本文從演算法的角度探討營運管理問題。我們首先提供了簡明的介紹，強調論文所研究問題的基本動機。接下來，本文專注於兩個主要的問題領域：以數據驅動方式處理的均衡定價問題，以及受限預算限制的消防員問題。這些具體問題是論文的主要焦點，並在隨後的章節中進行了詳細研究。我們研究了多期均衡定價問題，其中企業對其需求函數一無所知。每個時期，企業確定價格並得到來自消費者的隨機需求。每個企業的目標是在競爭環境下最大化總收入。我們設計了幾個協調動態定價算法，使企業能夠根據觀察到的銷售數據學習需求函數並相應調整定價策略。論文證明，隨著時間的推移，算法生成的定價決策會收斂到納什均衡價格。之後，我們將焦點轉移到疫苗接種問題，該問題圍繞著減少傳染病傳播影響的有效疫苗接種策略。目標是使用各種算法得到問題的最優和近似解。我們將問題建模為一個整數規劃問題並提供三種近似算法，以快速解決問題。最後我們對論文進行了總結，并在本文討論的結果和方法基礎上，指出一些未來的研究方向。

The thesis explores operations management problems from an algorithmic perspective. We first proved a concise introduction, highlighting the underlying motivation behind the problems investigated in the thesis. Subsequently, the thesis concentrates on two main problem domains: the equilibrium pricing problem approached in a data-driven fashion, and the firefighter problem constrained by limited budgets. These specific problems are the primary focus of the thesis, and they are examined in detail throughout the subsequent chapters. We study a multiperiod equilibrium pricing problem where firms have no knowledge of their demand functions. At each period, firms determine their prices and face stochastic demand from consumers. The goal of each firm is to maximize total revenue under competition. We design several coordinated dynamic pricing algorithms, enabling firms to learn the demand functions based on observed sales data and adjust pricing strategies accordingly. The thesis demonstrates that, over time, the pricing decisions generated by the algorithms converge to the Nash equilibrium prices. Next, we shift focus to the vaccination problem, which revolves around the efficient strategies of vaccinations to reduce the impact of spreading infectious diseases. The objective is to identify optimal and approximate solutions to this problem using various algorithms. We model the problem as an integer program and provide three approximation algorithms aimed at quickly solving the problem. We conclude the thesis and point out several potential avenues for future research, building upon the findings and methodologies discussed throughout this thesis.

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