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Kansas City, Missouri, Streetlight Electric Vehicle Charging: Strategies and challenges for site selection of streetlight electric vehicle infrastructure in Kansas City, Missouri (Final Report)

Public streetlight charging, whether on streets in central business districts or residential areas, provides easy charging access for apartment residents and homeowners alike. While most electric vehicle (EV) drivers charge at home, they do so in garages or on driveways they own. For renters and residents of multifamily housing (MFH), however, this may not be an option. EVs have a lower cost of ownership compared to conventional vehicles, and a used EV may be an affordable option for a lower-income household. But without easy access to charging, even a low-cost used EV may not be an option for a prospective buyer. An affordable curbside charging network has the potential to expand EV adoption into neighborhoods that have to date seen minimal interest and uptake of the technology and associated charging infrastructure. Streetlight charging networks can provide an economical, scalable, and effective approach to providing equitable and convenient charging. Metropolitan Energy Center (MEC) is dedicated to the mission of creating resource efficiency, environmental health, and economic vitality in the Kansas City region and beyond. Since 1983, MEC has provided resources, outreach, and training to make alternative fuels and energy efficiency commonplace. MEC led a streetlight charging pilot project that installed limited EV charging infrastructure on the streetlight system in Kansas City, Missouri, to demonstrate and test the benefits of curbside charging for EVs at existing on-street parking locations. The project aimed to cost-effectively expand the charging network in Kansas City to support residential charging and provide infrastructure in one or more charging deserts throughout the city. This pilot evaluates the impact and overall success of streetlight charging based on community feedback, utilization of charging infrastructure, technical feasibility, and cost. The project has pursued a data- and community-driven site selection process designed to identify sites with high demand and high opportunity for EV charging. This project was funded by the U.S. Department of Energy (DOE) and awarded to MEC through a competitive proposal process. The novelty and complexity of this project required an organization that could facilitate collaboration across levels of government, community members, and industry partners. For the past 25 years, through Kansas City Regional Clean Cities, MEC has worked with numerous public and private fleets on a variety of projects to improve the environmental performance and efficiency of the regional vehicle fleet. To advance affordable, efficient, and clean transportation efforts, DOE Clean Cities and Communities coalitions create local networks of public and private sector stakeholders and engage communities. Rooted within their local communities, the coalitions serve as experts and ambassadors, bringing to bear the collective knowledge, experience, and practical know-how of the entire network from within DOE, its national laboratories, and diverse stakeholders in the field. MEC and its project partners made in-kind contributions to leverage federal dollars for the benefit of the Kansas City community. Findings from this project will help determine the best applications for streetlight charging technologies to maximize funding impact and serve community needs. The team evaluated locations based on expected charging demand, technical feasibility, safety considerations, and enhanced charging network siting needs. Throughout the project, the team gathered feedback and evaluated ways to make public charging for EVs available to all community members. The insights will help Kansas City and other communities streamline future efforts to support EV drivers through public charging in the city right-of-way. Furthermore, this project will inform citywide guidance for future installations. MEC is committed to a transparent and publicly accessible approach that encourages the collaborative evaluation of streetlight charging. The project has engaged the community to proactively identify and evaluate the benefits and impacts of streetlight charging. It was a priority for the project to ensure the benefits of this pilot are distributed equitably to all members of the Kansas City community and that new charging opportunities and associated resources are available in diverse neighborhoods across the city. The charging infrastructure supports an affordable curbside charging network that will enable more drivers to choose EVs and provide easy charging access for all community members interested in driving an EV. The community feedback received through this project informed future resources and opportunities to make EVs more accessible to all members of the Kansas City community. MEC worked with several community partners on this project, including Missouri University of Science and Technology (MST), Pennsylvania State University (Penn State), the National Renewable Energy Laboratory (NREL); the city of Kansas City, Missouri; Evergy; Black and McDonald (B&M); LilyPad EV; EVNoire; and Westside Housing Organization (WHO). Project partners contributed to the cost match required for DOE grants through capital expenditures, personnel, and other in-kind contributions. Detailed descriptions of project team organizations can be found in Appendix A. Project Partners. Analysts at NREL and MST/PennState developed site maps based on demand and equity considerations. MEC conducted outreach to community members to garner input on project design and site selection, and received approval from the Missouri Public Service Commission (PSC) for Evergy’s EV charging station ownership. MEC worked with all partners to gather additional siting criteria and developed a site selection evaluation checklist, and partners conducted site visits to proposed installation sites. Next, B&M, Evergy, and the city executed all site agreements, conducted site-specific engineering design, acquired associated permits, and issued notices to proceed site by site or in small batches. Finally, from January to April 2023, the project team installed 23 EV charging stations built on Kansas City’s streetlight system in six council districts. Evergy will own, operate, and monitor the stations for 10 years, sharing charging data with MEC for at least 1 year.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Form and Objective of the Decision Rule in Absolute Identification

In several conditions of a line length identification experiment, the subjects' decision making strategies were systematically biased against the responses on the edges of the stimulus range. When the range and number of the stimuli were small, the bias caused the percentage of correct responses to be highest in the center and lowest on the extremes of the range. Two general classes of decision rules that would explain these results are considered. The first class assumes that subjects intend to adopt an optimal decision rule, but systematically misrepresent one or more parameters of the decision making context. The second class assumes that subjects use a different measure of performance than the one assumed by the experimenter: instead of maximizing the chances of a correct response, the subject attempts to minimize the expected size of the response error (a "fidelity criterion"). In a second experiment, extended experience and feedback did not diminish the bias effect, but explicitly penalizing all response errors equally, regardless of their size, did reduce or eliminate it in some subjects. Both results favor the fidelity criterion over the optimal rule.

Balakrishnan, J. D.↗

Charge-coupled device (CCD) television camera for NASA's Galileo mission to Jupiter

The CCD detector under construction for use in the slow-scan television camera for the NASA Galileo Jupiter orbiter to be launched in 1985 is presented. The science objectives and the design constraints imposed by the earth telemetry link, platform residual motion, and the Jovian radiation environment are discussed. Camera optics are inherited from Voyager; filter wavelengths are chosen to enable discrimination of Galilean-satellite surface chemical composition. The CCO design, an 800 by 800-element 'virtual-phase' solid-state silicon image-sensor array with supporting electronics, is described with detailed discussion of the thermally generated dark current, quantum efficiency, signal-to-noise ratio, and resolution. Tests of the effect of ionizing radiation were performed and are analyzed statistically. An imaging mode using a 2-1/3-sec frame time and on-chip summation of the signal in 2 x 2 blocks of adjacent pixels is designed to limit the effects of the most extreme Jovian radiation. Smearing due to spacecraft/target relative velocity and platform instability will be corrected for via an algorithm maximizing spacial resolution at a given signal-to-noise level. The camera is expected to produce 40,000 images of Jupiter and its satellites during the 20-month mission.

Klaasen, K. P.↗

Seasonal variation of the 11 year solar cycle effect on the middle atmosphere: Role of the quasi biennial oscillation

Before the introduction of the Quasi Biennial Oscillation (Q.B.O.) in the study of the solar atmosphere relationship by Labitzke (1987) and Labitzke and Van Loon (1988), the only region of the atmosphere where an effect of a change in solar activity was generally admitted was the mesosphere. The response of the mesosphere, in phase with the solar activity, was found to be about one order of magnitude above model expectancy (around 10 to 20 Kelvin). It was observed independently of the season and maximized around 70 km (Chanin et al. 1987). However, from the same study, it was shown that the response of the stratosphere of opposite sign, clearly seen during winter and autumn, was at the threshold of detection in spring and summer. In the stratosphere, it was shown later that the separation of the data taking into account the sign of the Q.B.O. amplifies the negative correlation of the stratospheric temperature with solar activity in winter; it then becomes more significantly negative for the East phase of the Q.B.O. than when the data are all mixed (Labitzke and Chanin 1988). The studies of the seasonal response of the atmosphere to solar effect is crucial to understand the possible mechanism responsible of such a solar activity Q.B.O. relationship, knowing that the global dynamic circulation is quite different according to the seasons. The question is examined as to whether such separation of the data according to the phase of the Q.B.O. has any impact on the solar response of the middle atmosphere for seasons other than winter.

Keckhut, P.↗

Interaction and Synergism of Microbial Fuel Cell Bacteria within Methanogenesis

Biological hydrogen production from waste biomass has both terrestrial and Martian advanced life support applications. On earth, biological hydrogen production is being explored as a greenhouse neutral form of clean and efficient energy. In a permanently enclosed space habitat, carbon loop closure is required to reduce mission costs. Plants are grown to revitalize oxygen supply and are consumed by habitat inhabitants. Unharvested portions must then be recycled for reuse in the habitat. Several biological degradation techniques exist, but one process, biophotolysis, can be used to produce hydrogen from inedible plant biomass. This process is two-stage, with one stage using dark fermentation to convert plant wastes into organic acids. The second stage, photofermentation, uses photoheterotrophic purple non-sulfur bacteria with the addition of light to turn the organic acids into hydrogen and carbon dioxide. Such a system can prove useful as a co-generation scheme, providing some of the energy needed to power a larger primary carbon recovery system, such as composting. Since butyrate is expected as one of the major inputs into photofermentation, a characterization study was conducted with the bacterium Rhodobacter sphaeroides SCJ, a novel photoheterotrophic non-sulfur purple bacteria, to examine hydrogen production performance at 10 mM-100 mM butyrate concentrations. As butyrate levels increased, hydrogen production increased up to 25 mM, and then decreased and ceased by 100 mM. Additionally, lag phase increased with butyrate concentration, possibly indicating some product inhibition. Maximal substrate conversion efficiency was 8.0%; maximal light efficiency was 0.89%; and maximal hydrogen production rate was 7.7 Umol/mg/cdw/hr (173 ul/mg cdw/hr). These values were either consistent or lower than expected from literature.

Klaus, David↗

Factorization Of Positive Definite, Banded Hermitian Matrices

Report discusses application of Cholesky factorization algorithm to positive definite, banded Hermitian matrices. Begins by extending Cholesky factorization algorithm to cover uniformly-partitioned, banded, positive definite matrices of rank n that is real symmetric or Hermitian. Then two stratagems given for use of algorithm in concurrent-processing system in which N less than it has to be to enable factorization of matrix in as few serial steps as possible and where uniformly high efficiency expected from all processing elements. One of major purposes of this and related studies to maximize speedup and efficiency in system of concurrent-data-processing elements.

Salama, Moktar A.↗

Analysis of modified SMI method for adaptive array weight control

An adaptive array is applied to the problem of receiving a desired signal in the presence of weak interference signals which need to be suppressed. A modification, suggested by Gupta, of the sample matrix inversion (SMI) algorithm controls the array weights. In the modified SMI algorithm, interference suppression is increased by subtracting a fraction F of the noise power from the diagonal elements of the estimated covariance matrix. Given the true covariance matrix and the desired signal direction, the modified algorithm is shown to maximize a well-defined, intuitive output power ratio criterion. Expressions are derived for the expected value and variance of the array weights and output powers as a function of the fraction F and the number of snapshots used in the covariance matrix estimate. These expressions are compared with computer simulation and good agreement is found. A trade-off is found to exist between the desired level of interference suppression and the number of snapshots required in order to achieve that level with some certainty. The removal of noise eigenvectors from the covariance matrix inverse is also discussed with respect to this application. Finally, the type and severity of errors which occur in the covariance matrix estimate are characterized through simulation.

Dilsavor, R. L.↗

Prediction modeling of physiological responses and human performance in the heat with application to space operations

This institute has developed a comprehensive USARIEM heat strain model for predicting physiological responses and soldier performance in the heat which has been programmed for use by hand-held calculators, personal computers, and incorporated into the development of a heat strain decision aid. This model deals directly with five major inputs: the clothing worn, the physical work intensity, the state of heat acclimation, the ambient environment (air temperature, relative humidity, wind speed, and solar load), and the accepted heat casualty level. In addition to predicting rectal temperature, heart rate, and sweat loss given the above inputs, our model predicts the expected physical work/rest cycle, the maximum safe physical work time, the estimated recovery time from maximal physical work, and the drinking water requirements associated with each of these situations. This model provides heat injury risk management guidance based on thermal strain predictions from the user specified environmental conditions, soldier characteristics, clothing worn, and the physical work intensity. If heat transfer values for space operations' clothing are known, NASA can use this prediction model to help avoid undue heat strain in astronauts during space flight.

Pandolf, Kent B.↗

Fluid Physics and Macromolecular Crystal Growth in Microgravity

The first protein crystallization experiment in microgravity was launched in April, 1981 and used Germany's Technologische Experimente unter Schwerelosigkeit (TEXUS 3) sounding rocket. The protein P-galactosidase (molecular weight 465Kda) was chosen as the sample with a liquid-liquid diffusion growth method. A sliding device brought the protein, buffer and salt solution into contact when microgravity was reached. The sounding rocket gave six minutes of microgravity time with a cine camera and schlieren optics used to monitor the experiment, a single growth cell. In microgravity a strictly laminar diffusion process was observed in contrast to the turbulent convection seen on the ground. Several single crystals, approx 100micron in length, were formed in the flight which were of inferior but of comparable visual quality to those grown on the ground over several days. A second experiment using the same protocol but with solutions cooled to -8C (kept liquid with glycerol antifreeze) again showed laminar diffusion. The science of macromolecular structural crystallography involves crystallization of the macromolecule followed by use of the crystal for X-ray diffraction experiments to determine the three dimensional structure of the macromolecule. Neutron protein crystallography is employed for elucidation of H/D exchange and for improved definition of the bound solvent (D20). The structural information enables an understanding of how the molecule functions with important potential for rational drug design, improved efficiency of industrial enzymes and agricultural chemical development. The removal of turbulent convection and sedimentation in microgravity, and the assumption that higher quality crystals will be produced, has given rise to the growing number of crystallization experiments now flown. Many experiments can be flown in a small volume with simple, largely automated, equipment - an ideal combination for a microgravity experiment. The term "protein crystal growth" is often historically used to describe these microgravity experiments. This is somewhat inaccurate as the field involves the study of many varied biological molecules including viruses, proteins, DNA, RNA and complexes of those structures. For this reason we use the term macromolecular crystal growth. In this chapter we review a series of diagnostic microgravity crystal growth experiments carried out principally using the European Space Agency (ESA) Advanced Protein Crystallization Facility (APCF). We also review related research, both experimental and theoretical, on the aspects of microgravity fluid physics that affect microgravity protein crystal growth. Our experiments have revealed some surprises that were not initially expected. We discuss them here in the context of practical lessons learnt and how to maximize the limited microgravity opportunities available.

Helliwell, John R.↗

Dynamics of Galaxy Clusters and Expectations from Astro-H

Galaxy clusters span a range of dynamical states, from violent mergers -- the most energetic events in the Universe -- to systems near hydrostatic equilibrium that allow us to map their dark matter distribution using X-ray observations of the intracluster gas. Accurate knowledge of the cluster physics, and in particular, the physics of the hot intracluster gas, is required to realize the full potential of clusters as cosmological probes. So far, we have been studying the cluster dynamics indirectly, deducing merger geometries, cluster masses, etc., using X-ray brightness and gas temperature mapping. For the first time, the calorimeter onboard Astro-H will provide direct measurements of line-of-sight velocities and turbulent broadening in the intracluster gas, testing many of our key assumptions about clusters. This talk will summarize expectations for cluster dynamic studies with this new instrument.

Markevitch, Maxim↗

Romie: A Domain-Independent Tool for Computer-Aided Robust Operations Management

Romie is a decision support tool based on AI's latest advances in the domain of robust scheduling. Unlike all its predecessors, the tool allows to (i) visually model the operational problem and context entirely (ii) optimize to find near-optimal schedules while taking uncertainty into account and deals with (iii) a combination of various {key performance indicators (KPIs). It comes with a web user interface. Part or all of the modelled activities may be associated to random variables describing their stochastic durations, in order to produce schedules that are robust w.r.t. temporal uncertainty. Hence, depending on the pursued KPIs, the schedules maximize a combination of the following terms: the probability of satisfying the problem constraints, the expected return/efficiency, the expected outcome quality, and even the operators' wellness by minimizing its expected extra-hours. Initially developed for spatial exploration and demonstration in the context of Mars analog missions, this versatile tool is here applied to operations management in both biotechnology manufacturing and robots parametrization in a cave exploration context.

Chien, Steve A.↗

Optimal sampling and sensitivity limits of integrating detector arrays in a space environment

The performance of integrating detectors with either destructive read-out or nondestructive direct read-out in a space environment subject to charge-particle and radiation hits was investigated by determining the optimal integration time for maximizing the performance in the presence of a given hit rate. The performance relative to that expected for background-limited performance was evaluated using a combination of analytic techniques and Monte Carlo simulations. Results are used to estimate the performance degradation, due to cosmic rays, of the long-wavelength spectrometer of the Space Infrared Telescope Facility. It was found that its performance may be a factor of 1-5 worse than the background limited performance.

Herter, T.↗

The Global Precipitation Measurement (GPM) Mission: An Overview

The Global Precipitation Measurement (GPM) Mission is an international satellite mission that uses advanced precipitation radar with a constellation of passive microwave radiometers to improve the accuracy, sampling, and coverage of global precipitation measurements. It is a science mission with integrated applications goals focusing on (1) advancing the knowledge of the global watedenergy cycle variability and freshwater availability and (2) improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM Mission is currently a partnership between NASA and the Japanese Aerospace Exploration Agency (JAXA), with opportunities for additional domestic and international partners in satellite constellation buildup and ground validation activities. The GPM Core satellite, which carries a JAXA-provided dual-frequency precipitation radar and a NASAprovided microwave radiometers with high-frequency capabilities for light rain and frozen precipitation measurements, is expected to be launched in the 2010 timeframe. The GPM Core will serve as a precipitation physics laboratory and a calibration system for improved precipitation measurements by a heterogeneous constellation of dedicated and operational microwave radiometers. NASA also plans to provide a "wild card" constellation member with a copy of the radiometer carried on the GPM Core to be placed in an orbit that maximizes the coverage and sampling of the constellation. An overview of the GPM mission concept, instrument capabilities, ground validation plans, and the expected scientific and societal benefits will be presented.

Hou, Arthur Y.↗

Evaluating science return in space exploration initiative architectures

Science is an important aspect of the Space Exploration Initiative, a program to explore the Moon and Mars with people and machines. Different SEI mission architectures are evaluated on the basis of three variables: access (to the planet's surface), capability (including number of crew, equipment, and supporting infrastructure), and time (being the total number of man-hours available for scientific activities). This technique allows us to estimate the scientific return to be expected from different architectures and from different implementations of the same architecture. Our methodology allows us to maximize the scientific return from the initiative by illuminating the different emphases and returns that result from the alternative architectural decisions.

Budden, Nancy Ann↗

Effect of Anoxic Iron Corrosion on WIPP Brine Geochemistry FY23 Final Report (U)

A 280-day study was completed to evaluate the effect of zero-valent iron (Fe 0 ) on the Waste Isolation Pilot Plant (WIPP) brine geochemistry under anticipated reducing conditions. Hydrogen (H 2 ) gas is expected to be present in the repository after closure due to the anoxic corrosion of a vast quantity of iron contained in the waste forms disposed at WIPP; therefore, a background argon atmosphere containing H 2 was chosen for this study. WIPP groundwater brine pH and E h will impact the mobility and fate of plutonium within the repository. Modeling and laboratory results for Castile WIPP brine indicate that equilibrium fa values relative to the standard hydrogen electrode (SHE) are 40 mV more reducing (i.e., more negative) than those for Salado WIPP brine (-480 mV vs. -440 mV, respectively) because of the higher pH of the Castile brine (pH 9 .3 for Castile vs. pH 8.8 for Salado). The E h and pH data were corrected for the effects of high ionic strength. The experimental results for both brines are consistent with thermodynamic predictions using OLI Systems' Mixed Solvent Electrolyte chemical equilibrium model. The measured and corrected pH and E h data from this study are provided in Table ES-I and Table ES-2, respectively. The experimental study, with four test conditions in triplicate, was performed in a dual glovebox with a nominally 3 vol.% H 2 in argon atmosphere (target H 2 range: 3 ± I vol.%). Simulants containing MgO only ( experimental control) and MgO+Fe 0 (WIPP base case) were prepared for both the Salado and Castile brines. MgO was included in all simulants to account for the use of bulk magnesium oxide in the WIPP repository. Fe 0 was included in some simulants to incorporate the effects of the anoxic corrosion of iron and in-situ hydrogen generation in the study. The brine compositions were developed by Sandia National Laboratory (SNL; Xiong, 2008) and have been used in previous WIPP evaluations. The test method (agitation, etc.) is partially based on ASTM D3987-12. Twelve rounds of periodic measurements of pH and E h were performed over the course of the study. Chemical analysis results for liquids and solids (ICP-MS, ICP-ES, IC Anion, TIC, SEM-EDX) are consistent with the pH, E h , and thermodynamic modeling results. This study included the following conditions that deviate from anticipated post-closure conditions following brine intrusion, but were selected to facilitate bench-scale testing to validate modeling of pH and E h for the post-closure WIP P repository: an anoxic glove box atmosphere containing ≤ 4 vol. % H 2 vs. substantially higher H 2 gas concentrations assumed in the WIPP Performance Assessment (PA); a significantly higher liquid-to-solid test ratio compared to the much lower phase ratio anticipated in the WIP P repository; agitation of the simulant bottles to maximize mass transfer; and finally the use of Fe 0 reagents having a much greater surface area than expected in the WIP P repository. Non-representative conditions were chosen for various reasons such as: to provide bounding conservative results, to provide a margin of safety for testing, or to facilitate simulant sub-sampling and analysis. In a parallel effort, aqueous electrolyte thermodynamic models were developed for the synthetic Salado and Castile brines to inform the experimental design, facilitate laboratory data interpretation, and allow extension of evaluations beyond the parameters tested. Thermodynamic modeling simulations including the MgO and Fe 0 additives that are directly relevant to the experimental measurements (e.g., pH calibration curve, ORP corrections) are included in this report. The measured fa of the simulants was close to the OLI model predictions for both brines and was largely controlled by the background H 2 partial pressure in the vapor phase as well as H 2 generated in situ in the aqueous phase by the Fe 0 corrosion. The H 2 gas-phase concentration tested and thermodynamically evaluated was much lower than is assumed in the WIPP PA; however, H 2 (g) concentrations significantly below this level are still predicted to result in very reducing conditions. In conclusion: • The experimental results are consistent with thermodynamic model predictions for fa, pH, and the effects of high ionic strength. • Evidence to date suggests that the H2 concentration in the glovebox atmosphere ultimately determined the final E h values of the simulants and resulted in highly reducing conditions. As a result, little difference was observed between the control simulants containing only MgO and the WIPP base-case simulants that contained MgO and Fe 0 . • This test methodology is recommended for future studies evaluating WIPP repository conditions. The methodology includes: (1) background H 2 in argon with agitation ( or could alternatively include in-situ-generated H 2 in sealed bottles); (2) carefully measured and corrected ORP data ( with much effort focused on allowing the probes to fully stabilize); and (3) ionic-strength-corrected pH data. Other best practices, such as simulant sparging/handling, ORP probe replacement, etc., should also be considered. • The coupling of experimental studies and thermodynamic modeling is also highly recommended because these methods inform and direct one another leading to greater confidence in and understanding of the results.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Are better combinations of DERs more profitable?: Combinatorial optimization for aggregation of DERs in wholesale electricity markets

Recently, regulatory changes in various countries have enabled the participation of small-scale distributed energy resources (DERs) aggregated in virtual power plants (VPPs) in wholesale electricity markets. The inherent uncertainty and variability of resources comprising VPPs can lead to imbalances between forecasted and metered outputs, potentially resulting in the deficient settlement of generation under imbalance settlement rules. To address this challenge, it is essential to manage variability in the planning phase and uncertainty in the operation phase. Most current research focuses on managing forecasting errors in the operational phase, with insufficient attention given to the planning phase. Here, to bridge this gap, this paper proposes an optimal combination strategy for DERs to maximize the market participation revenue of VPPs by proactively managing variability in the planning phase. To estimate the expected revenue, we conducted analyses for homogeneous and heterogeneous DERs using Monte Carlo simulations and genetic algorithms. Remarkably, the proposed method demonstrated approximately 8 % higher revenue compared to the neighboring group case when considering diversity in DER set configuration with equal proportions of photovoltaics and wind.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A multi-item maintenance center inventory model for low-demand reparable items

In many military and commercial contexts, complex equipment undergoes scheduled maintenance overhauls at regular intervals during which all failed components are replaced. Failure to have replacements on hand for all failed parts requires emergency measures at premium cost. When reparable parts are highly reliable and expensive, both holding and shortage costs are high. This model determines the reparable parts inventory for a maintenance center under three alternative criteria: (1) maximizing job-completion rate subject to constraint on total holding costs, (2) minimizing total holding costs plus expected job noncompletion costs, and (3) minimizing total holding costs subject to a required minimum job-completion rate. Exact solutions may be obtained using dynamic programming. Approximate solutions, found easily by marginal analysis, have readily computed bounds on possible error. The solution methods for the three formulations are illustrated in a simple example.

Schaefer, M. K.↗

Undecidability in macroeconomics

In this paper we study the difficulty of solving problems in economics. For this purpose, we adopt the notion of undecidability from recursion theory. We show that certain problems in economics are undecidable, i.e., cannot be solved by a Turing Machine, a device that is at least as powerful as any computational device that can be constructed. In particular, we prove that even in finite closed economies subject to a variable initial condition, in which a social planner knows the behavior of every agent in the economy, certain important social planning problems are undecidable. Thus, it may be impossible to make effective policy decisions. Philosophically, this result formally brings into question the Rational Expectations Hypothesis which assumes that each agent is able to determine what it should do if it wishes to maximize its utility. We show that even when an optimal rational forecast exists for each agency (based on the information currently available to it), agents may lack the ability to make these forecasts. For example, Lucas describes economic models as 'mechanical, artificial world(s), populated by ... interacting robots'. Since any mechanical robot can be at most as computationally powerful as a Turing Machine, such economies are vulnerable to the phenomenon of undecidability.

Chandra, Siddharth↗