\begin{theindexindex} \item\indexheading{A} \item AAV, \see{examples, applications, autonomous vehicle}{93} \item agent, \see{solitary agent model, agent}{4} \item agent model, \see{solitary agent model}{3} \item AGV, \see{examples, applications, autonomous vehicle}{93} \item applications, \see{examples, applications}{93} \item artificial intelligence, \hyperpage{93} \item assumptions, \see{solitary agent model, assumptions}{6} \item automation, \see{examples, applications}{93} \item autonomous air vehicles, \see{examples, applications, autonomous vehicle}{93} \item autonomous ground vehicles, \see{examples, applications, autonomous vehicle}{93} \item average, \see{stochasticity, statistics, expectation}{6} \indexspace \item\indexheading{B} \item bang-bang control, \indexdef{47} \item Borel sets, \see{mathematics, sets, Borel algebra}{6} \indexspace \item\indexheading{C} \item capital budgeting, \see{finance, capital budgets}{72} \item central limit theorem (CLT), \see{stochasticity, central limit theorem}{46} \item central moments, \see{stochasticity, statistics, central moments}{20} \item choice, \see{solitary agent model, choice}{4} \item classical OFT, \see{optimal foraging theory}{1} \item classical optimal foraging theory, \see{optimal foraging theory}{1} \item CLT, \see{stochasticity, central limit theorem}{46} \item cognition, \hyperpage{93} \item combined prey and patch model, \see{combined task-type and processing-length choice problem}{11} \item combined task-type and processing-length choice problem, \hyperpage{11}, \hyperpage{87} \item compound objectives, \see{optimality, multiobjective optimization}{35} \item Concorde fallacy, \see{sunk-cost effect}{55} \item constraints, \see{optimization constraints}{66} \item contributions \subitem biology, \hyperpage{94--96} \subitem engineering, \hyperpage{93--94} \item costs, \see{solitary agent model, costs}{4} \item currency, \see{solitary agent model, currency}{4} \indexspace \item\indexheading{D} \item dynamic optimization, \hyperpage{46} \indexspace \item\indexheading{E} \item ecological rationality, \hyperpage{55}, \hyperpage{58, 59} \item efficiency, \see{excess efficiency}{55} \item EPR, \see{extreme-preference rule}{84} \item equilibrium process rate of net gain, \see{equilibrium renewal process rate of net gain}{42} \item equilibrium renewal process rate of net gain, \hyperpage{42--43} \item Erlang-2, \see{stochasticity, distributions, Erlang-2}{99} \item \expost {} performance measure, \hyperpage{47} \item examples \subitem analytical solutions, \indexdef{90--92} \subsubitem discounted net gain, \indexdef{91} \subsubitem excess efficiency, \indexdef{92} \subsubitem rate of excess net gain, \indexdef{90--91} \subitem applications, \indexdef{93--94} \subsubitem autonomous vehicle, \hyperpage{1}, \hyperpage{4}, \hyperpage{31}, \hyperpage{94} \subsubitem military, \hyperpage{94} \subsubitem queueing, \hyperpage{94} \subsubitem surveillance, \hyperpage{31} \subsubitem temperature control, \indexdef{94} \subitem graphical solutions \subsubitem excess efficiency, \indexdef{56--58} \subsubitem rate of excess net gain, \indexdef{53--55} \subsubitem reward-to-variability ratio, \indexdef{59} \subsubitem reward-to-variance ratio, \indexdef{61} \item excess efficiency, \indexdef{55--56}, \hyperpage{56--58} \subitem graphical optimization, \hyperpage{56--58} \item expectation, \see{stochasticity, statistics, expectation}{6} \item expected utility, \see{utility theory}{72} \item expected value, \see{stochasticity, statistics, expectation}{6} \item extreme-preference rule (EPR), \indexdef{84}, \indexglo{106} \indexspace \item\indexheading{F} \item finance \subitem capital budgets, \hyperpage{72} \subitem investment returns, \hyperpage{72} \subitem modern portfolio theory (MPT), \indexdef{33}, \indexglo{106} \subitem portfolios, \hyperpage{72} \subitem post-modern portfolio theory (PMPT), \indexdef{34}, \hyperpage{70--73}, \indexglo{106} \subitem stochastic dominance (SD), \indexdef{72--73}, \indexglo{106} \subsubitem first-order (FSD), \indexdef{72--73}, \indexglo{106} \subsubitem third-order (TSD), \hyperpage{73}, \indexglo{106} \item finite expectation, \see{stochasticity, statistics, finite expectation}{8} \item foraging, \see{optimal foraging theory}{3} \item foraging model, \see{solitary agent model}{3} \item frontier, \see{optimality, Pareto efficient}{36} \item future directions, \hyperpage{70}, \hyperpage{96--97} \indexspace \item\indexheading{G} \item gain, \see{solitary agent model, point gain}{4} \item gain success threshold, \hyperpage{44--45}, \hyperpage{52}, \hyperpage{55}, \hyperpage{58}, \hyperpage{61} \item gain threshold, \see{gain success threshold}{44} \item Gaussian distribution, \see{stochasticity, distributions, normal}{46} \item gross gain success threshold, \hyperpage{55} \indexspace \item\indexheading{I} \item \iid , \see{stochasticity, random variable, \iid }{8} \item independent and identically distributed (\iid ), \see{stochasticity, random variable, \iid }{8} \item independent random variables, \see{stochasticity, random variable, independent}{6} \item investment returns, \see{finance, investment returns}{72} \indexspace \item\indexheading{K} \item Karush-Khun-Tucker (KKT) conditions, \see{optimality, KKT conditions}{36} \item KKT conditions, \see{optimality, KKT conditions}{36} \item Kuhn-Tucker conditions, \see{optimality, KKT conditions}{36} \indexspace \item\indexheading{L} \item Lagrange multiplier method, \see{optimality, Lagrange multiplier method}{36} \item location, \see{stochasticity, distributions, location-scale family}{45} \item location-scale, \see{stochasticity, distributions, location-scale family}{45} \item long-term average rate of net gain, \indexdef{19}, \indexdef{27}, \hyperpage{39--44} \subitem graphical optimization, \hyperpage{43--44} \subitem justification, \hyperpage{39--40} \subitem limit, \hyperpage{40--41} \subitem opportunity cost, \hyperpage{41--42} \item long-term rate of net gain, \see{long-term average rate of net gain}{27} \item lower-partial moment, \see{stochasticity, statistics, lower-partial moment}{70} \item lower-partial variance, \see{stochasticity, statistics, lower-partial variance}{70} \item LPM, \see{stochasticity, statistics, lower-partial moment}{70} \item LPV, \see{stochasticity, statistics, lower-partial variance}{70} \indexspace \item\indexheading{M} \item marginal value theorem (MVT), \indexdef{44}, \hyperpage{87}, \indexglo{106} \item Markov renewal cycle \subitem OFT cycle, \indexglo{108} \item Markov renewal cycles \subitem OFT cycle, \see{solitary agent model, classical analysis, OFT cycle}{16} \subitem processing cycle, \see{solitary agent model, processing-only analysis, processing cycle}{25} \item Markov renewal process, \see{stochasticity, Markov renewal process}{98} \item mathematics, \indexglo{109--113} \subitem definition ($\triangleq $), \indexglo{109} \subitem equality ($=$), \indexglo{109} \subitem functions, \indexglo{111} \subsubitem convolution ($*$), \hyperpage{99}, \indexglo{112} \subsubitem gradient ($\nabla $), \indexglo{112} \subsubitem Hessian ($\nabla ^2$), \indexglo{112} \subsubitem integral ($\int $), \hyperpage{71}, \indexglo{112} \subsubitem partial derivative ($\partial $), \indexglo{111} \subsubitem total derivative ($\total $), \indexglo{111} \subitem functions(, \indexglo{111} \subitem limit ($\lim $ or $\to $), \indexglo{111} \subitem logic, \indexglo{111} \subsubitem equivalence ($\iff $), \indexglo{111} \subsubitem implication ($\implies $), \indexglo{111} \subitem $n$-tuple, \indexglo{110} \subitem numbers, \indexglo{109--110} \subsubitem Euclidean $n$-space ($\R ^n$), \indexglo{109} \subsubitem extended real numbers ($\extR $), \indexglo{109} \subsubitem integers ($\Z $), \indexglo{109} \subsubitem natural numbers ($\N $), \indexglo{109} \subsubitem rationals ($\Q $), \indexglo{109} \subsubitem real negative numbers ($\R _{<0}$), \indexglo{109} \subsubitem real non-negative numbers ($\R _{\geq 0}$), \indexglo{109} \subsubitem real non-positive numbers ($\R _{\leq 0}$), \indexglo{109} \subsubitem real non-zero numbers ($\R _{\neq 0}$), \indexglo{109} \subsubitem real number intervals, \indexglo{110--111} \subsubitem real numbers ($\R $), \indexglo{109} \subsubitem real positive numbers ($\R _{>0}$), \indexglo{109} \subsubitem whole numbers ($\W $), \indexglo{109} \subitem order, \indexglo{111} \subsubitem infimum ($\inf $), \indexglo{111} \subsubitem maximum ($\max $), \indexglo{111} \subsubitem minimum ($\min $), \indexglo{111} \subsubitem supremum ($\sup $), \indexglo{111} \subitem ordered pair, \indexglo{110} \subitem sets, \indexglo{110--111} \subsubitem Borel algebra ($\Borel $), \indexglo{112} \subsubitem Cartesian product ($\times $), \indexglo{110} \subsubitem empty set ($\emptyset $), \indexglo{110} \subsubitem exclusion ($\notin $), \indexglo{110} \subsubitem power set ($\Pow $), \indexglo{110} \subsubitem set complement (${}^c$), \indexglo{110} \subsubitem set difference ($\setdiff $), \indexglo{110} \subsubitem set element ($\in $), \indexglo{110} \subsubitem set intersection ($\cap $), \indexglo{110} \subsubitem set union ($\cup $), \indexglo{110} \subsubitem subset ($\subseteq $ or $\subset $), \indexglo{110} \subsubitem superset ($\supseteq $ or $\supset $), \indexglo{110} \subitem vector spaces, \indexglo{111--112} \subsubitem matrix transpose (${}^\T $), \indexglo{112} \subsubitem vector transpose (${}^\T $), \indexglo{112} \item maximal expected utility, \see{utility theory}{72} \item maximal utility, \see{utility theory}{72} \item mean, \see{stochasticity, statistics, expectation}{6} \item mean-lower-partial-moment (MLPM) analysis, \indexdef{71} \item mean-lower-partial-variance analysis, \indexdef{71} \item mean-semivariance analysis, \see{mean-lower-partial-moment analysis}{71}, \see{mean-lower-partial-variance analysis}{71} \item mean-variance analysis (MVA), \hyperpage{44--47}, \hyperpage{70}, \indexglo{106} \item merge before split approach, \hyperpage{13} \item merged Poisson process, \see{stochasticity, Poisson process, merged}{14} \item MLPM, \see{mean-lower-partial-moment analysis}{71} \item model, \see{solitary agent model}{3} \item model assumptions, \see{solitary agent model, assumptions}{6} \item model weaknesses, \see{solitary agent model, weaknesses}{30} \item modern portfolio theory (MPT), \see{finance, modern portfolio theory}{33} \item moments, \see{stochasticity, statistics, moments}{6} \item MPT, \see{finance, modern portfolio theory}{33} \item MSA, \see{mean-lower-partial-moment analysis}{71} \item multiobjective optimization, \see{optimality, multiobjective optimization}{35} \item mutually independent and identically distributed (\iid ), \see{stochasticity, random variable, \iid }{8} \item MVA, \see{mean-variance analysis}{70} \item MVT, \see{marginal value theorem}{44} \indexspace \item\indexheading{N} \item net gain success threshold, \see{gain success threshold}{58} \item net point gain, \see{solitary agent model, net point gain}{4} \item normal distribution, \see{stochasticity, distributions, normal}{46} \item numbers, \see{mathematics, numbers}{6} \indexspace \item\indexheading{O} \item OFT, \see{optimal foraging theory}{1} \item OFT cycle, \see{solitary agent model, classical analysis, OFT cycle}{16} \item opportunity cost, \see{long-term average rate of net gain, opportunity cost}{41} \item optimal foraging theory, \indexdef{1}, \hyperpage{3}, \hyperpage{5}, \hyperpage{12--22}, \hyperpage{27}, \indexglo{106} \item optimality \subitem compound objectives, \see{optimality, multiobjective optimization}{35} \subitem KKT conditions, \hyperpage{36}, \indexglo{106} \subitem Lagrange multiplier method, \hyperpage{36}, \hyperpage{38} \subitem multiobjective optimization, \hyperpage{35--36} \subsubitem linear combination, \hyperpage{36} \subsubitem maximin, \hyperpage{36} \subitem Pareto efficient, \hyperpage{36}, \indexdef{36} \subitem Pareto frontier, \see{optimality, Pareto efficient}{36} \subitem Pareto optimal, \see{optimality, Pareto efficient}{36} \item optimization constraints, \hyperpage{36--38}, \hyperpage{66--69} \subitem encounter-rate, \hyperpage{37} \subitem gain and cost, \hyperpage{68} \subitem gain and time, \hyperpage{67} \subitem mean and standard deviation, \hyperpage{69} \subitem mean and variance, \hyperpage{68--69} \subitem nutrients, \hyperpage{37} \subitem time, \hyperpage{36} \indexspace \item\indexheading{P} \item Pareto efficient, \see{optimality, Pareto efficient}{36} \item Pareto frontier, \see{optimality, Pareto efficient}{36} \item Pareto optimal, \see{optimality, Pareto efficient}{36} \item Pareto tradeoffs, \hyperpage{63--66} \subitem efficiency, \hyperpage{64} \subsubitem gain discounted by cost, \indexdef{64} \subitem gain and time, \hyperpage{64} \subsubitem gain discounted by time, \indexdef{64} \subitem mean and standard deviation, \hyperpage{65} \subsubitem mean discounted by standard deviation, \indexdef{65} \subitem mean and variance, \hyperpage{65--66} \subsubitem mean discounted by variance, \indexdef{65} \item patch model, \see{task processing-length choice problem}{11} \item patch overstaying, \hyperpage{48} \subitem rational explanation, \hyperpage{54} \item PMPT, \see{finance, post-modern portfolio theory}{34} \item point gain, \see{solitary agent model, point gain}{4} \item Poisson process, \see{stochasticity, Poisson process}{98} \item portfolios, \see{finance, portfolios}{72} \item post-modern portfolio theory (PMPT), \see{finance, post-modern portfolio theory}{34} \item prey model, \see{task-type choice problem}{11} \item probability, \see{stochasticity}{6} \item probability measure, \see{stochasticity, probability measure}{6} \item probability of success, \hyperpage{45} \item probability space, \see{stochasticity, probability space}{6} \item processing, \see{solitary agent model, processing}{4} \item processing cycle, \see{solitary agent model, processing-only analysis, processing cycle}{25} \item pseudo-deterministic, \see{stochasticity, random variable, pseudo-deterministic}{7} \indexspace \item\indexheading{Q} \item queueing, \see{examples, applications, queueing}{93} \indexspace \item\indexheading{R} \item random variables, \see{stochasticity, random variables}{6} \item randomness, \see{stochasticity}{6} \item rate maximization, \hyperpage{39--44}, \hyperpage{52} \item rate of excess net gain, \indexdef{52}, \hyperpage{52--55} \subitem analytical optimization, \hyperpage{90--91} \subitem graphical optimization, \hyperpage{52--55} \item rational agent, \see{utility theory}{72} \item rational objective function, \hyperpage{74--90} \subitem optimal solution \subsubitem constant disadvantage, \hyperpage{85--87} \subsubitem decreasing advantage-to-disadvantage, \hyperpage{87--90} \item rationality, \see{ecological rationality}{55} \item real numbers, \see{mathematics, numbers, real numbers}{6} \item renewal process, \see{stochasticity, Markov renewal process}{98} \item reward-to-variability \subitem graphical optimization, \hyperpage{47} \item reward-to-variability ratio, \indexdef{46}, \hyperpage{47}, \hyperpage{58}, \indexdef{58}, \hyperpage{58--59} \subitem graphical optimization, \hyperpage{58--59} \item reward-to-variance ratio, \hyperpage{61}, \indexdef{61}, \hyperpage{61} \subitem graphical optimization, \hyperpage{61} \item risk minimization, \see{risk sensitivity}{44} \item risk sensitivity, \hyperpage{44--47}, \hyperpage{52}, \hyperpage{65--66} \item robotics, \see{examples, applications}{93} \indexspace \item\indexheading{S} \item satisficing, \indexdef{49} \item scale, \see{stochasticity, distributions, location-scale family}{45} \item SD, \see{finance, stochastic dominance}{72} \item searching, \see{solitary agent model, searching}{4} \item semivariance, \see{stochasticity, statistics, lower-partial variance}{70} \item Sharpe ratio, \see{reward-to-variability ratio}{46} \item skewness, \see{stochasticity, statistics, skewness}{34} \item skewness preference, \hyperpage{35} \item solitary agent model, \hyperpage{3--5}, \indexdef{6--12}, \hyperpage{12--32} \subitem agent, \indexdef{4} \subitem assumptions, \indexdef{6--8} \subitem choice, \indexdef{4} \subitem classical analysis, \indexdef{13--22} \subsubitem limits, \indexdef{19} \subsubitem OFT cycle, \hyperpage{16}, \indexdef{16} \subsubitem optimization, \hyperpage{39--49}, \hyperpage{74--92} \subsubitem Poisson encounters, \indexdef{13--14} \subsubitem renewal process, \indexdef{16--17} \subsubitem reward processes, \indexdef{14--15}, \indexdef{18} \subsubitem statistics, \indexdef{14--16}, \indexdef{18--22} \subsubitem variance, \indexdef{20--22} \subitem comparison of analyses, \hyperpage{29--30} \subitem costs, \indexdef{4} \subitem currency, \indexdef{4} \subitem decision variables, \indexdef{11} \subitem net point gain, \indexdef{4} \subitem parameters, \indexdef{9--11}, \indexglo{106--108} \subitem point gain, \indexdef{4} \subitem processing, \indexdef{4} \subitem processing-only analysis, \hyperpage{5}, \indexdef{22--28} \subsubitem limits, \indexdef{26--27} \subsubitem optimization, \hyperpage{49--69}, \hyperpage{74--92} \subsubitem Poisson encounters, \indexdef{22--23} \subsubitem processing cycle, \hyperpage{25}, \indexdef{25} \subsubitem renewal process, \indexdef{25} \subsubitem reward processes, \indexdef{23--26} \subsubitem statistics, \indexdef{24}, \indexdef{26--28} \subsubitem variance, \indexdef{27--28} \subitem random processes, \indexdef{8--9}, \indexdef{12} \subitem searching, \indexdef{4} \subitem tasks, \indexdef{4} \subitem weaknesses, \indexdef{30--32} \item speed-accuracy tradeoff, \hyperpage{38} \item split before merge approach, \hyperpage{22} \item split Poisson process, \see{stochasticity, Poisson process, split}{22} \item stochastic dominance, \see{finance, stochastic dominance}{72} \item stochastic model, \see{solitary agent model}{3} \item stochasticity, \hyperpage{3}, \indexglo{112--113} \subitem central limit theorem (CLT), \hyperpage{46}, \indexglo{106} \subitem distributions, \hyperpage{72} \subsubitem double exponential, \hyperpage{45} \subsubitem Erlang-2, \hyperpage{99}, \indexdef{99} \subsubitem exponential, \hyperpage{45} \subsubitem location, \see{stochasticity, distributions, location-scale}{45} \subsubitem location-scale family, \indexdef{45}, \hyperpage{45--46} \subsubitem log-normal, \hyperpage{45} \subsubitem normal, \hyperpage{45, 46}, \indexdef{46} \subsubitem scale, \see{stochasticity, distributions, location-scale}{45} \subsubitem symmetry, \hyperpage{34}, \hyperpage{46} \subsubitem uniform, \hyperpage{45} \subitem Markov renewal process, \hyperpage{16--17}, \hyperpage{98--99} \subsubitem limits, \hyperpage{98--99} \subitem Markov renewal-reward process, \hyperpage{18}, \hyperpage{26} \subitem Poisson process, \hyperpage{98, 99} \subsubitem merged, \hyperpage{14, 15}, \hyperpage{22, 23} \subsubitem split, \hyperpage{22, 23} \subitem probability measure, \indexdef{6}, \indexglo{112} \subitem probability space, \indexdef{6}, \hyperpage{98}, \indexglo{112} \subitem random process, \indexglo{113} \subsubitem almost sure limit ($\aslim $ or $\xto {a.s.}$), \indexglo{113} \subitem random variable, \indexdef{6}, \hyperpage{34}, \hyperpage{72} \subsubitem cumulative distribution function ($F$), \indexglo{112} \subsubitem \iid , \indexdef{8}, \indexglo{106} \subsubitem independence, \indexdef{7}, \hyperpage{12} \subsubitem probability density function ($f$), \indexglo{112} \subsubitem pseudo-deterministic, \indexdef{7--8}, \hyperpage{12}, \hyperpage{20}, \hyperpage{27} \subsubitem uncorrelated, \indexdef{7} \subitem statistics \subsubitem central moments, \indexdef{20}, \hyperpage{34} \subsubitem conditional expectation, \indexglo{113} \subsubitem expectation ($\E $), \indexdef{6}, \indexglo{112} \subsubitem expectation of function, \indexglo{112} \subsubitem expected value, \see{stochasticity, statistics, expectation}{6} \subsubitem finite expectation, \hyperpage{8}, \indexdef{8}, \hyperpage{12} \subsubitem lower-partial moment (LPM), \indexdef{71}, \indexglo{106} \subsubitem lower-partial variance (LPV), \indexdef{70--71}, \indexglo{106} \subsubitem mean, \see{stochasticity, statistics, expectation}{6} \subsubitem moments, \indexdef{6} \subsubitem normal, \hyperpage{46} \subsubitem semivariance, \see{stochasticity, statistics, lower-partial variance}{70} \subsubitem skewness, \hyperpage{34--35}, \hyperpage{45} \subsubitem standard deviation, \hyperpage{44}, \indexdef{44} \subsubitem variance ($\var $), \indexdef{20} \item success threshold, \see{gain success threshold}{44} \item sunk-cost effect, \hyperpage{55}, \hyperpage{58} \item survival threshold, \see{gain success threshold}{44} \item symmetry, \see{stochasticity, distributions, symmetry}{34} \indexspace \item\indexheading{T} \item task processing-length choice problem, \hyperpage{11} \item task-type choice problem, \hyperpage{11}, \hyperpage{86} \item tasks, \see{solitary agent model, tasks}{4} \item threshold, \see{gain success threshold}{44} \indexspace \item\indexheading{U} \item UAV, \see{examples, applications, autonomous vehicle}{93} \item UGV, \see{examples, applications, autonomous vehicle}{93} \item uncorrelated random variables, \see{stochasticity, random variable, uncorrelated}{6} \item unmanned air vehicles, \see{examples, applications, autonomous vehicle}{93} \item unmanned ground vehicles, \see{examples, applications, autonomous vehicle}{93} \item utilitarianism, \see{utility theory}{72} \item utility function, \see{utility theory}{72} \item utility theory, \hyperpage{65--66}, \hyperpage{72--73} \indexspace \item\indexheading{V} \item variance, \see{stochasticity, statistics, variance}{20} \item vehicles, \see{examples, applications, autonomous vehicle}{93} \item von Neumann-Morgenstern utility, \see{utility theory}{72} \indexspace \item\indexheading{Z} \item $z$-score, \see{reward-to-variability ratio}{46} \item zero-one rule, \indexdef{84} \end{theindexindex}