研究建議

如前一章所提及，本研究仍然存在著一些限制，若可以改善將會使得研究的 結果更為精準、也更有價值。首先我們可以思考產能回復除了以線性表示外，是 否可以用其他的非線性函數表示，以更進一步的接近現實生活中的回復情形。再 來是模型的部分，如前所述，情形 3 不一定是最差的，或許我們可以去探討在甚 麼樣的情況下情形 3 的預期利潤反而會比情形 1 或情形 2 還好，影響這樣結果的 關鍵變數是那些，以讓模型結果產生更多可能。還有，本文討論的期間只有一期，

但製造商和供應商之間的關係常常都是長期的，因此未來的研究可以去探討若把 研究拉長成多期時是否存在其它影響廠商決策的關鍵變數，這些變數帶來的影響 又是甚麼，如此一來也將使得模型更為擬真。最後則是假設期初存貨量為零的部 分，在現實世界中，很多廠商都會準備一定的存貨量作為預備，因此也希望外來 有研究將存貨量也考慮進來，做一個全面性的最適化，以達到更棒、更好的決策 力。

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Proof of Proposition 1:

首先我們將 Case1 的預期利潤減去 Case2 的預期利潤得到以下式子並令其大於 零:

α × (𝑋𝑋_𝑏𝑏− 𝑋𝑋_𝑚𝑚) × 𝑄𝑄_𝑚𝑚× 𝑃𝑃₂− (𝑋𝑋_𝑏𝑏− 𝑋𝑋_𝑚𝑚) × 𝑄𝑄_𝑚𝑚× 𝐶𝐶₂− (𝑋𝑋_𝑏𝑏− 𝑋𝑋_𝑚𝑚) ×𝑇𝑇12

𝑋𝑋_𝑏𝑏 × 𝑋𝑋_𝑚𝑚× 𝑄𝑄_𝑚𝑚

× 𝐶𝐶ℎ− (1 − 𝛼𝛼) × (𝑋𝑋𝑏𝑏− 𝑋𝑋𝑚𝑚) × 𝑄𝑄𝑚𝑚× 𝑇𝑇2× 𝐶𝐶ℎ > 0

α × 𝑃𝑃₂− 𝐶𝐶₂−^𝑇𝑇_𝑋𝑋¹²

𝑏𝑏× 𝑋𝑋_𝑚𝑚× 𝐶𝐶_ℎ− (1 − 𝛼𝛼) × 𝑇𝑇₂ × 𝐶𝐶_ℎ > 0

(𝑃𝑃₂ + 𝑇𝑇₂× 𝐶𝐶_ℎ) × 𝛼𝛼 > 𝐶𝐶₂+^𝑇𝑇_𝑋𝑋¹²

𝑏𝑏 × 𝑋𝑋_𝑚𝑚× 𝐶𝐶_ℎ



α >

𝑇𝑇12×𝑋𝑋𝑚𝑚×𝐶𝐶ℎ

𝑋𝑋𝑏𝑏 +𝑇𝑇₂×𝐶𝐶_ℎ 𝑃𝑃₂+𝑇𝑇₂×𝐶𝐶_ℎ

故可得知當

α >

𝑋𝑋𝑏𝑏 +𝑇𝑇₂×𝐶𝐶_ℎ

𝑃𝑃₂+𝑇𝑇₂×𝐶𝐶_ℎ 時 Case1 的預期利潤會大於 Case2。

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