I NTRODUCTION TO MANAGERIAL DECISION MODELING. Objectives. Define management science Define decision model and describe its importance Classify decision models List and explain steps involved in developing decision models in practice Remind breakeven analysis with computer applications
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Management Science is the scientific approach to executive decision making, which consists of:1. The artof mathematical modeling of complex situations,2. The scienceof the development of solution techniques used to solve these models,3. The ability to effectively communicate the results to the decision maker
What is Management Science?
They can be applied when:
(by purpose of the model)
Optimization Models seek to maximize a quantity (eg. profit) or minimize a quantity (eg. cost, time, etc.) that may be restricted by a set of constraints (limitations on the availability of capital, workers, supplies, machines etc.)
At times however, the function of a model is not to maximize or minimize any particular quantity, but to describe or predict events given certain conditions These models are known as Predictive Models. These techniques do not generate an answer or a recommended decision. Instead they provide descriptive results: results that describe the system being modeled. They usually provide important input to optimization models
(by the degree of certainty of the data)
Management Science Process (1 of 3)
Management Science Process (2 of 3)
Management Science Process (3 of 3)
Developing a model requires to:
An appropriate solution technique may be an optimization algorithm (series of steps repeated until the best solution is attained) or a heuristic algorithmMost algorithmsare intended to provide an optimal solution for a model. Sometimes, however, problems can prove to be too complex or time consuming to employ optimization algoritms. In such cases a heuristicprocedure may be preferred
Analyzing the results and sensitivity analysis.
Examine changes in optimal solution as a result of changes in input values and model parameters
Variables: X = number of units (decision variable)
Z = total profit
Model: Z = $20X - $5X (objective function)
4X = 100 lb of steel (resource constraint)
Parameters: $20, $5, 4 lbs, 100 lbs (known values)
Formal Specification of Model:
maximize Z = $20X - $5X
subject to 4X = 100
(1 of 4)
(2 of 4)
Profit = Total Revenue - Total Cost
Profit = Revenue - Fixed Cost - Variable Cost
Revenue= [Sales price ($/unit) x Number (units)]
Variable Cost = [Variable cost ($/unit) x Number (units)]
Fixed Cost = $ necessary to invest in facilities (buildings, equipment, processes, etc.) = constant dollar value.
(4 of 4)
Z = vp - cf – vcv
Set profit equal to 0:
vp = cf + vcv
Compute the Break-Even Point:
Break-even quantity = cf/(p - cv)
(1 of 10)
Example: Western Clothing Company
cf = $10000
cv = $8 per pair
p = $23 per pair
V = 666.7 pairs, break-even point
(2 of 10)
(3 of 10)
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Price
Sensitivity Analysis : Break-Even Model with a Change (Increase) in Variable Cost
(5 of 10)
Sensitivity Analysis : Break-Even Model with Changes in Fixed and Variable Costs
Excel QM Computer Solution (8 of 10)
Example II: Break-Even Analysis-QM for Windows Computer Solution (9 of 10)
Example II: Break-Even Analysis-QM for Windows Computer Solution (10of 10)
Bill's company, Pritchett's Precious Time Pieces, buys, sells, and repairs old clocks and clock parts. Bill sells rebuilt springs for unit price $10. Fixed cost of equipment to build springs is $1,000. Variable cost per unit is $5 for spring material.
Profit = $10X - $1,000 - $5X
Break-even quantity = cf/(p - cv)
BE = $1,000 / [$10 - $5 ] = 200 springs.
BEP$ = Fixed cost + Variable cost per unit x BEP
$1,000 + $5 x 200 = $2,000
1.Linear Mathematical Programming Techniques
a. Linear Programming Models
b. Transportation Models
c. Assignment Models
d. Integer Programming Models
e. Goal Programming
2. Probabilistic Techniques
a. Decision Analysis
b. Waiting Line (Queuing) Models
c. Simulation Models
d. Forecasting Models
3. Network Techniques
a. Network Flow
b. Project Management Techniques (PERT/CPM)
4. Other Techniques
a. Non-Linear Programming Models
b. Inventory Models
- Project Planning
- Capital Budgeting
- Inventory Analysis
- Production Planning
Impact on Other Departments.
Developing a Model.
Fitting Textbook Models.
Understanding the Model.Possible Problems in Developing Decision Models- (1 of 2)
Using Accounting Data.
Validity of Data.
Developing a Solution.
Only One Answer is Limiting.
Analyzing Results.Possible Problems in Developing Decision Models (2 of 2)