Info3010, Week 3 notes
Info3010, Week 3 notes Info3010
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This 5 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 28 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 January 25 th Bland Brewery (continued from week 2) Bland Brewery produces ale and lager beer which are always in demand but whose production is limited by raw materials that are in short supply. The scarce raw materials are corn (availability of 480 lbs.), hops (availability of 160 ozs.) and malt (availability of 1190 lbs.). One barrel of ale requires 5lbs. of corn, 4 ozs. of hops and 35 lbs. of malt while one barrel of lager requires 15 lbs. of corn, 4 ozs. of hops and 20 lbs. of malt. The brewery sells ale at a profit of $13/barrel and lager at a profit of $23/barrel. How many barrels of ale and lager should the brewery produce in order to maximize profits? Deterministic Modeling Conceptual formulation (copied from last class) 1. Decision: How many barrels of ale and lager to produce? a. X1= # of barrels of ale X 2 # of barrels of lager 2. Maximize Profit a. Profit= 13X 1 23X 2 3. Constraint: Raw material limitation a. Corn: 5X 1 15X ≤ 280 lbs b. Hops: 4X +14X ≤ 260 ozs c. Malt: 35X 1 20X ≤ 2190 lbs d. Non-negativity constraint: X ,1X ≥20 Only valid for the total amount our constraints are limited by (ex. Suppose only have 400 lbs of corn-what happens? Or change price so get $15/ale-new max?) Excel (answer above questions) Datasolvervalues (from last class)”solve”right bar reports options hit “sensitivity”okcreate sensitivity report in a new tab (bottom left of screen) Constraint table: o “constraint r.h. side” column represents the total amount availability o “final value” amount of total availability that is used o “shadow price” represents how much your optimal profit would increase by $x amount for 1 extra unit of increase of the total availability Ex. If hops availability increases by 10 units (from 160 to 170) and has a $2 shadow price then the optimal value of the objective increases by ($2)(10 units) = $20 Shadow price of $0 for malt because we have not used the entire available resource; if positive shadow price then you have used total available resources o “allowable increase” shows the maximum that the total availability can increase Cannot get decision numbers from report, but have to resolve with new numbers using solver and a new model table Variable cells table: o Objective coefficient: coefficients in maximization equation (in this case price per ale and price per lager) o Final value: optimal values for x1 and x2 o Ignore reduced cost (no useful info for us) o Allowable increase: amount of $ can increase the cost per barrel by and produce the same number of barrels total o Overall table is for the objective functions Create copy of model 1 model 3; increase profit per barrel to $15 th Notes from Class on January 27 Flakey Cereals Company The Flakey Cereals Company sells a brand of low-fat breakfast cereal that appeals to people of all age groups and both genders. The company advertises this cereal in a variety of 30 second ads, and these ads can be placed in a variety of television shows. The ads in different shows vary by cost – some 30 second slots are much more expensive than others – and by the type of viewers they are likely to reach. A rating service can supply data on the number of viewers in each of these categories who will watch a 30-second ad on any particular television show. Each such viewer is called an exposure. The company has determined the required number of exposures for each group. It wants to know how many ads to place on each of several television shows to obtain these required exposures at minimum cost. The data on costs per ad, number of exposures per ad, and minimal required exposures are listed in the table below, where the number of exposures are expressed in millions, and costs in thousands of dollars. What should the company do? Viewer Desperate Monday The Sports The Lifetime CNN Law & Minimal group/TV Housewive Night Simpso Centre Real Evening Order required Show s Football ns World Movie SVU exposure (MTV) s Men 18- 5 6 5 0.5 0.7 0.1 0.1 3 60 35 Men 36- 3 5 2 0.5 0.2 0.1 0.2 5 60 55 Men 1 3 0 0.3 0 0 0.3 4 28 over 55 Women 6 1 4 0.1 0.9 0.6 0.1 3 60 18-35 Women 4 1 2 0.1 0.1 1.3 0.2 5 60 36-55 Women 2 1 0 0 0 0.4 0.3 4 28 over 55 Cost per $140 $100 $80 $9 $13 $15 $8 $140 ad Flakey Cereal Conceptual Formulation 1. Decisions a. How many ad sports to buy in each TV show b. X 1 # ads bought in desperate housewives….X = # ads8bought in Law and Order 2. Objective a. Minimize cost of buying ads b. Cost=$140X + …1+ $140X 8 3. Constraint a. 5X +16X + 2+ 3X ≥ 60 8Men 18-35) b. Similar exposure constraints for all the remaining audiences segments c. Non-negativity: X +1… + X ≥ 08 Excel 1. Sum Product a. =SUMPRODUCT(Entire range of decision, entire range of costs) b. Ex. =SUMPRODUCT(Number of ads purchased, cost per ad) c. Multiplies first cell in first range by first cell in second range and so on d. Ex2. For actual exposure =SUMPRODUCT(number of ads purchased, exposure for each show) e. **Use COMMA in between range inputs when using sum product 2. Anchoring/Locking Cells a. PC use F4 b. Mac Command + T c. Ex. Lock number of ads purchased in place because will be the same for each sumproduct, but will change the other range (exposure per show) d. Ex. Changed from C12:J12 to $C$12:$J$12 3. Solver a. Under “Data” tab b. Set min (not max) bc trying to minimize cost c. “Set objective”: total cost cell d. “By changing variable cells”: number of ads purchased e. “Subject to constraints”: select both columns (actual exposure and required) **make sure inequality sign is correct f. Hit solve2 ndpop up screenSelect sensitivity to get a sensitivity report 4. Sensitivity Report a. Suppose the exposure requirement for the women 18-35 segment was changed to 70. What will be the new optimal cost? b. Shadow price is $10. So for everyone 1 unit increase the cost will increase by 10, so with an increase of 10 units x $10 there will be an $100 increase in optimal cost c. New optimal cost = $1870 + ($10)(10 exposure units) = $1970 Notes from Class on January 27 th Grand Prix Automobile Company The Grand Prix Automobile Company manufactures automobiles in three plants and then ships them to four regions of the company. The capacity of the plants, the customer demand by region and the unit shipping costs of shipping from each plant to each region are listed in the table below. Grand Prix wishes to find the lowest cost shipping plan for meeting demands of the four regions without exceeding the capacities of the plants. Region 1 Region 2 Region 3 Region 4 Capacity Plant 1 $131 $218 $266 $120 450 Plant 2 $250 $116 $263 $278 600 Plant 3 $178 $132 $122 $180 500 Demand 450 200 300 300 Once you find the optimal shipping plan, consider the following scenario. The demand in Region 3 increases by 100 autos. A sister company has agreed to provide the supply to meet this extra demand. What is the maximum dollar amount we should be willing to pay the sister company for this service? Conceptual Formulation 1. Decision: a. How much to ship from each plant to each region? b. X 1 1of units shipped from plant 1 to region 1 c. X 3 4 of units shipped from plant 3 to region 4 d. X plant number region number 2. Objective a. Minimize total shipping costs b. Total shipping costs= 131X 1 1+ 218X 1 2+ … + 180X 3 4 c. **Decisions must show up in objective 3. Constraints a. Constraints of capacity (supply) and demand b. Capacity limitations i. X 1 1 X 1 2 … + X 1 4≤ 450 ii. X2 1 X2 +2… + X 2 4 600 iii. X3 1 X 3 2 … + X 3 4≤ 450 c. Demand requirement i. X 1 1 X 2 1 X 3 1+ X4 1= 450 ii. X1 2 X 2 2 X 3 2+ X4 2= 200 iii. Etc. Region 1 Region 2 Region 3 Region 4 Plant 1 X1 1 X1 2 X1 3 X1 4 Plant 2 X2 1 X2 2 X2 3 X2 4 Plant 3 X3 1 X3 2 X3 3 X3 4 Excel 1. Sum product a. Can select an entire array of cells (ex. A rectangle of cells-not necessarily just a row) it will match the 1 cell to the 1 cell and so on b. Problem: =sumproduct(shipping costs, quantity from region) 2. Constraints a. MUST link constraints to decision cells-don’t just enter a number b. When change decision-the constraints will change as well c. For total shipped use =sum and select the amount in the rows to the left (see capacity constraints in conceptual model) d. Demand Constraints: use =sum() but for adding each region (the columns) 3. Solver a. X b. Changing variable cells: select decision cells (C10 to F12) c. Constraint: total shipped ≤ capacity (select column of 3 cells from each) d. Constraint: total received = demand (select row of 4 cells each) 4. Answer the problem a. The maximum amount we would pay the sister company = (194)(100) Shadow price=194 and 100=change in demand
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