最適貨櫃船型與船速之非線性規劃模式

A Nonlinear Programming Model for Optimizing Size and Speed of Containerships

訂造船舶的噸位為航商經營上重要的決策，最適船舶是由船型與船速的成本與收入相互抵換而決定的，能使航商獲得最大利潤。實務上，最適船型有逐期增大、船速加快的現象，這應是利潤函數內部分項目隨某些變數而變動使然。過去文獻著重以成本角度分析船型，而且忽略了船速的影響，易導致不適合的決策。因此，本研究以成本--數量--利潤分析法，建構適當的數學規劃模式，嘗試將這些變數納入模式中加以分析與釐清。此模式本質上是雙決策變數，沒有條件限制式，目標函數是嚴格凸向上函數，存在唯一的全域最佳解。本研究以遠東／北美航線為例，測試模式，及敏感度分析。本研究之結論有助於航商在規劃船型與船速時之決策參考。

One of the most important decisions for shipowners is to determine how big a containership to order. The optimum containership represents a trade-off between the cost and revenue resulting from ship size and speed. In reality, there is a tendency toward increasing containership size and speed, which is resulted from some factors related to profit. However, most of the past studies devoted their attention to the problem only from the cost perspective. These models neglected the effect of ship speed on profit, and might result in inadequate solutions to the problems. Based on the cost-volume-profit (CVP) analysis, this paper tries to formulate a model seeking the optimal size and speed of containerships that can maximize the profit for shipowners. The objective function is a strictly concave function, with two decision variables of ship size and ship speed, and its solution is globally optimal and unique. An example of the Trans-Pacific (Fareast-Northern America) Route is employed to test the model formulation and sensitivity analysis is conducted. The results would provide shipowners with a beneficial reference for planning the size and the speed of their containerships.