52:620:321 Management Science – I

1. 52:620:321Management Science – I Instructor: Dr. Neha Mittal Email: nmittal@camden.rutgers.edu Website: www.crab.rutgers.edu/~nmittal

2. Management Science - I • Book • Introduction to Management Science – Anderson, Sweeney and Williams, 12th edition • Exams and Assignments • Grading • Exam 1: 25% • Exam 2: 25% • Exam 3: 25% • In-class Assignment: 25% • Course Overview

3. Chapter 1:Introduction to Management Science

4. What is Management Science? Is the body of knowledge involving quantitative approaches to decision making. It is also referred as Operations research Decision science Frederic W. Taylor of the early 1900’s provided the foundation for use of quantitative methods. MS research originated during the World War II times and flourished later on with the aid of computers. 4

5. 5 Steps of Decision Making; 7 steps of Problem Solving Define the problem. Identify the set of alternative solutions. Determine the criteria for evaluating alternatives. Evaluate the alternatives. Choose an alternative (make a decision). --------------------------------------------------------------------- Implement the chosen alternative. Evaluate the results. What is Decision Making 5

6. Quantitative Analysis and Decision Making Decision-Making Process Structuring the Problem Analyzing the Problem Define the Problem Identify the Alternatives Determine the Criteria Evaluate the Alternatives Choose an Alternative

7. The Management Science Approach Structure the problem Analyze the problem Implement the solution Evaluate the results 7

8. Single-criterion decision analysis • When the objective is to find the best solutions w.r.t one criterion, problems are referred as single-criterion. • Multi-criterion decision analysis • When the objective is to find the best solutions w.r.t multiple criterion, problems are referred as multi-criterion.

9. Qualitative Analysis • based largely on the manager’s judgment and experience • includes the manager’s intuitive “feel” for the problem • is more of an art than a science • Quantitative Analysis • concentrates on the quantitative facts or data associated with the problem • develops mathematical expressions/ models that describe the objectives, constraints, and other relationships that exist in the problem

10. Model Development • Models are representations of real objects or situations • Three forms of models are: • Iconic models - physical replicas (scalar representations) of real objects • Analog models - physical in form, but do not physically resemble the object being modeled • Mathematical models - represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses

11. Mathematical Models Objective Function – a mathematical expression that describes the problem’s objective, such as maximizing profit or minimizing cost Constraints – a set of restrictions or limitations, such as production capacities Uncontrollable Inputs/Parameters – factors that are not under the control of the decision maker Decision Variables – an unknown quantity representing a decision that needs to be made. It is the quantity the model needs to determine. 11

12. Model Solution The analyst attempts to identify the alternative (the set of decision variable values) that provides the “best” output for the model. The “best” output is the optimal solution. If the alternative does not satisfy all of the model constraints, it is rejected as being infeasible, regardless of the objective function value. If the alternative satisfies all of the model constraints, it is feasible and a candidate for the “best” solution. 12

13. Mathematical Models • Deterministic Model – if all parameters to the model are known and cannot vary • Stochastic (or Probabilistic) Model – if any parameter is uncertain and subject to variation

14. Example: Iron Works, Inc. Iron Works, Inc. manufactures two products made from steel and just received this month's allocation of b pounds of steel. It takes a1 pounds of steel to make a unit of product 1 and a2 pounds of steel to make a unit of product 2. Let x1 and x2 denote this month's production level of product 1 and product 2, respectively. Denote by p1 and p2 the unit profits for products 1 and 2, respectively. Iron Works has a contract calling for at least m units of product 1 this month. The firm's facilities are such that at most u units of product 2 may be produced monthly. Develop a mathematical model which maximizes profit. 14

15. Max p1x1 + p2x2 s.t. a1x1 + a2x2<b x1>m x2<u x1 , x2> 0 Constraints Objective Function “Subject to” 15

16. Max 100x1 + 200x2 s.t. 2x1 + 3x2< 2000 x1> 60 x2< 720 x2> 0 Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u = 720, p1 = 100, p2 = 200. Rewrite the model with these specific values for the uncontrollable inputs. The optimal solution to the current model is x1 = 60 and x2 = 626 2/3.

17. A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 profit, and each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits? Problem

18. Management Accounting: Cost, Volume and Profit Models • Cost and Volume Models: • Cost is function of the volume produced • Fixed, Variable and Marginal Cost • Revenue and Volume Models: • Revenue associated with selling of units • Marginal Revenue • Profit and Volume Models: • Profit = Revenue – Cost • When revenue = cost, it is called ‘breakeven point’

19. Example: Ponderosa Development Corp. Ponderosa Development Corporation (PDC) is a small real estate developer that builds only one style house. The selling price of the house is $115,000. Land for each house costs $55,000 and lumber, supplies, and other materials run another $28,000 per house. Total labor costs are approximately $20,000 per house. Ponderosa leases office space for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month. The one salesperson of PDC is paid a commission of $2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given on the next slide. 19

20. EmployeeMonthly Salary President $10,000 VP, Development 6,000 VP, Marketing 4,500 Project Manager 5,500 Controller 4,000 Office Manager 3,000 Receptionist 2,000 20

21. Question: Identify all costs and denote the marginal cost and marginal revenue for each house. Answer: Fixed costs salaries, leases, utilities Marginal / variable costs commission, land, materials, labor Revenue selling price of each house 21

22. Question: Write the monthly cost function c (x), revenue function r (x), and profit function p (x). Answer: c (x) = variable cost + fixed cost = 105,000x + 40,000 r (x) = 115,000x p (x) = r (x) - c (x) = 10,000x - 40,000

23. Question: What is the breakeven point for monthly sales of the houses? Answer: r (x ) = c (x ) x = 4 Question: What is the monthly profit if 12 houses per month are built and sold? Answer: p (x) = r (x) – c (x) p (12) = $80,000 23

24. Example: Ponderosa Development Corp. 1200 Total Revenue = 115,000x 1000 800 600 Thousands of Dollars Total Cost = 40,000 + 105,000x 400 200 Break-Even Point = 4 Houses 0 0 1 2 3 4 5 6 7 8 9 10 Number of Houses Sold (x) 24

25. As part of a loan application to buy Lakeside Farm, (a property Joe hopes to develop as a bed-and-breakfast operation), the prospective owners have projected: Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000 Variable cost per occupied room per night $ 20 Revenue per occupied room per night $ 75 Write the expression for total cost per month. Assume 30 days per month. Write the expression for total revenue per month. If there are 12 guest rooms available, can they break even? Assignment: Breakeven Analysis