Joseph C. Hartman

THE RELEVANT INTERNAL RATE OF RETURN

In this article we present a method for determining project acceptability in the presence of multiple internal rates of return. An internal rate of return is an interest rate that equates the present worth of a cash flow stream to zero. When unique, it provides valuable information about the return on the investment and is often viewed as a measure of efficiency. Unfortunately, this analysis is clouded when there are multiple internal rates of return, which can occur when a project is defined by a mixture of positive and negative cash flows. While many methods have been presented in the literature to deal with this problem, we believe ours to be unique in that it does not rely on the computation of another measure of worth, but rather, the identification of the relevant rate of return from the set of internal rates of return. We show that this rate always produces decisions consistent with present worth under the assumption that at least one real internal rate of return exists. In doing so, we provide new definitions of when a project is borrowing from, or loaning to, the firm. These definitions help in understanding the meaning of multiple internal rates of return, which is also discussed.

Finite-horizon equipment replacement analysis

The optimal solution to the infinite-horizon equipment replacement problem with stationary costs is to continually replace an asset at its economic life. The economic life is the age that minimizes the Equivalent Annual Cost (EAC), which includes purchase, operating and maintenance costs less salvage values. We explore the question of whether this is a good policy for the finite-horizon problem, which occurs when companies only require an asset for a specified length of time, usually to fulfill a specific contract. We identify cases, according to capital costs, operating costs, and the interest rate, when this policy is good and when it deviates significantly from optimal. Furthermore, we provide a bound on the minimum number of times that an asset is retained at its economic life over a finite horizon. This is facilitated through a new dynamic-programming formulation to the problem based on the integer-knapsack problem with nonlinear costs. The bound can be derived from any feasible solution, although we provide a closed-form solution for the case of convex EAC values.

The parallel replacement problem with demand and capital budgeting constraints

A generalized parallel replacement problem is considered with both fixed and variable replacement costs, capital budgeting, and demand constraints. The demand constraints specify that a number of assets, which may vary over time, are required each period over a finite horizon. A deterministic, integer programming formulation is presented as replacement decisions must be integer. However, the linear programming relaxation is shown to have integer extreme points if the economies of scale binary variables are fixed. This allows for the efficient computation of large parallel replacement problems as only a limited number of 0–1 variables are required. Examples are presented to provide insight into replacement rules, such as the “no-splitting-rule” from previous research, under various demand scenarios.

An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets

This paper addresses a fleet-sizing problem in the context of the truck-rental industry. Specifically, trucks that vary in capacity and age are utilized over space and time to meet customer demand. Operational decisions (including demand allocation and empty truck repositioning) and tactical decisions (including asset procurements and sales) are explicitly examined in a linear programming model to determine the optimal fleet size and mix. The method uses a time-space network, common to fleet-management problems, but also includes capital cost decisions, wherein assets of different ages carry different costs, as is common to replacement analysis problems. A two-phase solution approach is developed to solve large-scale instances of the problem. Phase I allocates customer demand among assets through Benders decomposition with a demand-shifting algorithm assuring feasibility in each subproblem. Phase II uses the initial bounds and dual variables from Phase I and further improves the solution convergence without increasing computer memory requirements through the use of Lagrangian relaxation. Computational studies are presented to show the effectiveness of the approach for solving large problems within reasonable solution gaps.

Multiple asset replacement analysis under variable utilization and stochastic demand

Abstract The economic life of an asset is dependent on a variety of factors, including deterioration and obsolescence. While obsolescence is generally a result of changes external to the asset, such as technological change, deterioration is generally a result of how the asset is utilized over its lifetime. If multiple assets are available to meet demand and the assets must not continually operate at maximum capacity, then a decision-maker may have some control over asset utilization patterns by allocating workload. These utilization patterns directly impact operating costs and salvage values and thus have a strong influence on the optimal replacement time of the assets. In this paper, we examine asset replacement decisions, based on age and cumulative utilization, under variable periodic utilization with multiple, parallel assets under various cost and demand assumptions. We provide an efficient optimal solution procedure through the use of stochastic dynamic programming, illustrate a threshold optimal policy under common cost assumptions and provide a method to easily examine solutions for the two-asset case. Extensions to the n -asset case are also discussed.

CASE STUDY: BUS FLEET REPLACEMENT

Parallel replacement analysis is concerned with determining minimum cost replacement schedules for a group of assets that are economically interdependent and operate in parallel. That is, keep and replace decisions are required for each asset among a group of assets over a specified horizon. The assets are economically linked through economies of scale or budgeting constraints. One application of parallel replacement analysis is fleet replacement. We recently studied the operations, including fleet replacement policies, for a city transit bus operator in Europe. Key factors in their replacement decisions included the ability to choose from multiple manufacturers, purchase price, and government regulations. We explore these and other factors, by solving a heterogeneous replacement problem with fixed costs, budgeting constraints, and demand constraints. Through extensive sensitivity analysis we analyze the impact of various parameters on decisions, in terms of the choice of replacement assets, as well as the optimal time to retain assets. Additionally, we provide motivation for future research in this application area, which is important for many cities.

Asset management with reverse product flows and environmental considerations

Abstract Today many business enterprises employ capital assets in the form of electronic equipment, such as personal computers, workstations and peripherals, in large quantities. Due to rapid technological progress (leading to a short life cycle for these products), and hazardous material content in electronic products (which is an environmental problem and a disposal challenge), leasing or procurement contracts with take-back considerations can be attractive. For a large electronic equipment leasing company, optimal management of assets supported by good logistics and end-of-life processing decisions is crucial, and may provide a significant competitive advantage. There is currently no analytic approach for making these decisions in an integrated fashion. In this research, a mixed integer linear programming (MILP) model is developed to facilitate better leasing and logistics decisions (including end-of-life disposal options) from the perspective of an electronic equipment leasing company. A case study with representative industry data is used to validate the approach and potential applications of the model are illustrated for alternative scenarios. This research contributes new models and understanding to the intersection of the fields of reverse logistics and equipment replacement.

MULTIPLE OPTIONS IN PARALLEL REPLACEMENT ANALYSIS: BUY, LEASE OR REBUILD

An integer programming model solving the demand constrained finite horizon parallel replacement problem with homogeneous assets is presented here with asset purchases, leases and rebuilds as viable replacement options. The model minimizes the purchase, operating, maintenance and salvage costs of a fleet of assets while meeting demand requirements. The formulation is adapted to handle both capital and expense rationing constraints. Computational experience with real sized problems in the transportation industry is discussed and small examples are provided for illustration.

The series–parallel replacement problem

Abstract Traditional equipment replacement models focus on single machine problems. However, the capacity of many production facilities is defined by multiple, heterogeneous machines. In this situation, optimal replacement (and expansion) decisions must consider all machines and their integration simultaneously as they define system capacity and are therefore economically interdependent. We model a multiple machine replacement problem that is characterized as a parallel flow shop environment. Work flows through processes in a facility according to a predetermined processing order for the product(s). For a given process, numerous machines, which may differ according to type (different manufacturers), capacity, and/or age, operate in parallel. A series of these processes defines a line and in our analysis, a plant is comprised of multiple, parallel lines. In this preliminary investigation, we present an integer programming formulation to determine optimal purchase, salvage, utilization and storage decisions for each asset over a finite horizon. We illustrate that this model is difficult to solve. We provide valid inequalities to improve the lower bound provided by the linear programming relaxation and a dynamic programming approach to provide initial upper bounds.

ON THE EQUIVALENCE OF NET PRESENT VALUE AND MARKET VALUE ADDED AS MEASURES OF A PROJECT'S ECONOMIC WORTH

ABSTRACT The metric Economic Value Added, or EVA, has recently become quite popular for analyzing company balance sheets, determining executive compensation packages and even project selection. The analysis entails comparing net after-tax operating profit against the allocated cost of capital for a given period. This paper shows, in general, that Market Value Added (MVA), which is the present value of a series of EVA values, is economically equivalent to the traditional NPV measure of worth for evaluating an after-tax cash flow profile of a project if the cost of capital is used for discounting. Additionally, insight is provided into the rationale behind EVA analysis through an interpretation of its capital and income allocation procedure for investment projects.