OPERATIONS MANAGEMENTfor MBAs Topic 5: Decision Making, Strategic Allocation of Resources, & Simulation
Outline • About the best alternative under various outcome scenarios. • Break Even Analysis • Preference Matrix • Certainty • Uncertainty • Risk • Expected Value • Decision Trees • Strategic Allocation of Resources • Simulation • Homework
Break-Even Analysis • Evaluating Services or Products • Is the predicted sales volume of the service or product sufficient to break even (neither earning a profit nor sustaining a loss)? • How low must the variable cost per unit be to break even, based on current prices and sales forecasts? • How low must the fixed cost be to break even? • How do price levels affect the break-even quantity?
Break-Even Analysis • Break-even analysis is based on the assumption that all costs related to the production of a specific service or product can be divided into two categories: variable costs and fixed costs • Variable cost, c, is the portion of the total cost that varies directly with volume of output • If Q = the number of customers served or units produced per year, total variable cost = cQ • Fixed cost, F, is the portion of the total cost that remains constant regardless of changes in levels of output
Finding the Break-Even Quantity EXAMPLE A hospital is considering a new procedure to be offered at $200 per patient. The fixed cost per year would be $100,000, with total variable costs of $100 per patient. What is the break-even quantity for this service? Use both algebraic and graphic approaches to get the answer.
Preference Matrix • A Preference Matrix is a table that allows you to rate an alternative according to several performance criteria • The criteria can be scored on any scale as long as the same scale is applied to all the alternatives being compared • Each score is weighted according to its perceived importance, with the total weights typically equaling 100 • The total score is the sum of the weighted scores (weight × score) for all the criteria and compared against scores for alternatives
Evaluating an Alternative EXAMPLE The following table shows the performance criteria, weights, and scores (1 = worst, 10 = best) for a new thermal storage air conditioner. If management wants to introduce just one new product and the highest total score of any of the other product ideas is 800, should the firm pursue making the air conditioner?
Preference Matrix Example Weight Score
Decisions Under Certainty • A manager knows with certainty which event or outcome will occur. • Pick the alternative with the best payoff for the known outcome. Example: New product introduction. Build a large or small facility?
Decision Making Under Uncertainty • Maximin • Maximax • Laplace
Decisions Under Risk • Similar to Laplace technique, but we use estimated probabilities (not equal) for the outcomes.
Decision Trees Model of alternatives along with potential consequences. Square Nodes – decision points. Circular Nodes – chances/probabilities that must sum to one. Branches – represent alternatives or different possibilities. Payoffs Payoffs EV
Low demand [0.4] Don’t expand Expand High demand [0.6] Small facility 2 Do nothing Advertise 1 Modest response [0.3] Sizable response [0.7] 3 Large facility Low demand [0.4] High demand [0.6] Analyzing a Decision Tree $200 $223 $270 $40 $800 $20 $220
Applications Include • Strategic Product or Service Mix Planning • Financial Portfolios • Choosing the Right Mix (ingredients, diet) • Transportation Problems • Staff Scheduling • Routing • Optimize an Objective Function • Minimize Costs • Maximize Profits • Constraints
Example-Transportation Problem Delorian motors has 2 distribution centers (DCs) for their 3 dealerships. Delorian automobiles are shipped from the centers to the dealerships. The shipping cost per auto, monthly dealership requirements, and distribution center levels are shown below. How many automobiles should be shipped per month from each DC to each dealership to minimize shipping costs and satisfy dealership demand?
Example A local brewery produces three types of beer: premium, regular, and light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 3.6 pounds of barley and 1.2 pounds of hops, a gallon of regular requires 2.9 pounds of barley and .8 pounds of hops, and a gallon of light requires 2.6 pounds of barley and .6 pounds of hops. The brewery is able to acquire only 55,000 pounds of barley and 20,000 pounds of hops next month. The brewery’s largest seller is regular beer, so it wants to produce at least twice as much regular beer as it does light beer. It also wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 4000 gallons each of light beer and premium beer, but not more than 12,000 gallons of these two beers combined. The brewery makes a profit of $3.00 per gallon on premium beer, $2.70 per gallon on regular beer, and $2.80 per gallon on light beer. The brewery manager wants to know how much of each type of beer to produce next month in order to maximize profit.
Example LP Formulation: ST capacity barley hops 2:1 ratio minimum P requirement minimum L requirement maximum requirement
Simulation – Flip 3 Coins 3H $20 2H $10 1H $2 0H $0 0.000 0.125 0.500 0.875 1.000 0 1 2 3 4 5 6 7 8
Sim1 • The management of Maderia Manufacturing is considering the introduction of a new product. The fixed cost to begin production of the product is $30,000. The variable cost for the product is uniformly distributed between $16 and $24 per unit. The product will sell for $50 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1200 units and a standard deviation of 300 units. Develop a spreadsheet simulation to answer the following managerial issues: • What is the expected mean profit for the new product? • What is the probability the project will result in a loss for us? • Develop a histogram that describes the profit picture. • What is your recommendation concerning introduction of the new product? Sim2 Octane Contracting is preparing a bid on a new construction project against three other contractors bidding on the same project. Based on past bidding practices, bids from the other contractors can be described by the distributions below: • If Octane submits a bid of $750,000, what is the probability they will win? • If Octane wants to be at least 80% sure they will win, what should they bid? • Provide a short managerial description of your simulation results.
LP #1 1. The Ohio Creek Ice Cream Company is planning production for next week. Demand for Ohio Creek premium and light ice cream continue to outpace the company’s production capacities. Ohio Creek earns a profit of $100 per hundred gallons of premium and $100 per hundred gallons of light ice cream. Two resources used in ice cream production are in short supply for next week: the capacity of the mixing machine and the amount of high-grade milk. After accounting for required maintenance time, the mixing machine will be available 140 hours next week. A hundred gallons of premium ice cream requires .3 hours of mixing and a hundred gallons of light ice cream requires .5 hours of mixing. Only 28,000 gallons of high-grade milk will be available for next week. A hundred gallons of premium ice cream requires 90 gallons of milk and a hundred gallons of light ice cream requires 70 gallons of milk.
LP #2 2. The Sureset Concrete Company produces concrete in a continuous process. Two ingredients in the concrete are sand, which Sureset purchases for $6 per ton, and gravel, which costs $8 per ton. Sand and gravel together must make up exactly 75% of the weight of the concrete. Furthermore, no more than 40% of the concrete can be sand, and at least 30% of the concrete must be gravel. Each day 2,000 tons of concrete are produced.
LP #3 3. A ship has two cargo holds, one fore and one aft. The fore cargo hold has a weight capacity of 70,000 pounds and a volume capacity of 30,000 cubic feet. The aft hold has a weight capacity of 90,000 pounds and a volume capacity of 40,000 cubic feet. The shipowner has contracted to carry loads of packaged beef and grain. The total weight of the available beef is 85,000 pounds; the total weight of the available grain is 100,000 pounds. The volume per mass of the beef is 0.2 cubic foot per pound, and the volume per mass of the grain is 0.4 cubic foot per pound. The profit for shipping beef is $0.35 per pound, and the profit for shipping grain is $0.12 per pound. The shipowner is free to accept all or part of the available cargo; he wants to know how much meat and grain to accept in order to maximize profit.
LP #4 4. The White Horse Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.60 to produce a jar of applesauce and $0.85 to produce a bottle of apple juice. The company has a policy that at least 30% but not more than 60% of its output must be applesauce. The company wants to meet but not exceed the demand for each product. The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent to promote apple juice. The company has $16,000 to spend on producing and advertising applesauce and apple juice. Applesauce sells for $1.45 per jar; apple juice sells for $1.75 per bottle. The company wants to know how many units of each to produce and how much advertising to spend on each in order to maximize profit.
LP #5 5. MadeRite, a manufacturer of paper stock for copiers and printers, produces cases of finished paper stock at Mills 1, 2, and 3. The paper is shipped to Warehouses A, B, C, and D. The shipping cost per case, the monthly warehouse requirements, and the monthly mill production levels are: Monthly Mill Destination Production A B C D (cases) Mill 1 $5.40 $6.20 $4.10 $4.90 15,000 Mill 2 4.00 7.10 5.60 3.90 10,000 Mill 3 4.50 5.20 5.50 6.10 15,000 Monthly Warehouse Requirement (cases)9,000 9,000 12,000 10,000 How many cases of paper should be shipped per month from each mill to each warehouse to minimize monthly shipping costs?
DM #1 DM #2
DM #4 A firm must decide whether to construct a small, medium, or large stamping plant. A consultant’s report indicates a .20 probability that demand will be low and a .80 probability that demand will be high. If the firm builds a small facility and demand turns out to be low, the net present value will be $42 (million). If demand turns out to be high, the firm can either subcontract and realize a NPV of $42 or expand greatly for an NPV of $48. The firm could build a medium size facility as a hedge: If demand turns out to be low, its NPV is estimated at $22; if demand turns out to be high, the firm could do nothing and realize a NPV of $46, or it could expand and realize a NPV of $50. If the firm builds a large facility and demand is low, the NPV will be -$20, whereas high demand will result in a NPV of $72. Analyze this issue using a decision tree. What would be the maximin alternative?