Optimizing capital investments under technological change and deterioration: A case study on MRI machine replacement

ABSTRACT

We study the multiple style and type parallel asset replacement problem (MST-PRES), which determines an optimal policy for keeping or replacing a group of assets that operate in parallel under a limited budget. Operating assets generally suffer from deterioration, which results in high operation and maintenance (O&M) cost and decreased salvage value, and technological improvements make it possible for new assets to operate more efficiently at a lower cost. In order to address these issues, we formulate a multi-objective mixed-integer programming (MIP) model that minimizes fixed and variable costs of purchasing new assets, O&M cost, inventory cost, and penalty cost for unmet demand minus salvage values, while considering technological advances and deterioration as a gain and loss in capacity, respectively. We apply our model to a case study involving two different styles of assets: a full-body magnetic resonance imaging (MRI) machine and a smaller extremity magnetic resonance imaging (eMRI) machine. Each has two types: high-field and low-field. We perform computational experiments and analyses using key model parameters and illustrate optimal replacement strategies considering the impact of technological advances and deterioration. Results show that the proposed MIP model provides valuable insights and strategies for companies, decision makers, and government entities on the capital asset management.     

CASE STUDY: US ARMY UTILITY HELICOPTER FLEET MODERNIZATION ANALYSIS

The US Army has relied heavily on helicopter support for more than 30 years. These aircraft have been used for a variety of purposes, with the most widely identified category being the utility, or general-purpose transport, mission area. Currently, the US Army is confronting the problem of managing an aging equipment fleet (its helicopters) in the face of significant budgetary constraints, a very large-scale fleet replacement problem. By the nature of its business, the US Army is not working toward a desired profit margin, but it must maintain a level of military capability to meet its national defense obligations. The US Army recently commissioned the Utility Helicopter Fleet Modernization Analysis to determine the most cost and operationally effective strategy for fleet replacement or modernization. This case study presents a synopsis of how multi-criteria decision analysis techniques were integrated with total cost of ownership considerations to develop a multi-billion dollar equipment modernization strategy, a strategy that is being implemented by the US Army today.     

CONCURRENT ENGINEERING: CONTEMPORARY ISSUES AND MODERN DESIGN TOOLS EDITED BY HAMID R. PARSAEJ AND WILLIAM G. SULLIVAN Chapman & Hall,London, 1993, xiii + 497 pp. ISBN 0-412-46510-8. List: $75.00.

In a recent paper, Jones and Zydiak [2] discuss the steady state fleet design problem, which has no natural initial distribution of vehicles. For this problem, they develop a new optimality criterion of minimizing annual equivalent cost per vehicle because the traditional optimally criterion of minimizing annual equivalent cost can lead to paradoxical results, as shown by example, when applied to the fleet design problem. In a subsequent note, Hartman [1] argues that this paradox is actually a result of a replacement convention that ignores opportunity costs. In this response, we demonstrate that paradoxical replacement behavior can occur with the traditional criterion even when opportunity costs are accounted for in the replacement analysis. We further conclude that the problems considered respectively by Jones and Zydiak [2] and Hartman [1] are fundamentally different in nature.     

AFTER-TAX ECONOMIC REPLACEMENT ANALYSIS

This paper examines after-tax serial replacement analysis under current United States tax law. The law explicitly defines the difference between an asset disposal (retirement) and a like-for-like exchange (replacement). A gain or loss is only realized when an asset is retired while a replacement leads to the transfer of any residual book value balance to the acquired asset. This transferal greatly complicates analysis and leads to non-stationary solutions, even with time invariant costs. We analyze the effect of this movement in book value for assets on replacement decisions. Furthermore, a dynamic programming formulation is presented with a state space defined by asset age and initial book value, as current replacement models cannot correctly capture the after-tax cash flow implications of this balance transfer. The new model is compared to traditional after-tax replacement models which assume that a gain or loss is realized at each asset sale over the horizon. Examples illustrate that this assumption can lead to widely different solutions, especially in the cases where gains or losses from asset sales are large.     

A Review of: BUSINESS COST-BENEFIT ANALYSIS

This paper reports the findings of a survey of 427 large hospitals nationwide. The survey provided information regarding the techniques employed as primary and secondary tools of capital budgeting, the percentage of capital projects formally evaluated, the methods used in capital budgeting, the qualitative factors which influence the capital budgeting decisions and the extent of their impact in determining the acceptance decision, and the nature and frequency of involvement of the medical staff in major capital investment decisions.     

A Review of: “ECONOMIC DECISION MODELS FOR ENGINEERS AND MANAGERS” By James L. Riggs McGraw-Hill Book Company 1968 pp.xvi,401 $11.50

This study breaks down the use of capital budgeting procedures between industries. While it is easy to state that the use of capital budgeting analysis has become more sophisticated over the decades, the question remains as to whether different industries have followed the same pattern. Three hundred two Fortune 1,000 companies responded to a survey organized along industry lines. Chi-square independence of classification tests indicated that a null hypothesis of no significant relationship between industry classification and capital budgeting procedures could be rejected in a number of decision-making areas including goal setting, rates of return, and portfolio considerations. Just as industry patterns affect financing decisions (debt vs. equity), they also affect capital budgeting decisions, and this study emphasizes that point.     

SOLVING LARGE REPLACEMENT PROBLEMS WITH BUDGET CONSTRAINTS

Traditional replacement models assume unlimited capital. In practice, however, firms frequently use budgets to control their expenditures. Budget constraints necessitate that all replacement decisions be considered as a portfolio, creating a difficult combinatorial problem. In previous research, we developed a branch-and-bound algorithm for solving moderately-sized problems optimally. In this paper, we propose a dual heuristic for dealing with large, realistically sized problems. First, we solve the individual replacement problems ignoring the budget constraints. Then, we reduce, or eliminate, if possible, budget violations by solving a Lagrangian dual problem. The computational tests suggest that the effectiveness of the approach increases with problem size.     

A REVIEWS OF “THE ZERO-SUM SOCIETY,by Lester C. Thurov,Basic Books,Inc., New York, 1980, 230 pages,list, $12.95.”

Linear Programming Formulations of capital budgeting under conditions of pure capital rationing frequently assume that the dual variables of the budget constraints muse be equal to the corresponding discount factors. This paper shows that this assumption leads to solutions in which the maximum objective function is zero. From this it follows that the dual variables of the budget constraints are zero for this case as well as for that where lending or carryforward is Included.     

REIT Capital Budgeting and Equity Marginal q

Equity marginal  q  is the change in the market value of a company's equity in response to a one-unit unexpected change in its asset base. Hence, it is a profitability index that evaluates a firm's capital budgeting decisions at the margin. We estimate the equity marginal  q  for real estate–managing public corporations, namely, real estate investment trusts (REITs), in an attempt to understand how the various costs and benefits of being a public corporation play a role in managing this important asset class. Using the universe of equity REITs for the period from 1993 to 2005, we find that REITs with greater idiosyncratic volatility, higher stock turnover and smaller bid-ask spread have a higher equity marginal  q . In addition, both the holdings of institutional investors and their investment horizons are respectively positively related to equity marginal  q.  With these firm characteristics taken into account, firm size is found to be negatively related to equity marginal  q . Our findings are economically important as well, because the equity marginal  q  ratio alone accounts for approximately one-third of the total REIT shareholder wealth change during the study period.     

Capital budgeting under uncertainty: An extended goal programming approach

Mathematical programming techniques have long been recognized as the most suitable approach to the complex problem of capital budgeting in corporations. This is because contrary to conventional single-project appraisal techniques such as the net present value method, financial planners do not normally engage in project-by-project analysis to determine the projects that would be included in capital budgets. In addition, the existing chance-constrained (both single and multiple objectives) models developed to deal with the problem of uncertainty in capital budgeting are grossly defective, since they, indeed, address the problem of risk, rather than uncertainty. This paper presents an extended goal programming methodology to address the problem of capital budgeting under uncertainty to overcome the defects of chance-constrained capital budgeting models. In particular, since financial planners frequently deal with the complex problem of capital budgeting by aggregating large numbers of small investment proposals into families of large projects, the paper presents necessary and sufficient conditions for the acceptance of a set of investment projects by a business enterprise. The results indicate that under uncertainty, firms faced with capital rationing are less economically efficient than others that are not so faced. Also, the results show that optimal allocation policy under uncertainty requires the actual discount rate to be greater than the market cost of capital, a finding which is consistent with corporate finance practice.     

Using Copula Functions in Bayesian Analysis: A Comparison of the Lognormal Conjugate

Bayesian techniques have been applied to analyze sequential investment decisions in the capital budgeting literature. This article introduces copula-based Bayesian analysis as an alternative to the traditional approach where conjugate relationships do not exist. Using a numerical example, we illustrate the steps involved in the copula-based Bayesian approach. Graphical techniques for selecting an appropriate copula are also discussed. The unique ability of copulas to model nonlinear dependence rationalizes the use of copula functions as an alternative technique.     

Parallel machine replacement under horizon uncertainty

Construction projects usually get delayed for several time periods. When the planning horizon of a project is extended, projections for purchase and salvage of machinery within the planning horizon become inaccurate and less beneficial and often lead to unexpected costs. In this article, we formulate a parallel machine replacement (PMR) problem as a two-stage stochastic program with an uncertain planning horizon. We consider renting as an alternative to purchasing and maintaining the machinery. We show the application of the model through a case study in construction projects. Through numerical analysis, we derive managerial implications and show the value of the stochastic model.     

A review of “ Edited by Richard H. Bernhard,North Carolina State University ” THE BUSINESS OF RISK by Peter G. Moore,Cambridge University Press,New York, 1984, x + 244 pages,ISBN 0521-24174 X ( hard cover), List $ 44.50; ISBN 0521-28497 X (paperback), List $ 16.95

Four replacement scenarios were analyzed for a vehicle fleet designed to haul sensitive packages at two different customer locations. In addition to completing an economic replacement analysis study, each option was analyzed according to availability requirements and other intangible attributes. Finally, a thorough sensitivity analysis was performed to examine the impact of reliability assumptions on both life cycle costs and the expected economic life of each option. Once all factors were analyzed, each critical input was graded and scored, leading to the final recommendation to replace the current equipment with a new technology.     

Do Tax‐Deferred Exchanges Impact Purchase Price? Evidence from the Phoenix Apartment Market

Many authors have commented on the compliance risk associated with tax-deferred exchanges. However, no published studies explicitly address whether the risks associated with the exchange process impact the price at which exchanged assets trade. Using a unique data set that documents transactions for nondirect exchanges, this study examines the price impact of tax-deferred exchanges on apartment transactions in the Phoenix, Arizona, market. Consistent with the price pressure hypothesis originally developed by Scholes (1972) and Kraus and Stoll (1972) and the tax capitalization hypothesis proposed by Oates (1969), the data show that exchange participants pay an economically significant premium to acquire replacement assets. A conventional hedonic price index is generated to investigate the rational bounds of the exchange premium.     

Optimised asset replacement strategy in the presence of lead time uncertainty

This paper develops an optimal replacement strategy for capital intensive equipment with long delivery lead time. The strategy is based on an extended version of the real options approach to repeated replacement decisions, in which the goal is to determine the operating cost and delivery lead-time conditions upon which a replacement should be ordered.The real options approach to capital replacement problems is superior to traditional net present value (NPV) approaches, as it values of the option to adapt decisions based on current (rather than predicted) system conditions. However, previous applications of the real options approach to repeated replacement have not considered the impact of long and uncertain lead times, and have therefore focused on when to replace rather than when to order. Delivery lead times are an important consideration in an expanding mining sector in which demand for heavy mobile equipment (HME) exceeds the capacity of suppliers to provide the equipment in a timely manner.The inclusion of a lead time element results in a decision with an “option” period and an “option-less” period. Simulations are used to demonstrate the improved outcome of real options based replacement strategies compared with those derived using a traditional NPV approach, both with and without lead times. Further the performance of the order placement strategy with different boundary conditions, bounded and reflecting, is explored. No appreciable difference in performance of these strategies was identified. The optimal order placement strategy incorporating delivery lead times is displayed on a simple chart which is accessible to fleet management personnel.     

Fuzzy logic in manufacturing: A review of literature and a specialized application

Manufacturing decisions inherently face uncertainties and imprecision. Fuzzy logic, and tools based on fuzzy logic, allow for the inclusion of uncertainties and imperfect information in decision making models, making them well suited for manufacturing decisions. In this study, we first review the progression in the use of fuzzy tools in tackling different manufacturing issues during the past two decades. We then apply fuzzy linear programming to a less emphasized, but important issue in manufacturing, namely that of product mix prioritization. The proposed algorithm, based on linear programming with fuzzy constraints and integer variables, provides several advantages to existing algorithm as it carries increased ease in understanding, in use, and provides flexibility in its application.     

Present Worth of Interest Tax Credits

The widely used concept of a cash flow per project in capital budgeting has serious weaknesses when resources are shared by different projects. Accordingly, the concept of cash flow per project is not used herein. Instead, the project portfolio approach is used in which costs are considered only in the acquisition and utilization of resources; when these costs actually occur. The main conclusion from this approach is that better capital budgeting decisions can be made if the concept of cash flow per project is avoided when resources are shared.     

An R & D planning and control servosystem: A case study*

This paper describes a planning and control system (PACS) to aid R & D decision-making which has been developed and used at the Monsanto Company, St. Louis, Missouri, U.S.A. The planning model portion of the integrated system is a two-dimensional dynamic programming resource allocation algorithm which performs project selection, budgeting and scheduling. Behavioral parameters that can be used to simulate certain organizational factors are included in the planning model. The control model portion of the integrated system develops cost-effectiveness measures of variances between actual and planned performances for ongoing projects over time, which provide early warnings of pending project failures and guide control action. Applications of the system at Monsanto indicate that it significantly aids the development of satisfactory organizational decisions and also provides a laboratory for pretesting decisions.     

Case Study: Solving a Rental Fleet Sizing Model with a Large Time–Space Network

This article addresses a rental fleet sizing problem (RFS) in the context of the truck rental industry, subject to uncertain customer travel time and nonstationary customer demand that is dependent on geographical location, time, and the economic cycle of the industry. We integrate tactical (asset purchases and sales) and operational (empty truck movement and vehicle assignment) decisions, with the explicit incorporation of an asset age factor, to achieve lower cost solutions. Typically, the length of time horizon and number of locations under consideration are quite large, which makes the RFS model computationally challenging to solve. Aggregation procedures are employed for location clustering and end-of-horizon effects are examined through demand scenario-based analyses. For the reduced time–space networks, decision analyses are conducted for the RFS model to provide insights into the truck rental business regarding asset movement decisions and asset procurement/disposal decisions over time and locations.     

Institutional Investors' Preferences for REIT Stocks

This article investigates the determinants of real estate investment trusts (REIT) portfolio investment and institutional REIT ownership using multivariate Tobit regressions. We contend that many institutional investors take larger positions in more liquid assets like REIT stocks, as compared with private real estate equities, because of liquidity considerations. Consistent with this contention, we find that liquidity constraints are significantly related to REIT portfolio investment by institutional investors. We also find that institutional investors have different preferences for REIT stocks than do other investors; they generally prefer larger, more liquid REIT stocks.