In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a -approximation algorithm with a time complexity of . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a -approximation algorithm with a time complexity of . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5-approximation algorithm with a time complexity of .© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

Lifetime experiments are common in many research areas and industrial applications. Recently, process monitoring for lifetime observations has received increasing attention. However, some existing methods are inadequate as neither their in control (IC) nor out of control (OC) performance is satisfactory. In addition, the challenges associated with designing robust and flexible control schemes have yet to be fully addressed. To overcome these limitations, this article utilizes a newly developed weighted likelihood ratio test, and proposes a novel monitoring strategy that automatically combines the likelihood of past samples with the exponential weighted sum average scheme. The proposed Censored Observation-based Weighted-Likelihood (COWL) control chart gives desirable IC and OC performances and is robust under various scenarios. In addition, a self-starting control chart is introduced to cope with the problem of insufficient reference samples. Our simulation shows a stronger power in detecting changes in the censored lifetime data using our scheme than using other alternatives. A real industrial example based on the breaking strength of carbon fiber also demonstrates the effectiveness of the proposed method.© 2017 Wiley Periodicals, Inc., 2017

The notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi-state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi-state systems with multi-state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi-state consecutive-*k*-out-of-*n* system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi-state system with multiple types of components is also presented.© 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

This paper considers optimal staffing in service centers. We construct models for profit and cost centers using dynamic rate queues. To allow for practical optimal controls, we approximate the queueing process using a Gaussian random variable with equal mean and variance. We then appeal to the Pontryagin's maximum principle to derive a closed form square root staffing (SRS) rule for optimal staffing. Unlike most traditional SRS formulas, the main parameter in our formula is not the probability of delay but rather a cost-to-benefit ratio that depends on the shadow price. We show that the delay experienced by customers can be interpreted in terms of this ratio. Throughout the article, we provide theoretical support of our analysis and conduct extensive numerical experiments to reinforce our findings. To this end, various scenarios are considered to evaluate the change in the staffing levels as the cost-to-benefit ratio changes. We also assess the change in the service grade and the effects of a service-level agreement constraint. Our analysis indicates that the variation in the ratio of customer abandonment over service rate particularly influences staffing levels and can lead to drastically different policies between profit and cost service centers. Our main contribution is the introduction of new analysis and managerial insights into the nonstationary optimal staffing of service centers, especially when the objective is to maximize profitability.© 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit-evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra-like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

A Markov population decision chain concerns the control of a population of individuals in different states by assigning an action to each individual in the system in each period. This article solves the problem of finding policies that maximize expected system utility over a finite horizon in Markov population decision chains with finite state-action space under the following assumptions: (1) The utility function exhibits constant risk posture, (2) the progeny vectors of distinct individuals are independent, and (3) the progeny vectors of individuals in a state who take the same action are identically distributed. The main result is that it is possible to solve the problem with the original state-action space without augmenting it to include information about the population in each state or any other aspect of the system history. In particular, there exists an optimal policy that assigns the same action to all individuals in a given state and period, independently of the population in that period and such a policy can be computed efficiently. The optimal utility operators that find the maximum of a finite collection of polynomials (rather than affine functions) yield an optimal solution with effort linear in the number of periods.© 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

In this article, we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the -queue that can be modeled as a QSF process on a two-dimensional state space. In addition, we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of for fixed mean arrival rate. © 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

We consider a dynamic pricing model in which the instantaneous rate of the demand arrival process is dependent on not only the current price charged by the concerned firm, but also the present state of the world. While reflecting the current economic condition, the state evolves in a Markovian fashion. This model represents the real-life situation in which the sales season is relatively long compared to the fast pace at which the outside environment changes. We establish the value of being better informed on the state of the world. When reasonable monotonicity conditions are met, we show that better present economic conditions will lead to higher prices. Our computational study is partially calibrated with real data. It demonstrates that the benefit of heeding varying economic conditions is on par with the value of embracing randomness in the demand process. © 2015 Wiley Periodicals, Inc. Naval Research Logistics, 2015

We analyze a supply chain of a manufacturer and two retailers, a permanent retailer who always stocks the manufacturer's product and an intermittent deal-of-the day retailer who sells the manufacturer's product online for a short time. We find that without a deal-of-the-day (DOTD) retailer, it is suboptimal for the manufacturer to offer a quantity discount while it is optimal for the retailer to offer periodic price discounts to consumers. With the addition of a DOTD retailer, it is likely to be optimal for the manufacturer to offer a quantity discount. We show that even without market expansion, i.e., no exclusive DOTD retailer consumers, opening the intermittent channel can leave the permanent retailer no worse-off while increasing the manufacturer's profit. We identify the regular and discounted wholesale prices and the threshold quantity at which the manufacturer should give the discount. We also identify the optimal retail prices. We find that opening the intermittent channel increases the profit of the manufacturer, is likely to decrease the average retail price and to increase sales, and may increase the permanent retailer's profit. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 505–528, 2016

This article investigates the method of allocating arriving vessels to the terminals in transshipment hubs. The terminal allocation decision faced by a shipping alliance has the influence on the scheduled arrival time of vessels and further affects the bunker consumption cost for the vessels. A model is formulated to minimize the bunker consumption cost as well as the transportation cost of inter-terminal transshipment flows/movements. The capacity limitation of the port resources such as quay cranes (QCs) and berths is taken into account. Besides the terminal allocation, the QC assignment decision is also incorporated in the proposed model. A local branching based method and a particle swarm optimization based method are developed to solve the model in large-scale problem instances. Numerical experiments are also conducted to validate the effectiveness of the proposed model, which can save around 14% of the cost when compared with the “First Come First Served” decision rule. Moreover, the proposed solution methods not only solve the proposed model within a reasonable computation time, but also obtain near-optimal results with about 0.1∼0.7% relative gap. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 529–548, 2016

A Markovian arrival process of order *n*, MAP(*n*), is typically described by two *n* × *n* transition rate matrices in terms of
rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is *n*^{2} for non-redundant MAP(*n*). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace-Stieltjes transform (LST) representations for MAP(*n*)s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3)s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3)s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016

This article describes the Distributed Interaction Campaign Model (DICM), an exploratory campaign analysis tool and asset allocation decision-aid for managing *geographically distributed* and *swarming* naval and air forces. The model is capable of fast operation, while accounting for uncertainty in an opponent's plan. It is intended for use by commanders and analysts who have limited time for model runs, or a finite budget. The model is purpose-built for the Pentagon's Office of Net Assessment, and supports analysis of the following questions: What happens when swarms of geographically distributed naval and air forces engage each other and what are the key elements of the opponents’ force to attack? Are there changes to force structure that make a force more effective, and what impacts will disruptions in enemy command and control and wide-area surveillance have? Which insights are to be gained by fast exploratory mathematical/computational campaign analysis to augment and replace expensive and time-consuming simulations? An illustrative example of model use is described in a simple test scenario. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 562–576, 2016

In this article, we define two different workforce leveling objectives for serial transfer lines. Each job is to be processed on each transfer station for *c* time periods (e.g., hours). We assume that the number of workers needed to complete each operation of a job in precisely *c* periods is given. Jobs transfer forward synchronously after every production cycle (i.e., *c* periods). We study two leveling objectives: *maximin workforce size*
() and *min range* (*R*). Leveling objectives produce schedules where the cumulative number of workers needed in all stations of a transfer line does not experience dramatic changes from one production cycle to the next. For and a two-station system, we develop a fast polynomial algorithm. The range problem is known to be NP-complete. For the two-station system, we develop a very fast optimal algorithm that uses a tight lower bound and an efficient procedure for finding complementary Hamiltonian cycles in bipartite graphs. Via a computational experiment, we demonstrate that range schedules are superior because not only do they limit the workforce fluctuations from one production cycle to the next, but they also do so with a minor increase in the total workforce size. We extend our results to the *m*-station system and develop heuristic algorithms. We find that these heuristics work poorly for *min range* (*R*), which indicates that special structural properties of the *m*-station problem need to be identified before we can develop efficient algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 577–590, 2016