Carlton H. Scott

Allocation of resources in project management

Resource allocation on a project planning network is modelled as a minimax convex program. A limited budget is to be distributed over the activities of a project so as to minimize the duration of the project or critical path. Conjugate duality is used to simplify the formulation for computational purposes

The analysis of entropy models with equality and inequality constraints

Entropy models are emerging as valuable tools in the study of various social problems of spatial interaction. With the development of the modelling has come diversity. Increased flexibility in the model can be obtained by allowing certain constraints to be relaxed from equality to inequality. To provide a better understanding of these entropy models they are analysed by geometric programming. Dual mathematical programs and algorithms are obtained.

Model for the allocation of electronics components to reuse options

This paper develops an optimal allocation procedure for the disassembled components of electronic equipment. It also reviews and discusses the reuse options available to high-tech companies when it comes to disassembly. A piecewise linear concave program is formulated to find the optimal disassembly strategy. The model is then applied to actual data from an electronics manufacturer. It is concluded that the landfill option, the most undesirable option available to most manufacturers, can be avoided if the manufacturer can find other options with non-negative returns.

Generalized geometric programming applied to problems of optimal control: Part I, theory

A modification to the formulation in Ref. 1 is given.

Duality in infinite-dimensional mathematical programming: Convex integral functionals

Abstract A completely symmetric duality theory is derived for convex integral functionals. As an example we derive an infinite-dimensional version of prototype geometric programming. In this case the dual problem may turn out to be finite-dimensional. Examples from statistics are included.

Location of a facility minimizing nuisance to or from a planar network

In this paper we investigate the location of a facility anywhere inside a planar network. Two equivalent problems are analyzed. In one problem it is assumed that the links of the network create a nuisance or hazard and the objective is to locate a facility where the total nuisance is minimized. An equivalent problem is locating an obnoxious facility where the total nuisance generated by the facility and inflicted on the links of the network is minimized. Exact and approximate solution methods for its solution are proposed and tested on a set of planar networks with up to 40,000 links yielding good results.

Selection of an optimal subset of sizes

For a company that produces a product in a range of sizes, it is sometimes possible to meet demand for a smaller size by substituting a larger size. In this paper, we give an integer linear programming model that addresses this issue. Various characteristics of the optimal policy are given. These properties are exploited when the formulation is extended to the multi-period stochastic demand case. This application was motivated by our experience with a company that manufactures a range of multiple-piece blind fasteners where savings in setup cost can be made using long-grip fasteners to meet the demand for short-grip fasteners.

Location of a distribution center for a perishable product

A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.

Conjugate duality in generalized fractional programming

The concepts of conjugate duality are used to establish dual programs for a class of generalized nonlinear fractional programs. It is now known that, under certain restrictions, a symmetric duality exists for generalized linear fractional programs. In this paper, we establish this symmetric duality for the nonlinear case.

Quadratic geometric programming with application to machining economics

Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.