Info3010, Week 5 notes
Info3010, Week 5 notes Info3010
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This 4 page Class Notes was uploaded by Rebecca Evans on Friday February 12, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 19 views. For similar materials see Business Modeling in Business at Tulane University.
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Date Created: 02/12/16
Notes from class on February 10th Dorian Auto Dorian Auto is considering manufacturing three types of cars (compact, midsize, and large) and two types of minivans (midsize and large). The resources required and the profit contributions yielded by each type of vehicle are shown in the table below. At present, 6500 tons of steel and 65,000 hours of labor are available. If any vehicles of a given type are produced then production of that type of vehicle is economically feasible only if at least a minimal number of that type are produced. These minimal numbers are also listed in the table below. Dorian wants to find a production plan that maximizes its profit. Compact car Midsize car Large car Midsize Large Minivan Minivan Steel 1.5 3 5 6 8 (tons/unit) Labor 30 25 40 45 55 (hours/unit) Minimum 1000 1000 1000 200 200 production (if any) Profit $2,000 $2,500 $3,000 $5,500 $7,000 contribution Conceptual Formulation 1 Decision Variable: a Which cars/minivans to produce and in what quantities? i Y 11 if compact cars are produced, Y =0, 1therwise ii Y 51, if large minivans are produced, =0 otherwise (binary) iii X 1# units of compact cars produced iv X =2 units of large minivans produced (numerical) 2 Objective a Maximize total profit b Total Profit=2,000X 1 2,500 X +23,000X + 3 500X + 7,4 0X 5 i Don’t multiply by Y variable because then nonlinear 3 Constraints a Threshold production level constraint i 1,000Y ≤1X ≤ 1 000,000Y 1 1 Explanation: lower limit=1,000Y and 1 per limit= 1,000,00 1 (artificial upper limitlarge number that doesn’t matter, can write infinity) 2 Suppose Y =01then 0 ≤ X ≤ 01 3 Suppose Y =11then 1,000 ≤ X ≤ 1,1 0,000 ii 200Y 5 X ≤5 ,000,000Y for5 arge minivans b Resource constraints i Labor constraint: 30X + 25X + … + 55X ≤ 6,500 hours 1 2 5 ii Steel constraint: 1.5X 1 3X 2 … + 8X ≤ 65 00 tons of steel c Binary constraint: Y ,1Y ,2…Y a5e binary Excel 4 Total profit is =sumproduct(units produced, contribution per unit) 5 Constraints a Resource constraints are =sumproduct(units produced, steel or labor hours per unit) b Units produced rowlink to decision units produced row c Lower limit(min. production) =minimum production*binary variable d Upper limit on production = 1,000,000 (or any large number) * binary variable 6 Solver a Objective: C17 (total profit cell) b Max c By changing variable cell: decision cells=produce? And units produced (Y and X variables conceptually) d Constraints i Steel and labor hours cells ≤ Resource available cells ii Minimum production row ≤ units produced iii Units produced ≤ upper limit on production iv Binary constraint: produce? Decision row is “bin” (binary) e No option for sensitivity report because using binary variables th Notes from class on February 12 The Javitz club in New York City has one jazz performance every weeknight (Mon to Thu). The expected ticket demand for weeknight performances is given by the relationship below: Demand = 333 – 3.33 × price The capacity of the club is 200 seats. 1) What is the optimal weeknight price that the club should charge? Nonlinear optimization model: most pricing problems are nonlinear Conceptual formulation 1. Decision Variable a. What price to charge for weeknight tickets? (p=price) 2. Objective a. Maximize revenue b. Revenue= p*q = price * quantity sold at price p c. Quantity demanded @ price= 3333.33 x price d. Revenue= p*(333 – 3.33 × price) e. =333p – 3.33p 2 i. Nonlinear because p is squared 3. Graph Q Price Slope= 3.33 and yintercept= 333 4. Constraint a. Capacity constraint i. Q ≤ 200 ii. 333 – 3.33 × price ≤ 200 b. Nonnegativity constraint i. P ≥ 0 Excel 1. Solver a. Objective: revenue cell b. Changing cell: price c. Constraint: tickets sold ≤ capacity (200 tickets) d. ***Choose solving method: GRG nonlinear Results Solution: choose a price where demand is below capacitymaximize revenue is goal (not filling to capacity) Advantage of more people: club sells other goods/service (drinks)higher secondary revenue (not take into account) In future modeling: goal programing=can have 2 objectives Review of Course this far: Modeling cycle Business situation”modeling step” conceptual formulation spreadsheet modelinsightsmanagerial insights Modeling world and real world Deterministic Model Application Production and transport Marketing and advertising Finance and investing linear Continuous linear programs optimization Integer/binary programs Nonlinear programs Mixed programs
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