North-West Corner Rule: Simple, but often not optimal.

Least Cost Method: Better initial solution, allocates to lowest cost cells first.

Vogel's Approximation Method (VAM): Usually best initial solution, calculates penalties.

Optimality Test: Stepping Stone Method / MODI Method.

Special case of transportation problem where sources and destinations are equal, and each source must be assigned to exactly one destination.
Hungarian Algorithm:
1. Subtract smallest element from each row.
2. Subtract smallest element from each column.
3. Cover all zeros with minimum number of lines.
4. If lines = matrix size, optimal assignment found.
5. Else, find smallest uncovered element, subtract from all uncovered, add to elements at line intersections. Repeat from step 3.

Find path with minimum total length between two nodes.
Dijkstra's Algorithm: For non-negative edge weights.
Bellman-Ford Algorithm: For negative edge weights (can detect negative cycles).

Find maximum amount of flow that can be sent from a source to a sink through a network.
Ford-Fulkerson Algorithm: Uses augmenting paths.
Max-Flow Min-Cut Theorem: Max flow = Min capacity of a cut.

Find a subset of edges that connects all vertices, without cycles, and with minimum total edge weight.
Prim's Algorithm: Grows a tree from an arbitrary starting node.
Kruskal's Algorithm: Adds edges in increasing order of weight, avoiding cycles.

CPM (Critical Path Method): Deterministic activity durations.
PERT (Program Evaluation and Review Technique): Probabilistic activity durations.
Key Concepts:
- Activity: Task requiring time and resources.
- Event/Node: Start/completion of activities.
- Predecessor: Activity that must be completed before another starts.
- Critical Path: Longest path through the network; determines project duration. Activities on this path have zero slack.
- Slack/Float: Amount of time an activity can be delayed without delaying the project.

Earliest Start (ES): Max of EF of all immediate predecessors.
Earliest Finish (EF): ES + Activity Duration.
Latest Finish (LF): Min of LS of all immediate successors.
Latest Start (LS): LF - Activity Duration.
Total Float (TF): LS - ES or LF - EF.
Free Float (FF): Amount an activity can be delayed without affecting ES of any successor.

Expected Time ($T_e$): $\frac{T_o + 4T_m + T_p}{6}$
Variance ($\sigma^2$): $\left(\frac{T_p - T_o}{6}\right)^2$
$T_o$: Optimistic time, $T_m$: Most likely time, $T_p$: Pessimistic time.
Project variance is sum of variances of critical path activities.
Use Normal Distribution for project completion probability. $Z = \frac{\text{Desired Time} - \text{Expected Project Time}}{\sqrt{\text{Project Variance}}}$