DECISION MAKING Pongsa Pornchaiwiseskul Pongsa.P@chula.ac.th http://pioneer.chula.ac.th/~ppongsa Faculty of Economics Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

DECISION MAKING TOOLS Statistics operations research (a mathematical optimization model of a complex system) deterministic, e.g., Linear Programming, transportation problem stochastic, e.g., decision tree, queuing theories Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

OPERATIONS RESEARCH Multiple objective Network system Inter-temporal (dynamic) system uncertainty (stochastic) Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Decision Making and Organization Management Pongsa’s Sessions Linear Programming(LP) LINDO program exercise Transportation Problem CPM/PERT Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

MATHEMATICAL PROBLEMS Decision Making and Organization Management MATHEMATICAL PROBLEMS Most decision making problems could be formulated as a mathematical problem. Decision making processes can be represented with mathematical functions and constraints. Some decision making problems involve optimization of an objective function. Others try to simulate the result of various decisions before the decision can be made. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

OPTIMIZATION PROBLEMS Decision Making and Organization Management OPTIMIZATION PROBLEMS maximize or minimize an objective function subject to various constraints. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

EXAMPLES OF OBJECTIVE FUNCTIONS Decision Making and Organization Management EXAMPLES OF OBJECTIVE FUNCTIONS net profit output or throughput cost or input time likeliness or probability variance or uncertainty Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

EXAMPLES OF CONSTRAINTS Decision Making and Organization Management EXAMPLES OF CONSTRAINTS staffing space budget time technology Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

LINEAR PROGRAMMING(LP) PROBLEM Decision Making and Organization Management LINEAR PROGRAMMING(LP) PROBLEM mathematical optimization problem its objective function and constraints are all linear Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

EXAMPLE OF AN LP PROBLEM Decision Making and Organization Management EXAMPLE OF AN LP PROBLEM A hypothetical hospital of 30 beds has two service departments (OPD and IPD). The In-Patient Department (IPD) needs 2 doctor-hours and 4 nurse-hours for every patient-day. In Out-Patient Department(OPD), each doctor-hour must be supported by 4 nurse-hours. The hospital can offer no more than 50 doctor-hours of OPD service in a day. The hospital can earn $120 for every patient-day in IPD and $80 for every doctor-hour in OPD. The hospital has a limited resource of 80 doctor-hours and 240 nurse-hours per day. Determine the resource allocation between OPD and IPD so that income of the hospital is maximized. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

STRUCTURE OF THE LP (for the example) Decision Making and Organization Management STRUCTURE OF THE LP (for the example) Objective = maximize income Constraints 1) # of doctor-hours 2) # of nurse-hours 3) # of beds 4) # of OPD service hours Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management DEFINE THE VARIABLES X1 = # of in-patients per day X2 = # of OPD doctor-hours per day Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management LP REPRESENTATION max Z = 120X1 + 80X2 X1 ,X2 s.t. 2X1 + X2 <= 80 --------(1) 4X1 + 4X2 <= 240 --------(2) X1 <= 30 --------(3) X2 <= 50 --------(4) X1 ,X2 >= 0 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management NOTE You will get a different LP representation if you define the variables differently. Anyway, all the LPs still represent the same decision-making problem Let’s define Y1 = # of IPD doctor-hours per day Y2 = # of OPD nurse-hours per day Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

ANOTHER LP REPRESENTATION Decision Making and Organization Management ANOTHER LP REPRESENTATION max Z = 60Y1 + 20Y2 Y1 ,Y2 s.t. Y1 + 0.25Y2 <= 80 --------(1’) 2Y1 + Y2 <= 240 --------(2’) Y1 <= 60 --------(3’) Y2 <= 200 --------(4’) Y1 ,Y2 >= 0 Replace X1 with 0.5Y1 and X2 with 0.25Y2 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

HOW TO SOLVE AN LP PROBLEM Decision Making and Organization Management HOW TO SOLVE AN LP PROBLEM Graphical Method Simplex method by hand (not discussed) by computer Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management GRAPHICAL METHOD good for LPs with two variables make it easy to understand solving an LP Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management SIMPLEX METHOD algebraic method developed by George Dantzig need to understand it very well if you want to do it by hand or develop a computer program to do it quite a few computer programs can do this,e.g., LINDO (DOS and Windows versions) LP83 (DOS) MPSX (IBM mainframe) Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

LP SOLUTIONS OR RESULTS Decision Making and Organization Management LP SOLUTIONS OR RESULTS Unique Solution no other values of LP variables will yield the same optimized value of objective function Alternative Solution (non-unique) infinitely many feasible solutions Infeasible solution No values of LP variables satisfying the constraints Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management LINDO Inputs MAX 120 x1 + 80 x2 SUBJECT TO 2) 2 x1 + x2 <= 80 3) 4 x1 + 4 x2 <=240 4) x1 <= 30 5) x2 <= 50 END Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management LINDO Report LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) 5600.000 VARIABLE VALUE REDUCED COST X1 20.000000 0.000000 X2 40.000000 0.000000 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management LINDO Report (cont’d) ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 40.000000 3) 0.000000 10.000000 4) 10.000000 0.000000 5) 10.000000 0.000000 NO. ITERATIONS= 3 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management DUAL SOLUTIONS For each constraint, there exist a dual variable sometimes called dual price Define mi = dual variable for constraint i = change in Z / change in RHS value Graphical method cannot give a dual solution (value of dual variables) but Simplex can Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

MEANING OF DUAL SOLUTION (First Representation) Decision Making and Organization Management MEANING OF DUAL SOLUTION (First Representation) m1 = opportunity cost of a doctor-hour m2 = opportunity cost of a nurse-hour m3 = opportunity cost of a bed-day m4 = opportunity cost of the OPD limit Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management HEREWORK The Malaria Division has to allocate 20,000 kg of insecticide and 150,000 blood test kits among two provinces(say A and B) so that the number of malaria cases will be minimized. The division has two control options. A unit of Option I is the use of 1 kg of insecticide and 10 test kits while a unit of Option II is 2 kg of insecticide and 5 blood test kits. Input/case reduced keeps increasing when the incidence decreases. Schedules of # of unit of inputs per case reduced shown in the table below. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

Decision Making and Organization Management Province A Decrease in cases Option I Option II 0- 5,000 1.0 1.0 5,000-10,000 1.5 2.0 10,000+ 3.0 3.5 Province B 0- 3,000 1.5 1.8 3,000-6,000 2.0 2.5 6,000+ 3.5 4.5 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

STRUCTURE OF THE LP (for the herework) Decision Making and Organization Management STRUCTURE OF THE LP (for the herework) Objective = maximize change in number of cases in Provinces A and B Constraints 1) insecticide 2) blood test kits 3) incidence functions(stepwise) Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997

QUESTIONS (for the herework) Decision Making and Organization Management QUESTIONS (for the herework) 1) Number of cases reduced in each province 2) Opportunity cost of insecticide and blood test kits in terms of malaria cases reduced Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University, December 1997