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ADM2302 Cheat Sheet.docx

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Davood Astaraky

Linear Programming To validate a constraint, plug in a number that you think would meet the requirements of the constraints and see if the ii) Assumptions constraint holds true. Then plug in numbers that do not meet 1) Conditions of certainty exist the constraint and see if the constraint fails. 2) Proportionality in objective function and constraints A few tricky constraints: 1) X1 as % of total production: X1(X1+Xn) > % 3) Additivity 4) Divisibility 2) X1 must be equal to 2/3 X2: X1 – 2/3X2 = 0 5) Non-negativity 3) Units produced of X1 must be more than 5X2: X1 > 5X2 4) Transshipment problem, constraint for distribution ii) Components center X: X11 + X12 – X21 – X22 = 0 1) Decision Variables- the unknown values 5) Inventory constraint: Beg inv + production + overtime + subcontracting – demand – ending inv = 0 2) Objective Function- the equation to min/max 3) Model constraints- the restrictions to be met 4) Model parameters- coefficients Graphical Method Step 1 - Assign 1 variable to each axis (X1 = x, X2 = y) Step 2 - Plot each of the constraints i) Equate all constraints and arrange into slope y-intercept form ii) To get x intercept, set y=0 and solve for x iii) To get y intercept, set x=0 and solve for y iv) Plot the 2 points and connect them Step 3 – Determine the feasible region and shade it in. For > shade below the constraint line, for < shade below the constraint line. Do this for each constraint until you have a region that satisfies all constraints. Step 4 – Solve to minimize cost or maximize profit Option 1: Plot the max or min function. For max, slide this line diagonally from (0,0) until you reach the furthest possible feasible point. For Min do the same, except we are looking for the first point the line touches sliding out from (0,0). Option 2: Calculate the x and y values at all intersecting lines (2 constr
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