具數量折扣及空間與預算限制之多產品報童模式最適決策品質研究

A Study on Optimal Decision Quality for Multi-Product Newsboy Model with Quantity Discounts and Spatial and Budget Constraints

10.6626/MR.201612_16(2).0001

黃允成(Yun-Cheng Huang)；潘彥如(Yen-Ru Pan)

報童模式 ； EM演算法 ； 數量折扣 ； 空間與預算限制 ； Newsboy Model ； EM algorithm ； Quantity Discounts ； Spatial and Budget Constraints

管理研究學報

16卷2期（2016 / 12 / 01）

1 - 30

繁體中文

本研究主要係針對單一週期多產品之報童模式在售價已知、數量折扣、空間與預算限制且需求為隨機變數條件下，建立總期望利潤之數學模型，以期望邊際分析法，即EM演算法(expect marginal algorithm)及數值積分演算法進行求解，找出最適訂購策略，以達總期望利潤最大化之目標。之後再對各參數進行敏感度分析，以瞭解各參數對最適訂購量與總期望利潤的影響，並以數值範例驗證本研究模型之可行性，最後則提出五點結論，以供實務運用及後續研究之參考。

This research mainly focused on constructing a mathematical model for expected total profit of the Newsboy model with single cycle multi-product under the conditions of known price, quantity discount, space and budget constraints. In addition, the demand of each product is a random variable. The purpose of this paper is to find out the optimal purchase strategy to maximum the total expected profit using by expected marginal profit algorithm (called as EM algorithm) and numerical integration technique. Then, a sensitivity analysis was conducted for each parameter to understand the relationship between optimal purchase quantity and expected total profit, furthermore, a numerical example was provided to verify the feasibility of the proposed model. Finally, five conclusions were drawn for practical applications and future studies.

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