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Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods. Our computational results using real and randomly generated data indicate that these models are quite effective in finding optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits. [ABSTRACT FROM AUTHOR]

We present an efficient solution method -- Direct Derivative Estimation (DDE) -- for computing optimal order-up-to levels for a discrete time non-stationary inventory control model. We generalize a number of non-stationary inventory control models (which underlie larger models of supply chains) that include forecast updates. seasonality, information sharing, and exchange-rate fluctuations. This procedure is different from the existing ones in that it computes, in a recursive manner, the derivative of the cost function and not the cost function itself. It can also handle a much wider variety of fluctuations in the problem parameters. In our computational testing it was found to be considerably faster than Dynamic Programming and Infinitesimal Perturbation Analysis. [ABSTRACT FROM AUTHOR]

We propose a new algorithm for solving integer programming (IF) problems that is based on ideas from algebraic geometry. The method provides a natural generalization of the Parkas lemma for IP, leads to a way of performing sensitivity analysis, offers a systematic enumeration of all feasible solutions, and gives structural information of the feasible set of a given IP. We provide several examples that offer insights on the algorithm and its properties. [ABSTRACT FROM AUTHOR]

For a single product, single-stage capacitated production-inventory model with stochastic, periodic (cyclic) demand, we find the optimal policy and characterize some of its properties. We study the finitehorizon, the discounted infinite-horizon and the infinitehorizon average cases. A simulation based optimization method is provided to compute the Optimal parameters. Based on a numerical study, several insights into the model are also provided. [ABSTRACT FROM AUTHOR]

Most models of multilevel production and distribution systems assume unlimited production capacity at each site. When capacity limits are introduced, an ineffective policy may lead to increasingly large order backlogs: The stability of the system becomes an issue. In this paper, we examine the stability of a multi-echelon system in which each node has limited production capacity and operates under a base-stock policy. We show that if the mean demand per period is smaller than the capacity at every node, then inventories and backlogs are stable, having a unique stationary distribution to which they converge from all initial states. Under i.i.d. demands we show that the system is a Harris ergodic Markov chain and is thus wide-sense regenerative. Under a slightly stronger condition, inventories return to their target levels infinitely often, with probability one. We discuss cost implications of these results, and give extensions to systems with random lead times and periodic demands. [ABSTRACT FROM AUTHOR]