Balancing and optimizing a portfolio of R&D projects

A mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), is presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multidimensional knapsack problem. Exact solution of such problems is generally difficult, but can be accomplished in reasonable time using specialized algorithms. The main contribution of this paper is an examination of two important issues related to formulation of project selection models such as the one presented here. If partial funding and implementation of projects is allowed, the resulting formulation is a linear programming (LP) problem which can be solved quite easily. Several plausible assumptions about how partial funding impacts project value are presented. In general, our examples suggest that the problem might best be formulated as a nonlinear programming (NLP) problem, but that there is a need for further research to determine an appropriate expression for the value of a partially funded project. In light of that gap in the current body of knowledge and for practical reasons, the LP relaxation of this model is preferred. The LP relaxation can be implemented in a spreadsheet (even for relatively large problems) and gives reasonable results when applied to a test problem based on GM's R&D project selection process. There has been much discussion in the literature on the topic of assigning a quantitative measure of value to each project. Although many alternatives are suggested, no one way is universally accepted as the preferred way. There does seem to be general agreement that all of the proposed methods are subject to considerable uncertainty. A systematic way to examine the sensitivity of project selection decisions to variations in the measure of value is developed. It is shown that the solution for the illustrative problem is reasonably robust to rather large variations in the measure of value. We cannot, however, conclude that this would be the case in general. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 18–40, 2001     

The selection allocation problem

The Selection Allocation Problem (SAP) is a single period decision problem which involves selecting profit‐maximizing (or cost‐minimizing) activities from various distinct groups, and determining the volume of those activities. The activities in each group are selected subject to the availability of that group's resource, which is provided by either pooling or blending raw inputs from several potential sources. Imbedded in the decision process is the additional task of determining how much raw input is to be allocated to each group to form the resource for that group. Instances of this problem can be found in many different areas, such as in tool selection for flexible manufacturing systems, facility location, and funding for social services. Our goal in this paper is to identify and exploit special structures in the (SAP) and use those structures to develop an efficient solution procedure. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 707–725, 1999     

Capacity improvement,penalties, and the fixed charge transportation problem

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch‐and‐bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three‐fold reduction in the CPU time for the branch‐and‐bound algorithm and nearly a tenfold reduction in the number of subproblems that need to be evaluated in the branch‐and‐bound enumeration tree. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 341–355, 1999     

On optimal aiming to hit a linear target

Typically weapon systems have an inherent systematic error and a random error for each round, centered around its mean point of impact. The systematic error is common to all aimings. Assume such a system for which there is a preassigned amount of ammunition of n rounds to engage a given target simultaneously, and which is capable of administering their fire with individual aiming points (allowing “offsets”). The objective is to determine the best aiming points for the system so as to maximize the probability of hitting the target by at least one of the n rounds. In this paper we focus on the special case where the target is linear (one‐dimensional) and there are no random errors. We prove that as long as the aiming error is symmetrically distributed and possesses one mode at zero, the optimal aiming is independent of the particular error distribution, and we specify the optimal aiming points. Possible extensions are further discussed, as well as civilian applications in manufacturing, radio‐electronics, and detection. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 323–333, 1999     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

Open shop scheduling to minimize the number of late jobs

We develop polynomial algorithms for several cases of the NP-hard open shop scheduling problem of minimizing the number of late jobs by utilizing some recent results for the open shop makespan problem. For the two machine common due date problem, we assume that either the machines or the jobs are ordered. For the m machine common due date problem, we assume that one machine is maximal and impose a restriction on its load. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 525–532, 1998     

Optimal control policies for a periodic review inventory system with emergency orders

We describe a periodic review inventory system where emergency orders, which have a shorter supply lead time but are subject to higher ordering cost compared to regular orders, can be placed on a continuous basis. We consider the periodic review system in which the order cycles are relatively long so that they are possibly larger than the supply lead times. Study of such systems is important since they are often found in practice. We assume that the difference between the regular and emergency supply lead times is less than the order-cycle length. We develop a dynamic programming model and derive a stopping rule to end the computation and obtain optimal operation parameters. Computational results are included that support the contention that easily implemented policies can be computed with reasonable effort. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 187–204, 1998     

An optimal structured policy for maintenance of partially observable aircraft engine components

This paper considers the maintenance of aircraft engine components that are subject to stress. We model the deterioration process by means of the cumulative jump process representation of crack growth. However, because in many cases cracks are not easily observable, maintenance decisions must be made on the basis of other information. We incorporate stress information collected via sensors into the scheduling decision process by means of a partially observable Markov decision process model. Using this model, we demonstrate the optimality of structured maintenance policies, which support practical maintenance schedules. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 335–352, 1998