Decision Science Notes

Establishes foundational concepts of operations research and mathematical modeling. Topics include the historical development, definition, scope, and phases of operations research in business decision-making; classification of OR models; Linear Programming Problem (LPP) formulation: defining decision variables, constructing the linear objective function (maximization or minimization), and formulating linear constraint equations and non-negativity restrictions; graphical solution method: plotting constraint boundary lines, identifying the feasible region (bounded vs unbounded), corner point/extreme point evaluation method; and graphical interpretations of unique optimal solutions, multiple optimal solutions, infeasible solutions, and unbounded solutions.

Delivers rigorous mathematical training in the algebraic Simplex optimization algorithm. Topics include converting LPP into standard canonical form; introduction of slack variables (for <= constraints), surplus variables, and artificial variables (for >= and = constraints); setting up the initial Simplex tableau; determining the pivot column (most negative Cj - Zj value for maximization), pivot row (minimum positive ratio rule), and key/pivot element; executing Gaussian row transformations to update the tableau; optimality condition (all Cj - Zj <= 0); handling artificial variables using the Big-M Method (Charnes' Penalty Method); and Duality in LPP: formulation of the Dual from the Primal problem, economic interpretation of dual variables (shadow prices), and fundamental duality theorems.

Examines mathematical distribution models to minimize freight transportation costs between multiple sources and destinations. Topics include mathematical formulation of the transportation problem; balanced versus unbalanced transportation problems (introducing dummy source/destination); methods for finding Initial Basic Feasible Solution (IBFS): North-West Corner Rule (NWCR), Least Cost Method (LCM / Matrix Minimum Method), and Vogel's Approximation Method (VAM - penalty calculation method); testing for degeneracy in transportation problems (m + n - 1 allocated cells condition); and testing for optimality using the Modified Distribution Method (MODI method / u-v method), calculating net evaluations (dij = cij - (ui + vj)) for unoccupied cells, and tracing closed loops to redistribute allocations and achieve minimum total transportation cost.

Covers one-to-one resource allocation optimization to minimize cost or maximize productivity. Topics include mathematical formulation of the assignment problem as a special case of the transportation model; the Hungarian Assignment Method (Flood's technique): row reduction step, column reduction step, drawing minimum number of horizontal and vertical lines to cover all zeros, modifying the matrix, and making final optimal zero assignments; variations in assignment problems: unbalanced assignment problems (adding dummy rows or columns with zero costs), prohibited/restricted assignments (assigning high penalty cost M to impossible routes), and maximization assignment problems (converting to minimization by subtracting all matrix elements from the highest element).

Addresses project scheduling optimization and waiting line operational analysis. Project Network Analysis covers fundamentals of network construction (nodes, arrows, events, activities: concurrent, predecessor, successor, dummy activities); rules for drawing valid network diagrams (avoiding looping and dangling); Critical Path Method (CPM): forward pass calculation (Earliest Event Time - TE, Earliest Start Time - ES, Earliest Finish Time - EF), backward pass calculation (Latest Event Time - TL, Latest Start Time - LS, Latest Finish Time - LF), calculation of Total Float, Free Float, and Independent Float, and identifying the Critical Path; Program Evaluation and Review Technique (PERT): stochastic three-time estimates (Optimistic time 'a', Most likely time 'm', Pessimistic time 'b'), expected activity time formula (te = (a + 4m + b)/6), activity variance (sigma^2 = ((b - a)/6)^2), project standard deviation, and calculating probability of project completion by a specified deadline using standard normal Z-tables; and Queuing Theory basics: components of a queuing system (arrival process, service mechanism, queue discipline), and single-server queuing model (M/M/1: infinity/FIFO) formulas for server utilization, average queue length, and waiting time.