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ςϨϏ$.ͷσʔλ෼ੳʹ͓͚Δ਺ཧ࠷దԽ ͷԠ༻ࣄྫ ਺ཧ࠷దԽ0QUJNJ[BUJPO/JHIU 3&7*4*0גࣜձࣾຊ઒఩࠸ 1

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ࣗݾ঺հ w ࢯ໊ɿຊ઒఩࠸ w ॴଐɿ3&7*4*0גࣜձࣾσʔλαΠΤϯςΟετ w ςϨϏͷࢹௌσʔλΛ༻͍ͨσʔλ෼ੳΛߦͳ͍ͬͯ·͢ w झຯɿήʔϜ👾ɾ௼Γ🎣 w ڵຯɿ౷ܭɾ਺ཧϞσϧɾػցֶशɾΤϯδχΞϦϯά 2

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࿩͢͜ͱ wςϨϏ$.ͷσʔλ෼ੳʹ͓͚Δ਺ཧ࠷దԽͷԠ༻ࣄྫ ʹ͍ͭͯ࿩͠·͢ʂ 3

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ςϨϏ$.ͷσʔλ෼ੳʹ͓͚Δ਺ཧ࠷దԽͷԠ༻ࣄྫ w ςϨϏ$.ग़ߘͷϓϥϯχϯάޮՌݕূ w λΠϜ$.ɿϨΪϡϥʔ൪૊ຊ୯ҐͰߪೖ͢Δ w εϙοτ$.ɿ์ૹہ͝ͱʹ$.౤ԼྔΛܾΊͯߪೖ͢Δ 4

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ςϨϏ$.ͷσʔλ෼ੳʹ͓͚Δ਺ཧ࠷దԽͷԠ༻ࣄྫ w ςϨϏ$.ग़ߘͷϓϥϯχϯάޮՌݕূ w λΠϜ$.ɿϨΪϡϥʔ൪૊ຊ୯ҐͰߪೖ͢Δ w εϙοτ$.ɿ์ૹہ͝ͱʹ$.౤ԼྔΛܾΊͯߪೖ͢Δ 5 ˢτʔλϧͰͷϢχʔΫϦʔνΛߟ͑Δ্ͰɺͦΕͧΕͷ ہ΁ͷ$.౤Լྔ͸Ͳͷ͘Β͍͕࠷దͳͷ͔Λ਺ཧ࠷దԽ Λ༻͍ͯղܾ͢Δ ہ#Ͱͷ Ϧʔν ہ$Ͱͷ Ϧʔν ہ"Ͱͷ Ϧʔν

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εϙοτ$.ʹ͓͚Δہ͝ͱग़ߘ഑෼ͷ࠷దԽ w Ϟνϕʔγϣϯɿޮ཰తʹଟ͘ͷਓʹςϨϏ$.ΛϦʔν͍ͤͨ͞ w ໰୊ઃఆɿεϙοτ$.΁ͷτʔλϧ༧ࢉ͕ܾ·͍ͬͯΔதͰɺ์ૹہ߹ࢉͰͷ ϢχʔΫϦʔνΛ࠷େԽͤ͞ΔΑ͏ʹɺ์ૹہ͝ͱͷग़ߘ഑෼Λ࠷దԽ͢Δ w ೖྗɿ์ૹہ͝ͱͷग़ߘྔɻςϨϏ$.ͷ৔߹ɺάϩεϦʔν͋ͨΓͷֹۚ ʢύʔίετʣ͕ܾ·͍ͬͯΔɻάϩεϦʔνʢہ΁ͷग़ߘྔʣͱύʔίετΛ ֻ͚Δ͜ͱͰہ΁ͷ౤ԼֹۚΛࢉग़Ͱ͖Δɻ 6 ςϨϏۀքͰ͸(31 (SPTT3BUJOH1PJOU ͱݺ͹ΕΔ

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ิ଍ɿάϩεϦʔνͱϢχʔΫϦʔν w άϩεϦʔνʢԆ΂ϦʔνɾΠϯϓϨογϣϯɾ(31ʣ w $.΁ͷԆ΂઀৮ਓ਺ʢׂ߹ʣ w ಉ͡ਓ͕ෳ਺ճ$.ʹ઀৮ͨ͠৔߹ɺԿ౓Ͱ΋Χ΢ϯτ͢Δ w ϢχʔΫϦʔνʢϦʔνɾϢχʔΫϢʔβׂ߹ʣ w $.ʹগͳ͘ͱ΋ճ઀৮ͨ͠ਓ਺ʢׂ߹ʣ w ಉ͡ਓ͕ෳ਺ճ$.ʹ઀৮ͯ͠΋ճ໨Ҏ߱͸Χ΢ϯτ͠ͳ͍ 7 ΑΓଟ͘ͷਓʹಧ͚Δͱ͍͏ҙຯͰ͸ɺ άϩεϦʔνͰ͸ͳ͘ϢχʔΫϦʔνΛ ޮ཰తʹ৳͹͢͜ͱ͕ॏཁ

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w ݸਓ ͕$.ʹҰ౓Ͱ΋઀৮ͨ͠Β ͠ͳ͚Ε͹ΛऔΔ֬཰ม਺Λ ͱ ͢ΔɻશମͷϢχʔΫϦʔνΛ ͱ͢Δͱɺ ͱͳΔ ΋֬཰ม਺ ɻ w ์ૹہ͸ ͷہͱ͢Δɻہ͝ͱͷάϩεϦʔν ग़ߘྔ Λ ͱ͠ɺہ͝ͱͷάϩεϦʔν͋ͨΓͷίετΛ ɺτʔλϧίετ εϙοτ$.શମͷ༧ࢉ Λ ͱ͢Δɻ w ͜ͷͱ͖ہ͝ͱͷ༧ࢉ഑෼Λௐ੔͠શମͰͷϢχʔΫϦʔνΛ࠷େԽ͢Δͱ͍͏ ໰୊͸ҎԼͷΑ͏ʹఆࣜԽͰ͖Δ i = 1,2,...,N Ri ¯ R ¯ R = 1 N N ∑ i=1 Ri ¯ R ℬ = {A, B, C, D, E} g = [gA , gB , gC , gD , gE ] c = [cA , cB , cC , cD , cE ] ¯ C max g E[ ¯ R|g] TU ∑ b∈ℬ cb gb = ¯ C, gb ≥ 0 (∀b ∈ ℬ) ࠷దԽ໰୊ͷఆࣜԽ 8

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ͷ෼ղ E[ ¯ R|g] w ͕ཅͳܗͰ෼͔Ε͹ղ͚Δɻͦ͜Ͱ໨తؔ਺Λ෼ղ͢Δɻ E[ ¯ R|g] 9 max g E[ ¯ R|g] TU ∑ b∈ℬ cb gb = ¯ C, gb ≥ 0 (∀b ∈ ℬ) E[ ¯ R|g] = E[ 1 N N ∑ i Ri |g] = 1 N N ∑ i E[Ri |g] = 1 N N ∑ i Pr(Ri = 1|g) E[ ¯ R|g] ≈ 1 N ∑ i Pr(R = 1|g) = Pr(R = 1|g) ≈ 1 − ∏ b∈ℬ (1 − Pr(Rb = 1|gb )) ͷ஋ΛऔΔ֬ ཰ม਺ͷظ଴஋͸Λ औΔ֬཰ʹ౳͍͠ ์ૹہ͝ͱͷ઀৮͕ಠཱͱԾఆ͢Δͱɺ์ૹہ߹ࢉ ͷ઀৮֬཰͸์ૹہ͝ͱͷඇ઀৮֬཰ͷੵΛ͔Β Ҿ͘͜ͱͰٻΊΒΕΔ ݸਓ ͝ͱʹάϩεϦʔνͰ৚݅෇͚ΒΕͨ ઀৮֬཰Λߟ͑Δͷ͸೉͍͠ͷͰɺ͜͜Ͱ ͸શݸਓͰҰఆͰ͋ΔͱԾఆ i

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ͷ෼ղ E[ ¯ R|g] w ์ૹہ߹ࢉͰͷ઀৮֬཰͸ɺ์ૹہ͝ͱͷ઀৮֬཰͕෼͔Ε͹ܭࢉՄೳ w ྫ͑͹ہͰߟ͑Δͱɺ w ์ૹہ͝ͱͷग़ߘྔ ͔Βɺہ୯ମͰͷϢχʔΫϦʔν Λ༧ଌग़དྷΕ͹ྑ͍ R(gA , gB ) = 1 − (1 − RA (gA ))(1 − RB (gB )) = 1 − (1 − RA − RB + RA RB ) = RA + RB − RA RB gb Rb 10 R(g) ≈ 1 − ∏ b∈ℬ (1 − Rb (gb )) R(g) = Pr(R = 1|g), Rb (gb ) = Pr(Rb = 1|gb ) RA RB RA RB max g {1 − ∏ b∈ℬ (1 − Rb (gb ))} TU ∑ b∈ℬ cb gb = ¯ C, gb ≥ 0 (∀b ∈ ℬ) ͱ͢Δ RA ͱ͢Δ RB

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์ૹہ͝ͱͷϦʔν ͷਪఆ Rb w ग़ߘྔάϩεϦʔνͱϢχʔΫϦʔνͷؔ܎͸ઢܗͰ͸ͳ͍ͨΊ ޿ࠂͷ௿ݮޮՌʣɺର਺ؔ਺ ͷΑ͏ͳඇઢܗϞσϧͰද͞ΕΔɻର਺ؔ਺ͩͱදݱྗ͕ऑ͍ͷͰɺҰൠతʹ͸IJMMؔ਺ ͱ͍͏ؔ਺ܗ͕Α͘࢖༻͞ΕΔʢ...ͳͲͷจ຺ʣɻͭ·Γɺ ͱͳΔɻ β log(x + 1) β x x + α Rb (gb ) = β gb gb + α 11 Ϧʔνσʔλ͸֬཰తγϛϡϨʔγϣϯ Ͱੜ੒ TDJQZPQUJNJ[FDVSWF@ f i

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਺஋࣮ݧ 12 ์ૹہ άϩεϦʔν(%) ϢχʔΫϦʔν(%) ౤Լίετ(ສԁ) A 38.7 31.0 483.8 B 35.8 28.4 429.5 C 38.3 29.0 421.4 D 44.4 29.0 354.9 E 41.4 26.1 310.5 Total 198.6 81.6 2000.0 ์ૹہ άϩεϦʔν1% ͋ͨΓͷίετ A 12.5ສԁ B 12ສԁ C 11ສԁ D 8ສԁ E 7.5ສԁ Total Budget 2000ສԁ TDJQZPQUJNJ[FNJOJNJ[F Ͱ࠷దԽՄೳɻ໨తؔ਺ Ҿ਺໊GVO Ͱ͸ͦΕͧΕͷ์ૹہ͝ͱʹਪఆ͞ΕͨIJMMؔ਺Λ༻͍ͯɺ์ૹہ ͝ͱͷϦʔνΛܭࢉ͠ɺ Λܭࢉ͢Δɻ ੍໿৚݅ Ҿ਺໊DPOTUSBJOUT Ͱ͸ɺ์ૹہ͝ͱͷύʔίετ ͱάϩεϦʔνͷੵͷ࿨͕τʔλϧ༧ࢉͱҰக͢Δ͜ͱΛදࣜ͢ Λ༩͑Δʢ౳੍ࣜ໿ʣ ࠷దԽख๏ Ҿ਺໊NFUIPE Ͱ͸l4-421zΛࢦఆ͢Δ͜ͱͰɺ ੍໿෇͖࠷దԽͷ࣮ߦ͕Մೳɻ R(g) ≈ 1 − ∏ b∈ℬ (1 − Rb (gb )) ∑ b∈ℬ cb gb − ¯ C = 0 ࠷దԽ

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ιʔείʔυ w IUUQTHJUIVCDPNNULX50QUJNJ[BUJPO/JHIU@ w ֬཰తͳγϛϡϨʔγϣϯͰϦʔνσʔλΛੜ੒ w γϛϡϨʔγϣϯσʔλʹରͯ͠࠷దԽΛ࣮ߦ͍ͯ͠Δ 13

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ิ଍ɿ์ૹہ߹ࢉͰͷϢχʔΫϦʔνͷิਖ਼ w ্هͷۙࣅ͸$.΁ͷ઀৮͕์ૹہ͝ͱʹಠཱͰ͋Ε͹͏·͍͕͘͘ɺ࣮ࡍʹ͸ͦ͏Ͱ͸ ͳ͍Մೳੑ͕ߴ͍ɻྫ͑͹ʮςϨϏΛΑ͘ݟΔݸਓ͸ͲͷہͰ΋઀৮͢Δ֬཰͕ߴ͍ʯ ʮ͋·ΓςϨϏΛݟͳ͍ਓ͸ͲͷہͰ΋઀৮͢Δ֬཰͕௿͍ʯͷΑ͏ͳؔ܎͕͋Δ৔߹ɺ աେɺ͋Δ͍͸աখʹϦʔνΛݟੵ΋ΔՄೳੑ͕͋Δɻ͜ͷΑ͏ͳࢹௌಛੑʹରͯ͠ิਖ਼ Λߦ͏͜ͱͰΑΓ໬΋Β͍͠ϦʔνਪఆΛ͢Δɻ 14 R(g) ≈ 1 − ∏ b∈ℬ (1 − Rb (gb )) RA RB RA RB RA RB < RAB ? RA RB > RAB ? w ͭͷΞΠσΟΞͱͯ͠͸γϯϓϧʹॏෳ߲ʹରͯ͠ิਖ਼܎਺ Λಋೖ͠ɺॏෳϦʔνͷ ࣮σʔλ͔Βਪఆ͢Δɻ θ ہͰߟ͑Δͱɺ R(gA , gB ) = RA + RB − θRA RB θ = ̂ RAB RA RB

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ࢀߟࢿྉ w ৿Լޫ೭ॿ σʔλෆ଍ʹ਺ཧϞσϧͰཱͪ޲͔͏+BQBO3 IUUQT TQFBLFSEFDLDPNESPQPVUKBQBOEPUS 15