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, 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, 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, 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 study an admission control model in revenue management with nonstationary and correlated demands over a finite discrete time horizon. The arrival probabilities are updated by current available information, that is, past customer arrivals and some other exogenous information. We develop a regret-based framework, which measures the difference in revenue between a clairvoyant optimal policy that has access to all realizations of randomness a priori and a given feasible policy which does not have access to this future information. This regret minimization framework better spells out the trade-offs of each accept/reject decision. We proceed using the lens of approximation algorithms to devise a conceptually simple regret-parity policy. We show the proposed policy achieves 2-approximation of the optimal policy in terms of total regret for a two-class problem, and then extend our results to a multiclass problem with a fairness constraint. Our goal in this article is to make progress toward understanding the marriage between stochastic regret minimization and approximation algorithms in the realm of revenue management and dynamic resource allocation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 433–448, 2016

This article considers a multistage channel with deterministic price-sensitive demand. Two systems for pricing decisions, that is, the bargaining system and the leader-follower system, are compared. We characterize the necessary and sufficient conditions on the power structure, under which the solution of the bargaining system Pareto dominates that of the leader-follower system. Also, under such conditions, we give a tight upper bound of channel efficiency of the bargaining system, which converges to 100% channel efficiency as the number of stages increases to infinity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 449–459, 2016

In this article, we introduce staffing strategies for the Erlang-A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper-parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016

Stochastic transportation networks arise in various real world applications, for which the probability of the existence of a feasible flow is regarded as an important performance measure. Although the necessary and sufficient condition for the existence of a feasible flow represented by an exponential number of inequalities is a well-known result in the literature, the computation of the probability of all such inequalities being satisfied jointly is a daunting challenge. The state-of-the-art approach of Prékopa and Boros, *Operat Res* 39 (1991) 119–129 approximates this probability by giving its lower and upper bounds using a two-part procedure. The first part eliminates all redundant inequalities and the second gives the lower and upper bounds of the probability by solving two well-defined linear programs with the inputs obtained from the first part. Unfortunately, the first part may still leave many non-redundant inequalities. In this case, it would be very time consuming to compute the inputs for the second part even for small-sized networks. In this paper, we first present a model that can be used to eliminate all redundant inequalities and give the corresponding computational results for the same numerical examples used in Prékopa and Boros, *Operat Res* 39 (1991) 119–129. We also show how to improve the lower and upper bounds of the probability using the multitree and hypermultitree, respectively. Furthermore, we propose an exact solution approach based on the state space decomposition to compute the probability. We derive a feasible state from a state space and then decompose the space into several disjoint subspaces iteratively. The probability is equal to the sum of the probabilities in these subspaces. We use the 8-node and 15-node network examples in Prékopa and Boros, *Operat Res* 39 (1991) 119–129 and the Sioux-Falls network with 24 nodes to show that the space decomposition algorithm can obtain the exact probability of these classical examples efficiently. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 479–491, 2016

Motivated by the flow of products in the iron and steel industry, we study an identical and parallel machine scheduling problem with batch deliveries, where jobs finished on the parallel machines are delivered to customers in batches. Each delivery batch has a capacity and incurs a cost. The objective is to find a coordinated production and delivery schedule that minimizes the total flow time of jobs plus the total delivery cost. This problem is an extension of the problem considered by Hall and Potts, *Ann Oper Res* 135 (2005) 41–64, who studied a two-machine problem with an unbounded number of transporters and unbounded delivery capacity. We first provide a dynamic programming algorithm to solve a special case with a given job assignment to the machines. A heuristic algorithm is then presented for the general problem, and its worst-case performance ratio is analyzed. The computational results show that the heuristic algorithm can generate near-optimal solutions. Finally, we offer a fully polynomial-time approximation scheme for a fixed number of machines. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 492–502, 2016