We study two-agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that depends on the completion times of its own jobs only. We consider several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. Our goal is to find an optimal schedule that minimizes the objective value of one agent, subject to an upper bound on the objective value of the other agent. For each problem under consideration, we provide either a polynomial-time or a pseudo-polynomial-time algorithm to solve it. We also devise a fully polynomial-time approximation scheme when both agents’ scheduling criteria are the weighted number of tardy jobs.

We propose a novel simulation-based approach for solving two-stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock-dependent uncertain demand both in single and multi-item (news-stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation-based optimization schemes. Finally, we conclude with directions for future research.

The cultural and creative industries (CCIs) in Taiwan have gradually contributed to the national economy under the impetus of government policies. We employ a two-stage data envelopment analysis model with an additive efficiency decomposition approach to measure the profitability and marketability of 22 Taiwanese cultural and creative companies. Furthermore, we employ the network-based ranking approach to identify benchmark inputs/outputs, and the strengths and weakness of each company. Our empirical results show that the profitability of the cultural and creative companies is better than their marketability. Companies in the industries of publishing, creative life, popular music, and cultural content averagely perform better than those in the other three types of CCIs in terms of profitability. Companies in the creative life industry are on average more efficient than those in the other five types of CCIs in terms of marketability. The profitability/marketability matrix of cultural and creative companies is also presented.

This article studies convergence properties of optimal values and actions for discounted and average-cost Markov decision processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic periodic-review inventory control problem with backorders, positive setup costs, and convex holding/backordering costs. The following results are established for MDPs with possibly non-compact action sets and unbounded cost functions: (i) convergence of value iterations to optimal values for discounted problems with possibly non-zero terminal costs, (ii) convergence of optimal finite-horizon actions to optimal infinite-horizon actions for total discounted costs, as the time horizon tends to infinity, and (iii) convergence of optimal discount-cost actions to optimal average-cost actions for infinite-horizon problems, as the discount factor tends to 1. Being applied to the setup-cost inventory control problem, the general results on MDPs imply the optimality of (*s*, *S*) policies and convergence properties of optimal thresholds. In particular this article analyzes the setup-cost inventory control problem without two assumptions often used in the literature: (a) the demand is either discrete or continuous or (b) the backordering cost is higher than the cost of backordered inventory if the amount of backordered inventory is large.© 2017 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2017

In standard stochastic dynamic programming, the transition probability distributions of the underlying Markov Chains are assumed to be known with certainty. We focus on the case where the transition probabilities or other input data are uncertain. Robust dynamic programming addresses this problem by defining a min-max game between Nature and the controller. Considering examples from inventory and queueing control, we examine the structure of the optimal policy in such robust dynamic programs when event probabilities are uncertain. We identify the cases where certain monotonicity results still hold and the form of the optimal policy is determined by a threshold. We also investigate the marginal value of time and the case of uncertain rewards.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

This article provides conditions under which total-cost and average-cost Markov decision processes (MDPs) can be reduced to discounted ones. Results are given for transient total-cost MDPs with transition rates whose values may be greater than one, as well as for average-cost MDPs with transition probabilities satisfying the condition that there is a state such that the expected time to reach it is uniformly bounded for all initial states and stationary policies. In particular, these reductions imply sufficient conditions for the validity of optimality equations and the existence of stationary optimal policies for MDPs with undiscounted total cost and average-cost criteria. When the state and action sets are finite, these reductions lead to linear programming formulations and complexity estimates for MDPs under the aforementioned criteria.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

We study a single-product fluid-inventory model in which the procurement price of the product fluctuates according to a continuous time Markov chain. We assume that a fixed order price, in addition to state-dependent holding costs are incurred, and that the depletion rate of inventory is determined by the sell price of the product. Hence, at any time the controller has to simultaneously decide on the selling price of the product and whether to order or not, taking into account the current procurement price and the inventory level. In particular, the controller is faced with the question of how to best exploit the random time windows in which the procurement price is low. We consider two policies, derive the associated steady-state distributions and cost functionals, and apply those cost functionals to study the two policies.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

This article analyzes a class of stochastic contests among multiple players under risk-averse exponential utility. In these contests, players compete over the completion of a task by simultaneously deciding on their investment, which determines how fast they complete the task. The completion time of the task for each player is assumed to be an exponentially distributed random variable with rate linear in the player's investment and the completion times of different players are assumed to be stochastically independent. The player that completes the task first earns a prize whereas the remaining players earn nothing. The article establishes a one-to-one correspondence between the Nash equilibrium of this contest with respect to risk-averse exponential utilities and the nonnegative solution of a nonlinear equation. Using the properties of the latter, it proves the existence and the uniqueness of the Nash equilibrium, and provides an efficient method to compute it. It exploits the resulting representation of the equilibrium investments to determine the effects of risk aversion and the differences between the outcome of the Nash equilibrium and that of a centralized version.© 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 a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player-specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non-empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm-Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.

In the literature two common macroscopic evacuation planning approaches exist: The dynamic network flow approach and the Cell–Transmission–Based approach. Both approaches have advantages and disadvantages. Many efficient solution approaches for the dynamic network flow approach exist so that realistic problem instances can be considered. However, the consideration of (more) realistic aspects (eg, density dependent travel times) results in non-linear model formulations. The Cell-Transmission-Based approach on the other hand considers realistic traffic phenomena like shock waves and traffic congestion, but this approach leads to long computational times for realistic problem instances. In this article, we combine the advantages of both approaches: We consider a Cell-Transmission-Based Evacuation Planning Model (CTEPM) and present a network flow formulation that is equivalent to the cell-based model. Thus, the computational costs of the CTEPM are enormously reduced due to the reformulation and the detailed representation of the traffic flow dynamics is maintained. We investigate the impacts of various evacuation scenario parameters on the evacuation performance and on the computational times in a computational study including 90 realistic instances.

Ranking is a common task for selecting and evaluating alternatives. In the past few decades, combining rankings results from various sources into a consensus ranking has become an increasingly active research topic. In this study, we focus on the evaluation of rank aggregation methods. We first develop an experimental data generation method, which can provide ground truth ranking for alternatives based on their “inherent ability.” This experimental data generation method can generate the required individual synthetic rankings with adjustable accuracy and length. We propose characterizing the effectiveness of rank aggregation methods by calculating the Kendall tau distance between the aggregated ranking and the ground truth ranking. We then compare four classical rank aggregation methods and present some useful findings on the relative performances of the four methods. The results reveal that both the accuracy and length of individual rankings have a remarkable effect on the comparison results between rank aggregation methods. Our methods and results may be helpful to both researchers and decision-makers.

We investigate the joint signature of coherent systems, under the assumption that the components have independent and identically distributed lifetimes. The joint signature, for a particular ordering of failure times, is an -dimensional matrix depending solely on the composition of the systems and independent of the underlying distribution function of the component lifetimes. The elements of the -dimensional matrix are formulated based on the joint signatures of numerous series of parallel systems. The number of the joint signatures involved is an exponential function of the number of the minimal cut sets of each original system and may, therefore, be significantly large. We prove that although this number is typically large, a great number of the joint signatures are repeated, or removed by negative signs. We determine the maximum number of different joint signatures based on the number of systems and components. It is independent of the number of the minimal cut sets of each system and is polynomial in the number of components. Moreover, we consider all permutations of failure times and demonstrate that the results for one permutation can be of use for the others. Our theorems are applied to various examples. The main conclusion is that the joint signature can be computed much faster than expected.

This study addresses the allocation of matched active redundancy components to coherent systems with base components having statistically dependent lifetimes. We consider base component lifetimes and redundancy component lifetimes which are both stochastic arrangement monotone with respect to a pair of components given the lifetimes of the other components. In this context, allocating a more reliable redundancy component to the weaker base component is shown to incur a stochastically larger system lifetime. Numerical examples are presented as an illustration of the theoretical results.

This article investigates joining strategies and admission control policy for secondary users (SUs) with retrial behavior in a cognitive radio (CR) system where a single primary user (PU) coexists with multiple SUs. Under a certain reward-cost structure, SUs opportunistically access the PU band when it is not occupied by the PU. If the band is available upon arrival, an SU decides with a probability either to use the band immediately or to balk the system. If the band is occupied, the SU must decide whether to enter the system as a retrial customer or to leave the system. Once the PU requests for service, the service of SU being served, if any, will be interrupted, and the interrupted SU leaves the band and retries for service after a random amount of time. In this article, we study the equilibrium behavior of non-cooperative SUs who want to maximize their benefit in a selfish, distributed manner with delay-sensitive utility function. The socially optimal strategies of SUs are also derived. To utilize the PU band more efficiently and rationally, an admission control policy is proposed to regulate SUs who enter the system in order to eliminate the gap between the individually and socially optimal strategies.