A robust regression technique using compound estimation

Least squares fitting of regression models is a widely used technique. The presence of outliers in the data can have an adverse effect on the method of least squares, resulting in a model that does not adequately fit to the bulk of the data. For this situation, robust regression techniques have been proposed as an improvement to the method of least squares. We propose a robust regression procedure that performs well relative to the current robust methods against a variety of dataset types. Evaluations are performed using datasets without outliers (testing efficiency), with a large percentage of outliers (testing breakdown), and with high leverage outliers (testing bounded influence). The datasets are based on 2-level factorial designs that include axial points to evaluate leverage effects. A Monte Carlo simulation approach is used to evaluate the estimating capability of the proposed procedure relative to several competing methods. We also provide an application to estimating costs for government satellites. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 125–139, 1998     

The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.     

Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking

Consider a continuous-time airline overbooking problem that relates to a single-leg flight and a single service class with a stationary fare. Passengers may cancel their reservations at any time and receive a full refund. Therefore fares can be thought of as being paid at flight time. At that time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. The wflight-time revenue, that is, fares received less bumping penalties paid, is quasiconcave in the number of reservations at that time. We model the reservations process as a continuous-time terminal-value birth-and-death process. A more general model than is necessary for an airline reservations system is considered, in which the airline controls both the reservation acceptance (birth) and the cancellation (death) rates. In current practice airlines do not control cancellation rates (though other industries do exercise such control, e.g., hotels) and control reservation acceptance rates by declining reservation requests. The more general model might be applied to other targeting applications, such as steering a vehicle through space toward a target location. For the general model a piecewise-constant booking-limit policy is optimal; that is, at all times the airline accepts reservation requests up to a booking limit if the current number of reservations is less than that booking limit, and declines reservation requests otherwise. When the airline is allowed to decline all reservation requests, as is the case in practice, the booking-limit optimal policy defined by using the greatest optimal booking limit at all times is piecewise constant. Moreover, these booking limits fall toward flight time. © 1996 John Wiley & Sons, Inc.     

Scheduling to minimize release-time resource consumption and tardiness penalties

We consider the problem of scheduling a set of jobs with a common due-date on a single-machine where the release time of a job is related to the amount of resource consumed. The objective is to minimize the total resource consumption and the total tardiness. While the problem is strongly NP-hard in general, we discuss two different special cases for which special properties are identified and used to develop efficient pseudo-polynomial time algorithms. © 1995 John Wiley & Sons, Inc.     

An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines

We consider the multitasking scheduling problem on unrelated parallel machines to minimize the total weighted completion time. In this problem, each machine processes a set of jobs, while the processing of a selected job on a machine may be interrupted by other available jobs scheduled on the same machine but unfinished. To solve this problem, we propose an exact branch‐and‐price algorithm, where the master problem at each search node is solved by a novel column generation scheme, called in‐out column generation, to maintain the stability of the dual variables. We use a greedy heuristic to obtain a set of initial columns to start the in‐out column generation, and a hybrid strategy combining a genetic algorithm and an exact dynamic programming algorithm to solve the pricing subproblems approximately and exactly, respectively. Using randomly generated data, we conduct numerical studies to evaluate the performance of the proposed solution approach. We also examine the effects of multitasking on the scheduling outcomes, with which the decision maker can justify making investments to adopt or avoid multitasking.     

Stochastic production capacity: A bane or a boon for quick response supply chains?

The quick response (QR) system that can cope with demand volatility by shortening lead time has been well studied in the literature. Much of the existing literature assumes implicitly or explicitly that the manufacturers under QR can always meet the demand because the production capacity is always sufficient. However, when the order comes with a short lead time under QR, availability of the manufacturer's production capacity is not guaranteed. This motivates us to explore QR in supply chains with stochastic production capacity. Specifically, we study QR in a two-echelon supply chain with Bayesian demand information updating. We consider the situation where the manufacturer's production capacity under QR is uncertain. We first explore how stochastic production capacity affects supply chain decisions and QR implementation. We then incorporate the manufacturer's ability to expand capacity into the model. We explore how the manufacturer determines the optimal capacity expansion decision, and the value of such an ability to the supply chain and its agents. Finally, we extend the model to the two-stage two-ordering case and derive the optimal ordering policy by dynamic programming. We compare the single-ordering and two-ordering cases to generate additional managerial insights about how ordering flexibility affects QR when production capacity is stochastic. We also explore the transparent supply chain and find that our main results still hold.     

Optimal policies for stochastic clearing systems with time-dependent delay penalties

We study stochastic clearing systems with a discrete-time Markovian input process, and an output mechanism that intermittently and instantaneously clears the system partially or completely. The decision to clear the system depends on both quantities and delays of outstanding inputs. Clearing the system incurs a fixed cost, and outstanding inputs are charged a delay penalty, which is a general increasing function of the quantities and delays of individual inputs. By recording the quantities and delays of outstanding inputs in a sequence, we model the clearing system as a tree-structured Markov decision process over both a finite and infinite horizon. We show that the optimal clearing policies, under realistic conditions, are of the on-off type or the threshold type. Based on the characterization of the optimal policies, we develop efficient algorithms to compute parameters of the optimal policies for such complex clearing systems for the first time. We conduct a numerical analysis on the impact of the nonlinear delay penalty cost function, the comparison of the optimal policy and the classical hybrid policy (ie, quantity and age thresholds), and the impact of the state of the input process. Our experiments demonstrate that (a) the classical linear approximation of the cost function can lead to significant performance differences; (b) the classical hybrid policy may perform poorly (as compared to the optimal policies); and (c) the consideration of the state of the input process makes significant improvement in system performance.     

From the sea to outer space: The command of space as the foundation of spacepower theory

Colin Gray once lamented the absence of a ‘Mahan for the final frontier’ and spacepower theory in strategic studies. This article proposes the command of space as the fundamental concept of spacepower theory, and that Mahan himself has much to offer in the endeavour of spacepower theory-making than has hitherto been realised. The theory is advanced by tempering versions of the ‘command of space’, stressing its educational intent, and explaining the nuanced sub-concepts of space control and denial through understanding some precedents set by seapower theory. In the process, aspects of Mahanian and Corbettian seapower theory are unified.     

The two-machine permutation flow shop with state-dependent processing times

If the processing time of each job in a flow shop also depends on the time spent prior to processing, then the choice of a sequence influences processing times. This nonstandard scheduling problem is studied here for the minimum makespan schedule in a flow shop with two machines. The problem is NP-hard in the strong sense and already contains the main features of the general case [10]. Restricting to the case of permutation schedules, we first determine the optimal release times of the jobs for a given sequence. Permutation schedules are evaluated for this optimal policy, and the scheduling problem is solved using branch-and-bound techniques. We also show the surprising result that the optimal schedule may not be a permutation schedule. Numerical results on randomly generated data are provided for permutation schedules. Our numerical results confirm our preliminary study [10] that fairly good approximate solutions can efficiently be obtained in the case of limited computing time using the heuristics due to Gilmore and Gomory [7]. © 1993 John Wiley & Sons, Inc.