use different approaches for estimating the optimal solution. Our new methods are guaranteed to converge almost surely to the set of global optimal solutions under mild conditions. We discuss under what conditions these new methods are expected to converge faster than the modified stochastic ruler algorithm. We also discuss how these methods can be used for solving discrete optimization problems when the values of the objective function are estimated using either transient or steady‐state simulation. Finally, we present numerical results that compare the performance of our new methods with that of the modified stochastic ruler algorithm when applied to solve buffer allocation problems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Pareto-optimality in classical inventory problems

In this paper the inventory problem with backorders both deterministic and stochastic is studied using trade-off analysis in the context of vector optimization theory. The set of Pareto-optimal solutions is geometrically characterized in both the constrained and unconstrained cases. Moreover, a new way of utilizing Pareto-optimality concepts to handle classical inventory problems with backorders is derived. A new analysis of these models is done by means of a trade-off analysis. New solutions are shown, and an error bound for total inventory cost is provided. Other models such as multi-item or stochastic lead-time demand inventory problems are addressed and their Pareto-optimal solution sets are obtained. An example is included showing the additional applicability of this kind of analysis to handle parametric problems. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 83–98, 1998     

Warranty reserves for nonstationary sales processes

Estimation of warranty costs, in the event of product failure within the warranty period, is of importance to the manufacturer. Costs associated with replacement or repair of the product are usually drawn from a warranty reserve fund created by the manufacturer. Considering a stochastic sales process, first and second moments (and thereby the variance) are derived for the manufacturer's total discounted warranty cost of a single sale for single‐component items under four different warranty policies from a manufacturer's point of view. These servicing strategies represent a renewable free‐replacement, nonrenewable free‐replacement, renewable pro‐rata, and a nonrenewable minimal‐repair warranty plans. The results are extended to determine the mean and variance of total discounted warranty costs for the total sales over the life cycle of the product. Furthermore, using a normal approximation, warranty reserves necessary for a certain protection level, so that reserves are not completely depleted, are found. Results and their managerial implications are studied through an extensive example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 499–513, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10023     

Stochastic framework for partially degradation systems with continuous component degradation‐rate‐interactions

Many conventional models that characterize the reliability of multicomponent systems are developed on the premise that for a given system, the failures of its components are independent. Although this facilitates mathematical tractability, it may constitute a significant departure from what really takes place. In many real‐world applications, system components exhibit various degrees of interdependencies, which present significant challenges in predicting degradation performance and the remaining lifetimes of the individual components as well as the system at large. We focus on modeling the performance of interdependent components of networked systems that exhibit interactive degradation processes. Specifically, we focus on how the performance level of one component affects the degradation rates of other dependent components. This is achieved by using stochastic models to characterize how degradation‐based sensor signals associated with the components evolve over time. We consider “Continuous‐Type” component interactions that occur continuously over time. This type of degradation interaction exists in many applications, in which interdependencies occur on a continuum. We use a system of stochastic differential equations to capture such “Continuous‐Type” interaction. In addition, we utilize a Bayesian approach to update the proposed model using real‐time sensor signals observed in the field and provide more accurate estimation of component residual lifetimes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 286–303, 2014     

A parallel machine replacement model

This paper considers a finite horizon parallel machine replacement problem where a fixed number of machines is in operation at all times. The operating cost for a machine goes up as the machine gets older. An older machine may have to be replaced by a new one when its operating cost becomes too high. There is a fixed order cost associated with the purchase of new machines. Machine purchase prices and salvage values may depend on the period in which they were purchased. The objective is to find a replacement plan that minimizes the total discounted cost over the problem horizon. We believe that the costs in our model are more commonly observed in practice than those previously used in the literature. The paper develops properties of optimal solutions and an efficient forward‐time algorithm to find an optimal replacement plan. A dominance property is developed that further limits the options to be considered, and a simple forecast horizon result is also presented. Future research possibilities are mentioned. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 275–287, 2002; Published online in Wiley InterScience (http://www.interscience.wiley.com). DOI 10.1002/nav.10012     

Dominating sets for rectilinear center location problems with polyhedral barriers

In planar location problems with barriers one considers regions which are forbidden for the siting of new facilities as well as for trespassing. These problems are important since they model various actual applications. The resulting mathematical models have a nonconvex objective function and are therefore difficult to tackle using standard methods of location theory even in the case of simple barrier shapes and distance functions. For the case of center objectives with barrier distances obtained from the rectilinear or Manhattan metric, it is shown that the problem can be solved in polynomial time by identifying a dominating set. The resulting genuinely polynomial algorithm can be combined with bound computations which are derived from solving closely connected restricted location and network location problems. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 647–665, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10038