Frank G. Landram

A Note on Integer Programming Formulations of the Real-Time Optimal Scheduling and Flight Path Selection of UAVs

In recent years, considerable attention has been given to research on various aspects of unmanned aerial vehicles (UAVs) applications. UAVs are currently used for various military and civilian missions in the air, sea, space, and on the ground. In two recent papers, Shima (2007) and Kim (2007) considered closely similar m-UAV problems. In Shima (2007), the problem is considered with each target being served by only one UAV to minimize the total travel distance across all UAVs (called load balancing), however, in Kim (2007), the problem is considered with maximum number of targets that each UAV can serve with the objective of minimizing load balancing. Kim presented mixed integer linear programming (MILP) formulations of the load balancing problem both for when the UAVs return to their original depot and when they do not. Shima presented a combinatorial optimization formulation of their model with a branch-and-bound solution procedure. The MILP formulation of the load balancing problem is also adaptable to Shima s problem. However, there are major inefficiencies with the MILP formulation presented in Kim s model. In fact, The MILP formulations presented in Kim are highly complicated with huge number of variables and constraints making them impractical for applications. The purpose of the present note is to provide explicit MILP formulations that dramatically reduce the number of variables and the number of constraints for variety of UAV tour assignment problems including the two models mentioned above and via simulation we show significance of these new formulations.

On the Flexible Demand Assignment Problems: Case of Unmanned Aerial Vehicles

Multiresource generalized assignment problem (MRGAP) has enormous applications in solving real problems of industries. In recent years, several generalizations of MRGAP have been proposed to tackle very difficult problems. An important generalization is called flexible demand assignment (FDA) problem. In this paper, a generalization of FDA is proposed that has many applications. Two features of our formulation are inclusion of: 1) acceptance of orders from a large set of available orders and 2) consideration of setup time between operations of two consecutive of tasks. We show an interesting application of generalized FDA is unmanned aerial vehicle (UAV) assignment problem. For the UAV assignment problem, we show our formulation considerably reduces the size of the problem compared to some recent results. To test effectiveness of the proposed model, computational experiment with CPLEX for the UAV assignment problem is presented.

Scheduling deteriorating jobs on a single machine to minimize the maximum processing times

In many real-world scheduling problems the processing time of a job is a variable and depends on a function of its starting time. The origin of the mathematical modelling of these types of sequencing problems is new and most studies have concentrated on minimizing the makespan, and minimizing the total completion times. This paper addresses the problem of sequencing a set of n independent jobs on a single machine when the processing time of a job is a linear function of its starting time, with the objective of minimizing the maximum processing times. A heuristic algorithm for the problem is presented. The effectiveness of the algorithm is computationally tested. The algorithm can optimally solve the problem for some important special cases.

Spreadsheet calculations of probabilities from the F, t, χ 2 , and normal distribution

By computing probabilities from the normalization of the F distribution (instead of by numerical integration methods), statistical capabilities in spreadsheet operations can be greatly expanded and enhanced.

Teaching multiple regression in elementary statistics

This is a starting point for those instructors who desire to enhance their teaching of elementary business statistics. The course must cover the fundamentals and there is not always time to discuss applications effectively. The discussion of applications is essential for the business student to be able to realise the relevance of statistical methods in decision-making. Therefore, the course is reorganised in order to exploit the dependence among topics. A modified outline for the business statistics course and a rationale are presented. Some of the benefits derived from the modified outline and feedback obtained from students and faculty are discussed.

Computing orthogonal polynomials

A simple transformation for achieving orthogonal polynomials of any order is described in this article. This transformation, called the residual procedure, is easy to understand, easy to implement in existing programs, and applicable for polynomial regression models whose data are unequally spaced. This same procedure is used in obtaining coefficients for orthogonal contrasts in the analysis of variance. The simplicity of this procedure also makes it easily adaptable to spread-sheet and data base applications.

A computational understanding of partial and part determination coefficients

A computational understanding of partial and part determination coefficients brings additional insight concerning their interpretations in regression. It also enables one to easily identify synergistic combinations. Benefits from the practical interpretation of synergism have yet to be fully explored and exploited. Hence, this study provides a new dimension in the analysis of data.

An Algorithm for Enhancing Spreadsheet Regression with Out-of-Sample Statistics

An innovative algorithm is developed for obtaining spreadsheet regression measures used in computing out-of-sample statistics. This algorithm alleviates the leave-one-out computational simulation complexity and memory size problems perceived in computing these statistics. Hence, the purpose of this article is to describe a computationally enhanced algorithm that gives spreadsheet users advanced regression capabilities thereby adding a new dimension to spreadsheet regression operations. These statistics include diagonals of the hat matrix, legitimate forecasting intervals, and PRESS residuals. These computational innovations promote learning while eliminating spreadsheet inadequacies thereby making spreadsheet regression attractive to academicians in teaching and practitioners in acquiring further application competence.