Engineering Management Lecture 4 PDF

‫كلية الهندسة – قسم الهندسة الكهربائية‬ ‫العام الدراسي‪2023 /2022 :‬م – الفصل الدراسي الثاني‬ ‫المقرر‪ :‬اإلدارة الهندسية‬ ‫الفرقة‪ :‬الرابعة‬ ‫رقم المحاضرة‪4 :‬‬ ‫‪DECISIO...

‫كلية الهندسة – قسم الهندسة الكهربائية‬ ‫العام الدراسي‪2023 /2022 :‬م – الفصل الدراسي الثاني‬ ‫المقرر‪ :‬اإلدارة الهندسية‬ ‫الفرقة‪ :‬الرابعة‬ ‫رقم المحاضرة‪4 :‬‬ ‫‪DECISION MAKING‬‬ ‫عنوان المحاضرة‪:‬‬ ‫‪Mr. MUBARAK MOHAMMED‬‬  SYLLABUS  Introduction to Engineering Management  Planning and Forecasting  Decision Making  Planning Production Activity  Leading Technical People  Organizing and Controlling  Engineering Project Management 2  OBJECTIVES  Identify the decision making.  Explain the types of decision making.  Identify the steps of making decision.  Discussing the methods decision making under certainty  Discussing the methods decision making under risk  Discussing the methods decision making under uncertainty  Decision Making  Decision Making: is the process of making a conscious choice between two or more alternatives producing most desirable results (benefits) relative to unwanted consequences (costs).  Needs of decision making: 1. Decision Making is essential part of Planning. 2. Decision Making also required also in:  Designing, Staffing, and Organization.  Developing Methods of Motivating Subordinates.  Identifying Corrective Actions on Control Process.  Decision Making  Occasions for Decision Making:  From authoritative communication from superiors.  From cases referred for decision by subordinates.  From cases originating in the initiative of the executive. Decision Making considered as the most important test of executive.  Decision Making  Types of Decisions: 1. Routine Decisions (as payroll processing, paying for suppliers)  Repeated frequently.  Involve standard decision procedures.  Has a minimum of uncertainty.  Clear structured situations 2. Non routine Decisions  Occurs in response to unusual, unpredictable opportunities and threats.  Unstructured and novel situations  Non repeating nature  Has a high level of uncertainty  Decision Making  Steps of decision making: (Process) 1. Identify the decision 2. Gather relevant information 3. Identify the alternatives 4. Weigh the evidence 5. Choose among alternatives 6. Take action 7. Review your decision & its consequences  Decision Making  Management Science & Decision Making  Management science characterized by:  A systematic view of problem  Steps of modeling:  Team Approach 1.Formulate problem  Emphasis on the use of formal 2.Construct a model mathematical models and statistical and 3.Test the model’s ability quantitative methods 4.Derive a solution from model. Model: Abstraction and simplification of 5. Apply the model’s reality (Designed to include Essential solution to real system. Features).  Decision Making  Categories of Decision Making 1. Decision Making Under Certainty: Linear programming 2. Decision Making Under Risk: expected value, decision trees, queuing theory, and simulation. 3. Decision Making Under Uncertainty: Game theory Payoff (Benefit) Table - Decision Matrix  Decision Making  Payoff (Benefit) Table - Decision Matrix A1, A2,…. Am : Decision alternatives N1 , N2 , Nj … Nn : Decision alternatives, state of nature. P1 P2 … Pj … Pn : Probability of occurrence Om1 Om2 … Omj … Omn : Outcomes  Decision Making  Payoff (Benefit) Table - Decision Matrix  Decision Making Under Certainty: The probability of Pj of future Nj is 1 and all other futures have zero probability.  Decision Making Under Risk: Each Nj has a known (or assumed) probability of Pj and there may not be one state that results best outcome.  Decision Making Under Uncertainty: Probabilities Pj of future states are unknown.  Decision Making  Decision Making Under Certainty  Linear Programming Method:  A desired benefit (profit or cost) expressed as a mathematical function of several variables.  Solution is to find independent variables giving the maximum benefit or minimum cost subject to certain limits (constraints).  This method solve the objective function and getting the maximum or minimum value within the constrains.  The solution can be obtained mathematically or graphically.  Decision Making  Example A factory is producing two products (X and Y). The profit of product X is $10 per unit and for product Y is $14 per unit. What is the production level of x units of product X and y units of product Y that maximizes the profit P? If the production (profit) is subject to the following resource limitations, or constraints:  The factory has 5 workers (3 machinists and 2 assemblers), each works only 40 hours a week.  Product X requires 3 hours of machining and 1 hour assembly per unit  Product Y requires 2 hours of machining and 2 hours of assembly per unit  Decision Making Solution: The objective function is to maximize the profit which is given by: 𝑃 = 10𝑥 + 14𝑦 Taking the following constrains into account: 𝑻𝒐𝒕𝒂𝒍 𝒂𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝒎𝒂𝒄𝒉𝒊𝒏𝒊𝒏𝒈 𝒉𝒐𝒖𝒓𝒔 = 𝟑 × 𝟒𝟎 = 𝟏𝟐𝟎 𝒉𝒐𝒖𝒓𝒔 𝑻𝒐𝒕𝒂𝒍 𝒂𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝒂𝒔𝒔𝒆𝒎𝒃𝒍𝒚 𝒉𝒐𝒖𝒓𝒔 = 𝟐 × 𝟒𝟎 = 𝟖 𝒉𝒐𝒖𝒓𝒔 𝑷𝒓𝒐𝒅𝒖𝒄𝒕 𝑿 𝒏𝒆𝒆𝒅𝒔 𝟑 𝒉𝒓𝒔 𝒎𝒂𝒄𝒉𝒊𝒏𝒊𝒏𝒈 & 𝑷𝒓𝒐𝒅𝒖𝒄𝒕 𝒀 𝒏𝒆𝒆𝒅𝒔 𝟐 𝒉𝒓𝒔 𝒎𝒂𝒄𝒉𝒊𝒏𝒊𝒏𝒈 (𝒑𝒆𝒓 𝒖𝒏𝒊𝒕): ∴ 𝟑𝒙 + 𝟐𝒚 ≤ 𝟏𝟐𝟎 −−−−−→ (𝟏) 𝑷𝒓𝒐𝒅𝒖𝒄𝒕 𝑿 𝒏𝒆𝒆𝒅𝒔 𝟏 𝒉𝒓 𝒎𝒂𝒄𝒉𝒊𝒏𝒊𝒏𝒈 & 𝑷𝒓𝒐𝒅𝒖𝒄𝒕 𝒀 𝒏𝒆𝒆𝒅𝒔 𝟐 𝒉𝒓𝒔 𝒎𝒂𝒄𝒉𝒊𝒏𝒊𝒏𝒈 (𝒑𝒆𝒓 𝒖𝒏𝒊𝒕): ∴ 𝒙 + 𝟐𝒚 ≤ 𝟖𝟏𝟐𝟎 −−−−−→ (𝟐)  Decision Making Solving Eq1 & Eq2 Simultaneously: 3x+2y  120 60 Units of product Y x + 2y  80 50 Constraint 1 3x+2y  120 ∴ x = 20 & y = 30 40 ∴ 𝑃 = 10𝑥 + 14𝑦 30 Constraint 2 = 10 × 20 + 14 × 30 = 𝟔𝟐𝟎 20 x + 2y  80 10 P=62 ∴ The maximum profit wilthin the constarins is $620 10 20 30 40 50 60 70 80 Units of product X  Decision Making  Decision Making Under Risk  Expected Values Method: n Ei = ෍ Pj Q ij j=1 The alternative Ai giving the highest expected value will chosen. Payoff table  Decision Making  Example A company is going to lunch one of three product (product I, product II, or product III) in new market. The demand level (low, moderate, high) will determine the profit or loss the company realize, as shown in payoff table. State of Nature (demand levels) Product Low (0.25) Moderate (0.45) High (0.3) I -500 $ 2950 $ 4000 $ Select the best decision using: II 200 $ 1550 $ 4100 $ 1. Expected value criteria. 2. Expected opportunity loss. III -2700 $ 700 $ 4900 $ Do Nothing 0 0 0  Decision Making Solution: 1. Calculate the expected value for each decision (alternative) and select the best (highest EV for profit) n State of Nature (demand levels) Ei = ෍ Pj Qij Product j=1 Low (0.25) Moderate (0.45) High (0.3) -500 $ 2950 $ 4000 $ E1 = −500 0.25 + 2950 0.45 I + 4000 0.3 = 𝟐𝟒𝟎𝟐. 𝟓$ 200 $ 1550 $ 4100 $ E2 = 200 0.25 + 1550 0.45 II + 4100 0.3 = 1977.5$ -2700 $ 700 $ 4900 $ E3 = −2700 0.25 + 700 0.45 III + 4900 0.3 = 1110$ E4 = 0 0.25 + 0 0.45 Do Nothing 0 0 0 + 0 0.3 = 0 $ Product I is the best  Decision Making Solution: 2. First obtain the Opportunity Loss Table (Regret Table) by substituting the original value by (Maximum value - original value) for each state State of Nature (demand levels) Product Low (0.25) Moderate (0.45) High (0.3) I (200 – (-500)) = 700$ (2950 – 2950) = 0 $ (4900 – 4000) = 900 $ II (200 – 200) = 0 $ (2950 – 1550) = 1400 $ (4900 – 4100) = 800 $ III (200 – (-2700)) = 2900$ (2950 – 700) = 2250 $ (4900 – 4900) = 0 $ Do Nothing (200 – 0) = 200 $ (2950 – 0) = 2950 (4900 – 0) = 4900 Opportunity Loss Table  Decision Making Solution: 2. Then Calculate the expected opportunity loss (EOL) for each decision (alternative) and select the best (lowest EOL for profit). n State of Nature (demand levels) Ei = ෍ Pj Qij Product j=1 Low (0.25) Moderate (0.45) High (0.3) E1 = 700 0.25 + 0 0.45 I 700 $ 0$ 900 $ + 900 0.3 = 𝟒𝟒𝟓$ E2 = 0 0.25 + 1400 0.45 II 0$ 1400 $ 800 $ + 800 0.3 = 870$ E3 = 2900 0.25 + 2250 0.45 III 2900 $ 2250 $ 0$ + 0 0.3 = 1737.5$ E4 = 200 0.25 + 2950 0.45 Do Nothing 200 $ 2950 $ 4900 $ + 4900 0.3 = 2847.5 $ Product I is the best  Decision Making  Decision Making Under Risk Note: If there are two or more alternatives have the same EV or EOL the best alternative is that which has the lowest variance or standard deviation. n 2 Variance: v(x) = ෍ Pj xj − xത j=1 Standard Deviatio: σ(x) = v(x)  Decision Making  Decision Making Under Uncertainty  The probabilities Pj of future states of nature Nj is unknown. Methods: 1. Max-Max (Optimistic) Probability of optimistic = α 2. Max-Min (Pessimistic) Probability of pessimistic = 1 − α 3. Min-Max (Regret) 𝐇𝐮𝐫𝐰𝐢𝐜𝐳 𝐯𝐚𝐥𝐮𝐞 4. Hurwicz (Coefficient of optimism) = Max in row × α + Min in row × 1−α For Profit 5. Equally likely (Laplace) 𝐇𝐮𝐫𝐰𝐢𝐜𝐳 𝐯𝐚𝐥𝐮𝐞 = Min in row × α + Max in row × 1−α For Cost  Decision Making  Example A company is going to lunch one of three product (product I, product II, or product III) in new market. The demand level (low, moderate, high) will determine the profit or loss the company realize, as shown in payoff table. State of Nature (demand levels) Product Select the best decision using: Low Moderate High 1. Maxi-Max (Optimistic) I -500 $ 2950 $ 4000 $ 2. Maxi-Min (Pessimistic) II 200 $ 1550 $ 4100 $ 3. Mini-Max (Regret) III -2700 $ 700 $ 4900 $ 4. Hurwicz (α = 0.75) 5. Equally likely (Laplace) Do Nothing 0 0 0  Decision Making Solution: 1. Maxi-Max (Optimistic): Find the optimistic value (best value ) for each decision (alternative) and select the best (highest value for profit). Find the maximum State of Nature (demand levels) Product value for each row Low Moderate High Max I -500 $ 2950 $ 4000 $ 4000 $ II 200 $ 1550 $ 4100 $ 4100 $ III -2700 $ 700 $ 4900 $ 4900 $ Product III Do Nothing 0 0 0 0 is the best  Decision Making Solution: 2. Maxi-Min (Pessimistic): Find the pessimistic value (worst value ) for each decision (alternative) and select the best (highest value for profit). Find the minimum State of Nature (demand levels) Product value for each row Low Moderate High Min I -500 $ 2950 $ 4000 $ -500 $ II 200 $ 1550 $ 4100 $ 200 $ III -2700 $ 700 $ 4900 $ -2700 $ Product II Do Nothing 0 0 0 0 is the best  Decision Making Solution: 3. Mini-Max (Regret): Find the maximum value (best value ) for each decision (alternative) and select the minimum. Find the maximum State of Nature (demand levels) Product value for each row Low Moderate High Max I -500 $ 2950 $ 4000 $ 4000 $ II 200 $ 1550 $ 4100 $ 4100 $ III -2700 $ 700 $ 4900 $ 4900 $ Product I Do Nothing 0 0 0 0 is the best  Decision Making Solution: 4. Hurwicz (α = 0.75): calculate the Hurwicz value for each decision (alternative) and select the best (highest value for profit). Hurwicz value = Max in row × α + Min in row × 1 − α State of Nature (demand levels) Hurwicz value Product Low Moderate High I -500 $ 2950 $ 4000 $ H1 = 4000 0.75 + −500 0.25 = 2875$ II 200 $ 1550 $ 4100 $ H2 = 4100 0.75 + 200 0.25 = 3125$ III -2700 $ 700 $ 4900 $ H3 = 4900 0.75 + −2700 0.25 = 3000$ Product II Do Nothing 0 0 0 H4 = 0 0.75 + 0 0.25 = 0 is the best  Decision Making Solution: 5. Equally likely (Laplace): calculate the average value for each decision (alternative) and select the best (highest value for profit). 1 n 𝐴𝑣𝑖 = σ x 𝑛 j=1 j State of Nature (demand levels) Hurwicz value Product Low Moderate High I -500 $ 2950 $ 4000 $ Av1 = −500 + 2950 + 4000 /3 = 2150$ II 200 $ 1550 $ 4100 $ Av1 = 200 + 1550 + 4100 /3 = 1950$ III -2700 $ 700 $ 4900 $ Av1 = −2700 + 700 + 4900 /3 = 966.67$ Product I Do Nothing 0 0 0 0 is the best 29 30