MA: Linear programming

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  • Created by: charlie
  • Created on: 26-05-17 17:21
Key factor analysis
used when one limited resource (scarce/ bottleneck if chain of processes)/ resource working at 100% capacity/ want to ration to achieve optimal benefit
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Key factor analysis ranking (5 steps)
(1) work out profit per resource (2) work out contribution per resource (3) find limiting factor per resource (usually lab/ mach hrs) (4) work out contribution per limiting factor (divide) (5) rank
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linear programming: graphical method
used for 2 products with 2 or more labour/ OH constraints (each product req. different amounts)
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linear programming: graphical method (7 steps)
(1) define unknowns (X+Y) (2) formulate obj. function (always max contn) (3) express 4 constraints as inequalities (4) plot constraints on graph (5) plot obj. function on graph (6) identify optimal (simultaneous eq.) (7) minus FC to get max profit
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marginal rate of substitution definition
rate at which consumer is willing to give up one good for another, whilst maintaing the same utility (optimal response to independent marginal increase in resource)
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dual value/ shadow price (opportunity cost) definition
value (contn) of an independent marginal increase of a scarce resource (premium worth paying for 1 extra unit) --> inc. in obj function from one more unit of scarce resource (binding constraint with no slack) at original price
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binding + non-binding constraints
only binding constraints (those deterring optimal solution) have a dual value not equal to 0
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dual value/ shadow price calculation
(1) add one more unit of output to original constraint equation (2) solve inequalities to get X + Y (3) put X + Y back into obj. function (contn) (4) difference is dual/ shadow price
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sensitivity analysis
how much contribution from one product can change before optimal solution changes (when gradient of obj. function >= gradient of constraint)
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sensitivity analysis calculation
(1) work out slope of constraint 1 (2) work out how much price coef of X can change keeping Y cst. on obj. function (vice versa) (3) work out slope of constraint 2. (4) work out how much price of X + Y can change of obj. function again
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(6) uses of linear programming (including opportunity costs)
(1) relevant costs for decision making (2) selling different products (new product) (3) max. to pay for additional scarce resource (4) control (optimised prod. tech strategy) (5) manage constraints 100% utilised (bottlenecks) (6) capital budgeting
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(6) assumptions/ limitations of linear programming
(1) linear (CRS + perfect competition) (2) infinite divisibility of products + resources (integer rounding) (3) validity of input data (4) one quantifiable obj. (5) only examine 2 products graphically (6) dual values only over certain range
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sensitivity analysis: optimum range (max. contn equation)
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slack arises when...
at optimal solution when resource is used less that resource available (not 100% capacity)
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Other cards in this set

Card 2

Front

Key factor analysis ranking (5 steps)

Back

(1) work out profit per resource (2) work out contribution per resource (3) find limiting factor per resource (usually lab/ mach hrs) (4) work out contribution per limiting factor (divide) (5) rank

Card 3

Front

linear programming: graphical method

Back

Preview of the front of card 3

Card 4

Front

linear programming: graphical method (7 steps)

Back

Preview of the front of card 4

Card 5

Front

marginal rate of substitution definition

Back

Preview of the front of card 5
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