Combining Demand Forecasts in a Newsboy Problem Using an Unequally Weighted Method

Abstract

需求預測對報童問題決策者十分重要，因為商品無法儲存至下期再販售。實務上，決策者常須在預算限制內選擇不同需求預測方法既而得到多個預測值，再加以組合。本文發展出一個存貨模型，幫助決策者以不等加權方式組合多個預測值來改善預測精確度。而最佳加權值是經由最小化組合預測變異數得來。本文發現兩不相關之預測值其加權值隨其變異數增加而遞減，因此當兩不相關之預測值在比較時，應、選擇變異數較小之預測值優先組合。理論上，最佳組合可以完全搜尋演算法找到。但當被組合預測值個數過多時，完全搜尋演算法就變得沒有效率。於是本文提出向前搜尋演算法、向後搜尋演算法和相關搜尋演算法來解決。

Demand forecasting is important for the decision maker facing a newsboy problem as goods cannot be carried over to be sold in the following period. In this paper, we develop a model to assist the decision maker using an unequally weighted method in combining forecasts to improve forecast accuracy. The optimal weights are decided by minimizing the variance of combined forecasts. We find that the optimal weights of uncorrelated forecasts decrease with their variances. When two uncorrelated forecasts are considered, one should select the forecast with smaller variance to combine with current forecasts in hand. Theoretically, the best combination of forecasts can be found by a complete search algorithm. We also propose three algorithms: a forward algorithm, a backward algorithm, and a correlated search algorithm to save computational time when the number of forecasts to be considered is large.