A cost-benefit analysis of military aircraft replacement policies

This paper describes a method of solving aircraft service life problems. The particular application concerns aircraft in the Naval Advanced Jet Training Command. The method of solution is comparative present value analysis of alternative replacement policies. The likely risks of estimation errors are reflected in the comparisons of present values. Differences are noted in the benefits associated with each policy, but external to Naval Aviation. Since the values of these benefits can be determined only at a higher level of decision-making, the result of the study is not a conclusive selection among policies, but a schedule of present values on the basis of which, together with values of the external benefits, a decision can be reached. This paper discusses replacement policies for aircraft used in the Naval Advanced Jet Pilot Training mission. Taking engineering technology and the training syllabus as given, four feasible plans for introducing replacement aircraft into service are evaluated in terms of the present values of differential costs associated with the plans and in terms of the likely errors in cost estimates used in calculation of the present values. The trade-off between present value of costs and planning flexibility is emphasized in choosing a recommended time pattern of aircraft replacement. The specific aircraft mixes considered are the TF–9J/TAF–9J and the TA–4F/A–4B. The first is the currently employed mix; the second is the proposed replacement. The problem is to select an optimal time-pattern of replacement of F–9's by A–4's, given technological differences favoring the A–4 and increasing costs of maintaining squadrons of F–9's. Replacements by aircraft types other than the A–4 are considered impractical. Four feasible plans for introducing A–4's through a 5-year period are evaluated in terms of current best estimates of the related costs of the plans and in terms of the flexibility of modifying each plan given future better information concerning the relevant costs. The method of analysis is comparative present value of expected costs.     

Heuristics for multicomponent joint replacement: Applications to aircraft engine maintenance

This paper considers the maintenance of aircraft engine components where economies exist for joint replacement because (a) the aircraft must be pulled from service for maintenance and (b) repair of some components requires removal and disassembly of the engine. It is well known that the joint replacement problem is difficult to solve exactly, because the optimal solution does not have a simple structured form. Therefore, we formulate three easy-to-implement heuristics and test their performance against a lower bound for various numerical examples. One of our heuristics, the base interval approach, in which replacement cycles for all components are restricted to be multiples of a specified interval, is shown to be robustly accurate. Moreover, this heuristic is consistent with maintenance policies used by commercial airlines in which periodic maintenance checks are made at regular intervals. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 435–458, 1998     

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

The parallel machine replacement problem consists of finding a minimum cost replacement policy for a finite population of economically interdependent machines. In this paper, we formulate a stochastic version of the problem and analyze the structure of optimal policies under general classes of replacement cost functions. We prove that for problems with arbitrary cost functions, there can be optimal policies where a machine is replaced only if all machines in worse states are replaced (Worse Cluster Replacement Rule). We then show that, for problems with replacement cost functions exhibiting nonincreasing marginal costs, there are optimal policies such that, in any stage, machines in the same state are either all kept or all replaced (No‐Splitting Rule). We also present an example that shows that economies of scale in replacement costs do not guarantee optimal policies that satisfy the No‐Splitting Rule. These results lead to the fundamental insight that replacement decisions are driven by marginal costs, and not by economies of scale as suggested in the literature. Finally, we describe how the optimal policy structure, i.e., the No‐Splitting and Worse Cluster Replacement Rules, can be used to reduce the computational effort required to obtain optimal replacement policies. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Optimal replacement of military aircraft: an economic approach

A nonlinear optimization model is developed in this paper to identify the optimal replacement strategy for military aircraft. In the model, the aircraft operating and maintenance (O&M) costs per available year are estimated as a function of age during the aircraft life cycle. After determining the optimal replacement policy, the model is applied to the CF Long-Range Patrol CP-140A Arcturus fleet. A sensitivity analysis is also carried out to assess the impact of some key model parameters on the result.     

Maintenance and flight scheduling of low observable aircraft

In this article, we focus on relatively new maintenance and operational scheduling challenges that are faced by the United States Air Force concerning low‐observable (LO) or stealth aircraft. The LO capabilities of an aircraft degrade stochastically as it flies, making it difficult to make maintenance scheduling decisions. Maintainers can address these damages, but must decide, which aircraft should be put into maintenance, and for how long. Using data obtained from an active duty Air Force F‐22 wing and interviews with Air Force maintainers and program specialists, we model this problem as a generalization of the well‐known restless multiarmed bandit superprocess. Specifically, we use an extension of the traditional model to allow for actions that require varying lengths of time, and generate two separate index policies from a single model; one for maintenance actions and one for the flying action. These index policies allow maintenance schedulers to intuitively, quickly, and effectively rank a fleet of aircraft based on each aircraft's LO status and decide, which aircraft should enter into LO maintenance and for how long, and which aircraft should be used to satisfy daily sortie requirements. Finally, we present extensive data‐driven, detailed simulation results, where we compare the performance of the index policies against policies currently used by the Air Force, as well as some other possible more naive heuristics. The results indicate that the index policies significantly outperform existing policies in terms of fully mission capable (FMC) rates. In particular, the experiments highlight the importance of coordinated maintenance and flying decisions. © 2015 Wiley Periodicals, Inc. 62:60–80, 2015     

Age replacement policies in two time scales

We develop and estimate optimal age replacement policies for devices whose age is measured in two time scales. For example, the age of a jet engine can be measured in the number of flight hours and the number of landings. Under a single‐scale age replacement policy, a device is replaced at age τ or upon failure, whichever occurs first. We show that a natural generalization to two scales is to replace nonfailed devices when their usage path crosses the boundary of a two‐dimensional region M, where M is a lower set with respect to the matrix partial order. For lifetimes measured in two scales, we consider devices that age along linear usage paths. We generalize the single‐scale long‐run average cost, estimate optimal two‐scale policies, and give an example. We note that these policies are strongly consistent estimators of the true optimal policies under mild conditions, and study small‐sample behavior using simulation. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 592–613, 2003.     

How old is too old? An economic approach to replacing military aircraft

The US Air Force is asking when to replace its aging aircraft. We develop a framework to identify economically optimal replacement strategies that recognizes cost trade-offs and incorporates age effects. We also preview a stochastic methodology. We use the framework to identify an optimal strategy, defined by the replacement age, for a generic fleet and conduct a sensitivity analysis. Quantitative illustrations show that the range of strategies that provides close-to-optimal outcomes widens as the operating and support (O&S) cost growth rate decreases and the ratio of the acquisition price to the initial O&S cost increases. A wider range implies more decision-making leeway.     

Optimal replacement policies with two or more loaded sliding standbys

This article defines optimal replacement policies for identical components performing different functions in a given system, when more than one spare part is available. The problem is first formulated for two components and any number of spare parts and the optimal replacement time y(x) at time x is found to have a certain form. Sufficient conditions are then provided for y(x) to be a constant y* for x > y*, and y(x) = x for x > y* (single-critical-number policy). Under the assumption that the optimal policies are of the single-critical-number type, the results are extended to the n-component case, and a theorem is provided that reduces the required number of critical numbers. Finally, the theory is applied to the case of the exponential and uniform failure laws, in which single-critical-number policies are optimal, and to another failure law in which they are not.     

Bounds on optimal cost for a replacement problem with partial observations

This paper characterizes the structure of optimal strategies for a replacement problem for two special cases of observation quality. It is shown that when the state of the system is either completely observed or completely unobserved at every decision epoch by the controller, reasonable assumptions are sufficient for the existence of optimal replacement strategies composed of policies having a generalized, control-limit form. These structural results are of particular interest since the optimal cost functions for the two special cases represent bounds on the optimal cost function for the general partially observed case, significant computational simplification can result for the two special cases due to their optimal strategy structure, and optimal strategies possessing a control-limit structure do not necessarily exist for the general partially observed case.     

Machine maintenance with workload considerations

Machine maintenance is modeled in the setting of a single‐server queue. Machine deterioration corresponds to slower service rates and failure. This leads to higher congestion and an increase in customer holding costs. The decision‐maker decides when to perform maintenance, which may be done pre‐emptively; before catastrophic failures. Similar to classic maintenance control models, the information available to the decision‐maker includes the state of the server. Unlike classic models, the information also includes the number of customers in queue. Considered are both a repair model and a replacement model. In the repair model, with random replacement times, fixed costs are assumed to be constant in the server state. In the replacement model, both constant and variable fixed costs are considered. It is shown in general that the optimal maintenance policies have switching curve structure that is monotone in the server state. However, the switching curve policies for the repair model are not always monotone in the number of customers in the queue. Numerical examples and two heuristics are also presented. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Revenue management with aircraft reassignment flexibility

A well‐studied problem in airline revenue management is the optimal allocation of seat inventory among different fare‐classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this paper, we study the seat inventory control problem considering the aircraft swapping option. For theoretical and practical purposes, we restrict our attention to the class of booking limit policies. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed‐capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal booking limits under the swapping possibility. We also develop an easy to implement heuristic for determining the booking limits under the swapping option and show, through a numerical study, that the heuristic generates revenues close to those under the optimal booking limits. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Preventive maintenance and replacement under additive damage

A system deteriorates due to shocks received at random times, each shock causing a random amount of damage which accumulates over time and may result in a system failure. Replacement of a failed system is mandatory, while an operable one may also be replaced. In addition, the shock process causing system deterioration may be controlled by continuous preventive maintenance expenditures. The joint problem of optimal maintenance and replacement is analyzed and it is shown that, under reasonable conditions, optimal maintenance rate is decreasing in the cumulative damage level and that beyond a certain critical level the system should be replaced. Meaningful bounds are established on the optimal policies and an illustrative example is provided.     

Optimal renewal policies for complex systems

Most maintenance and replacement models for industrial equipment have been developed for independent single-component machines. Most equipment, however, consists of multiple components. Also, when the maintenance crew services several machines, the maintenance policy for each machine is not independent of the states of the other machines. In this paper, two dynamic programming replacement models are presented. The first is used to determine the optimal replacement policy for multi-component equipment. The second is used to determine the optimal replacement policy for a multi-machine system which uses one replacement crew to service several machines. In addition, an approach is suggested for developing an efficient replacement policy for a multi-component, multi-machine system.     

On valuing appreciating human assets in services

This paper derives optimal policies for when to hire, train, and lay off employees in service organizations when worker productivity appreciates deterministically or stochastically under constant, monotonic, and cyclic service demand. The model, an extension of the machine replacement problem from the engineering economy literature, uses infinite horizon linear programming to produce optimal personnel planning strategies and dual prices that characterize the workforce's economic value. The effect of employee attrition is also considered. In its valuation of human assets, unlike pure accounting approaches that only try to measure, this paper proposes an approach to capture the interaction between firm decisions pertaining to human resources and human resource value. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

General trigger-off replacement procedures for two-unit systems

A trigger-off replacement policy, suggested and analyzed in [1], for two-unit systems composed of identical units, is generalized and extended in this work in several ways. In the first part of the paper we obtain the appropriate integral equations for nonidentical units and then use them for a complete solution of the case of two units, whose lifetimes are distributed according to general Erlang distributions. In the second part of the paper we extend the trigger-off policy itself by allowing preventive replacements of units which reach a certain critical age. The system stops working if either one of the two units fails or reaches its critical age. Both cases present natural replacement possibilities for the remaining unit, provided that its age exceeds a predetermined critical age. Finally, we consider the question of which policy parameters, i.e. control limits and critical ages, to choose when facing a real-life situation. Using the criterion of expected costs per unit time in the long run, we show how to find the optimal parameters which minimize this objective function. The fact that a restricted optimization, within the class of trigger-off replacement policies, leads to the global optimal policy has been proved in [2] by a different approach.     

Investigating optimal replacement of aging air force systems

An availability‐oriented approach has been developed to decide when to replace an aging system. For an existing system, it is optimal to operate another year if and only if the incremental cost per available year is less than the lifetime average cost per available year of a new aircraft. We illustrate our approach using United States Air Force KC‐135 tanker data. In demonstrating our approach, we find it will be optimal to replace the KC‐135 by the end of the decade.     

Optimal control of entry to an M/Ek/1 queue serving several classes of customers

The individual and social optimum control policies for entry to an M/M//1 queue serving several classes of customers have been shown to be control-limit policies. The technique of policy iteration provides the social optimum policy for such a queue in a straightforward manner. In this article, the problem of finding the optimal control policy for the M/E_k/1 system is solved, thereby expanding the potential applicability of the solutions developed. The Markovian nature of the queueing system is preserved by considering the service as having k sequential phases, each with independent, identically distributed, exponential service times, through which a customer must pass to be serviced. The optimal policy derived by policy iteration for such a system is likely to be difficult to use because it requires knowledge of the number of phases rather than customers in the system when an arrival occurs. To circumvent this difficulty, a heuristic is used to find a good usable (implementable) solution. In addition, a mixed-integer program is developed which yields the optimal implementable solution when solved.     

Dynamic server assignment policies for assembly‐type queues with flexible servers

We seek dynamic server assignment policies in finite‐capacity queueing systems with flexible and collaborative servers, which involve an assembly and/or a disassembly operation. The objective is to maximize the steady‐state throughput. We completely characterize the optimal policy for a Markovian system with two servers, two feeder stations, and instantaneous assembly and disassembly operations. This optimal policy allocates one server per station unless one of the stations is blocked, in which case both servers work at the unblocked station. For Markovian systems with three stations and instantaneous assembly and/or disassembly operations, we consider similar policies that move a server away from his/her “primary” station only when that station is blocked or starving. We determine the optimal assignment of each server whose primary station is blocked or starving in systems with three stations and zero buffers, by formulating the problem as a Markov decision process. Using this optimal assignment, we develop heuristic policies for systems with three or more stations and positive buffers, and show by means of a numerical study that these policies provide near‐optimal throughput. Furthermore, our numerical study shows that these policies developed for assembly‐type systems also work well in tandem systems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A bivariate optimal replacement policy for a cold standby repairable system with repair priority

In this article, an optimal replacement policy for a cold standby repairable system consisting of two dissimilar components with repair priority is studied. Assume that both Components 1 and 2, after repair, are not as good as new, and the main component (Component 1) has repair priority. Both the sequence of working times and that of the components'repair times are generated by geometric processes. We consider a bivariate replacement policy (T,N) in which the system is replaced when either cumulative working time of Component 1 reaches T, or the number of failures of Component 1 reaches N, whichever occurs first. The problem is to determine the optimal replacement policy (T,N)* such that the long run average loss per unit time (or simply the average loss rate) of the system is minimized. An explicit expression of this rate is derived, and then optimal policy (T,N)* can be numerically determined through a two‐dimensional‐search procedure. A numerical example is given to illustrate the model's applicability and procedure, and to illustrate some properties of the optimal solution. We also show that if replacements are made solely on the basis of the number of failures N, or solely on the basis of the cumulative working time T, the former class of policies performs better than the latter, albeit only under some mild conditions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self‐financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008