Optimization and Mathematical Programming

A Criteria Based Matrix (also called a Decision Matrix or Pugh Matrix) is a decision-making tool used to evaluate multiple solutions against weighted criteria. It helps teams systematically compare alternatives and select the best solution based on objective criteria rather than subjective judgment. The matrix scores each solution against predetermined criteria to identify the optimal choice.

Solver is Excel's optimization tool used to find optimal solutions for models with constraints. It can maximize, minimize, or set a target value by adjusting variable cells within specified constraints. Scenario Manager only compares different scenarios but doesn't optimize. 'Target value' is not a tool but rather a parameter used within Goal Seek or Solver.

Dynamic programming optimizes by storing solutions to subproblems to avoid recomputation. Huffman coding optimizes compression by using shorter codes for frequent characters. Greedy algorithms optimize by making locally optimal choices at each step. Cyclic coding is not a standard optimization technique in algorithms.

Boolean solvers can solve sets of constraints using numerical analysis techniques like Gaussian elimination, which systematically eliminates variables to solve systems of linear equations or constraints. This method is fundamental in constraint satisfaction problems. Options A, B, and D describe binary/boolean concepts but are not examples of constraint-solving techniques.

Oracle Inventory Planning includes both Min-Max Planning (maintains stock between minimum and maximum levels) and Reorder Point Planning (triggers reorder when stock falls below a threshold). These are the two primary manual planning methods available in the module. Option C correctly combines both methods.

It takes into account input variables, interrelationships among the variables, problem assumptions and constraints.

Loop jamming combines the multiple loops which perform different calculation for the same loop iteration.

Hill climbing search is a variant of generate and test strategy.

Linear Programming is indeed a mathematical optimization technique used to determine the best allocation of limited resources among competing activities. It maximizes or minimizes an objective function subject to constraints.

Linear programming is deterministic, not probabilistic. All parameters in an LPP (objective coefficients, constraint coefficients, RHS values) are assumed to be known with certainty. Stochastic programming handles probabilistic scenarios.

In an LPP, the number of decision variables and constraints are independent. You can have m constraints and n decision variables with no requirement that m = n. Simplex method works with m ≠ n.

The graphical method is specifically designed for LPPs with exactly two decision variables. It plots the feasible region and objective function on a 2D coordinate plane. For three+ variables, use simplex or other methods.

In a linear programming problem (LPP), the optimal solution can sometimes occur at a single extreme point (vertex) rather than along an entire edge connecting two vertices. Therefore, the claim that it always lies on at least two vertices is false.

When the objective function is parallel to a binding constraint edge, multiple optimal solutions exist. All points on that edge (including both endpoints) yield the same optimal objective value.

An unbounded solution occurs when the objective function can increase (maximization) or decrease (minimization) indefinitely within the feasible region. This typically means constraints don't bound the objective in that direction.