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Linear programming · graphical vertex method
Linear programming · graphical vertex method
2变量 · 可行域凸多边形 · 目标等值线 · 最优在顶点
maximize c₁x + c₂y over a feasible polygon — the optimum is a corner
Branch and bound · integer programming
Branch and bound · integer programming
整数规划 · LP松弛+分支 · 按界剪枝 · B&B树
maximize 5x + 4y, integer — relax, branch on fractions, prune by bound
Transportation problem · initial feasible solution
Transportation problem · initial feasible solution
供需运价表 · 西北角/最小元素法 · 总运费
ship from supplies to demands at least cost — Northwest-Corner vs Least-Cost
M/M/1 queue
M/M/1 queue
ρ=λ/μ · L=ρ/(1−ρ) · W=1/(μ−λ) · ρ→1爆炸
ρ = λ/μ · L = ρ/(1−ρ) · Lq = ρ²/(1−ρ) · W = 1/(μ−λ) · Wq = λ/(μ(μ−λ))
Little's Law
Little's Law
L=λ·W · Lq=λ·Wq · 与分布无关恒等式
L = λ · W (and Lq = λ · Wq) — a distribution-free identity
Network maximum flow
Network maximum flow
Ford-Fulkerson增广路 · 残量 · 最大流=最小割
Ford–Fulkerson augmenting paths · max-flow = min-cut
Newsvendor model · single-period order quantity
Newsvendor model · single-period order quantity
单期 · 临界比 Cu/(Cu+Co) · Q*=F⁻¹(临界比)
Critical ratio CR = Cu/(Cu+Co) · optimal Q* solves F(Q*) = CR
Reorder point · continuous-review (Q,R) system
Reorder point · continuous-review (Q,R) system
(Q,R)系统 · ROP=d·L+z·σ√L · 锯齿库存图
ROP = d·L + z·σ·√L · safety stock SS = z·σ·√L
Decision tree · expected-value rollback
Decision tree · expected-value rollback
决策节点取最优 · 机会节点EV=Σp·payoff · 回溯
Chance node: EV = Σ p·payoff · Decision node: pick max EV · fold leaves → root
The assignment problem · Hungarian algorithm
The assignment problem · Hungarian algorithm
匈牙利算法 · 行/列约简+覆盖零 · 最小代价匹配
Assign n workers to n jobs at minimum total cost — exactly one worker per job.
0/1 Knapsack · dynamic programming
0/1 Knapsack · dynamic programming
0/1背包 · dp[i][w]表 · 最优价值+回溯选物
Pick items to maximize value with total weight ≤ capacity W — each item taken at most once.
Single-machine job sequencing · SPT & EDD
Single-machine job sequencing · SPT & EDD
单机 · SPT最小平均流程时间 · EDD最小最大延迟
One machine, jobs run one after another. The order you choose decides average flow time and maximum lateness.