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Operation Research Development

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Operations Research OR - Development of OR
- England , world war  → determining the last utilization of limited resources - USA → 1947 → simplex method - Development → computer science - OR models mathematical model → variables, Function Optimal solution according to different techniques Simulated model → study for a specific system at Certain time period and simulate this system Heuristic model → empirical rules to find Approximate solution from point to another in the System

Mathematical Model 1- Decision variables and parameters unknown values we need to solve equations to get these values EX: parameter → determine system We need to determine level of production for a specific good based on raw material, machine capacity Unknown parameter→ level of production, Unknown variable → number of units produced

2- Constraints or restrictions → row material 3- Objective function → EX: profit function maximization cost function Minimization EX: production planning machine 1 2 3 Profit/unit Time per unit (minutes) Machine Product1 product2 product3 capacity 1 2 1 430 3 0 2 460 1 4 0 420 3 2 5

 OR mathematical model X1 → amount product1 X2 → amount product2 X3 → amount product3 Profit function: Constraints 1x1 + 2x2 + 1x3 ≤ 430 3x1 + 0x2 + 2x3 ≤ 460 1x1 + 4x2 + 0x3 ≤ 420 Additional non negativity constraints x1 ≥ 0 , x2 ≥ 0 , x3 ≥ 0 We are looking for optimum sol for x1 , x2 , x3 to maximize objective function subject to constraints

Introduction to optimization & linear programming Examples of decision making situations that depend on mathematical programming 1 - Product mix: each product require different amount of row materials and labor. Manger must decide how many of each product to produce in order to maximizes profit and minimize cost → EX (lecture 1) 2- Manufacturing: computer – controlled drilling machine must be programmed to drill in a given

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