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Technical Change and the Optimal Life of Assets
Abstract
In this paper the effects of technical change on the optimal lives of assets are explored. The generality of the dynamic programming approach to the problem of optimal asset life determination is contrasted with the traditional and highly restrictive "equal life" solution. Some of the possible effects of different forms of technical change on costs are examined and numerical examples of these are solved by dynamic programming to illustrate the consequences for the optimal lives of assets. We hypothesize that the likely effect of technical progress is a lengthening of the optimal replacement cycle.
... (Caplan, 1940) considers a premature renewal caused by a technological improvement. (Stapleton, et al., 1972). The prior machine is replaced with an improved one. ...
Electronic Manufacturing Services (EMS.) companies are in a highly competitive environment where investment in technology plays a significant role in the company's performance. The equipment efficiency is directly converted to revenue. The equipment efficiency decays over time; keeping the equipment represents a loss in productivity, and renewing the equipment requires an additional cost. There is a continuous decision process to determine the optimal time to replace the old equipment with a new one. Traditionally, the optimal time to renew is when the machine's revenue matches the cost. This paper studies the renewal decision using a real options approach, adding the uncertainty factor. The variables are modeled as Geometric Brownian Motions. We provide a literature review of renewal real options and describe the models we use. The one-factor model considers the revenue as stochastic; the two-factor model considers the revenue and cost as stochastic; the technological improvement models extend the two-factor model to include a premium in revenue for replacing the equipment. An overview of the electronic manufacturing dynamics is described; we select a product whose manufacturing process depends on machines. We provide a methodology for the model's implementation and how to determine the parameters; the results are compared to the deterministic approach. Finally, we discuss the models' advantages, disadvantages, and limitations.
The reliability characteristic such as probability of survival, mean time to failure, frequency of failures and mean down time depend on the design and topological layout of the system. This paper deals with a single unit system that is operating in an environment exposed to the hazards of common cases failures, under some general assumptions the optional replacement policies were developed with the help of proposed measure of cost differences for old and new system.
We examine the possibilities of premature and postponed replacement in a deterministic infinite horizon model when there is technological progress. Both revenue and operating cost deteriorate with age, but at different rates. The optimal deterministic replacement time is an implicit solution from the timing boundary obtained for the equivalent real option model using a dynamic programming framework, and then by setting the underlying volatilities equal to zero. A step change improvement characterizing technological progress in the initial operating cost level for the successor occurring during the economic lifetime of the incumbent justifies premature replacement, compared to the traditional present value approach. This finding can be extended to step change improvements in the initial revenue level for the successor and for the re-investment cost. In contrast, if the technological progress can be characterized by a constant declining rate for the initial operating cost level for the successor, then the replacement is postponed for certain parameter values. This finding can be extended to different assumed improvement rates in the initial revenue level for the successor and for the re-investment cost.
We propose a simple method for solving an equipment replacement problem. The algorithm yields alternative optimal solutions, if any, as well. It is expected that further extensions to this approach to solve group replacement problems may be possible.
We provide multi-factor real option models (and quasi-analytical solutions) for equipment capital budgeting under uncertainty, when there is either unexpected, or anticipated, or uncertain (volatile) technological progress. We calculate the threshold level of revenues and operating costs using the incumbent equipment that would justify replacement. Replacement is deferred for lower revenue thresholds. If progress is anticipated or highly uncertain, alert financial managers should wait longer before replacing equipment. Replacement deferral increases with decreases in the expected correlation between revenue and operating costs, and with increases in the revenue and/or operating cost volatility. Uncertain technological progress increases the real option value of waiting. The best approach for equipment suppliers is to reduce the expected revenue and/or cost volatility, and/or reduce the expected uncertainty of technological innovations, since then an incentive exists for the early replacement of old equipment when a technologically advanced version is launched.
This paper investigates the effect of equipment replacement on the design phase of multi-machine manufacturing systems, given a finite horizon and discounted costs. For the most part, manufacturing system design literature has focused on the design issue, ignoring equipment replacement and its economic impact. The design phase generally consists of equipment selection, process routing, and layout decisions. The authors propose an explicit mathematical form for the operating costs of equipment and their salvage values based on their previous experience of life cycle costing projects.The design phase of cellular manufacturing systems, the so-called cell formation problem, is used. The problem is formulated as a non-linear mixed integer programming model and solved using the defined branch-and-bound algorithm. The algorithm employs a depth-first branching strategy in conjunction with a bounding procedure with a heuristic method. Selected numerical examples demonstrate the applicability of the model and verify the performance of the defined algorithm. The results enable us to choose the best equipment-mix and product process routes based on the given horizon and economic factors; in addition, we know which equipment should be replaced and when.
We formulate a deterministic equipment replacement problem (which is normally solved through the use of dynamic programming) as a 0-1 linear programming problem. The advantage of such a formulation is that it does not require a high degree of expertise, insight or ‘art’ (i.e. it is thus rather easily understood by practitioners), does not suffer from the so-called ‘curse of dimensionality’, a short-coming of dynamic programming, and can always yield optimal solution to fairly big sized problems using available software. A numerical example is solved on a personal computer and interpretation of the results is provided.
In this paper, a general, framework for replacement modeling assumptions is introduced. This framework involves the classification of assumptions into the four major categories of structural, realistic, descriptive, and simplifying (limiting) assumptions. Examples of assumptions from the literature on replacement modeling are then grouped into these four major categories. It is contended that this proposed framework assists the analyst in understanding existing replacement models and facilitates new model construction
We study optimal replacement and abandonment decisions for real assets, when both revenues and costs are uncertain and deteriorate with age. We develop an implicit representation of the renewal boundary as the solution to a set of simultaneous equations. This quasi-analytical method has the merit of computational ease and transparency. We show that the correlation between revenues and operating costs has a significant influence on the renewal boundary, and that the increase in revenue immediately following a renewal has a greater relative influence on the boundary than either operating cost or renewal cost. The quasi-analytical method is sufficiently flexible to deal with other real option models involving 2 variables.
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