Notes, summaries, assignments, exams, and problems for Mathematics

Fundamentals of Operations Research

Goal Programming Basics

Goal Programming aims to Minimize W, the weighted sum of deviations from the goals. The fundamental relationship is:

Level Achieved – Amount Over + Amount Under = Goal

Introduction to Queueing Theory

The basis of Queueing Theory is the trade-off between the cost of improving service and the costs associated with making customers wait. Queues arise when the short-term demand for service exceeds the capacity (i.e., arrival rates exceed the service rates).

Key Components of a Queueing System

• Calling Population: Refers to the pool of potential customers.
• Customer Behavior: Customers can be patient or impatient (those who leave the line before receiving service).
• Queue Capacity: Can be finite

Vertex Cover ≤ CLIQUE

Suppose G has a clique S with |S| = k. Consider S' = V – S. Then, |S'| = |V| - k. To show S' is a cover, consider any edge (v, w) ∈ E'. Then, (v, w) ∉ E, at least one of v or w is not in S (since S forms a clique), and at least one of v or w is in S'; hence, (v, w) is covered by S'.

Suppose G' has a cover S' with |S'| = |V| - k. Consider S = V – S'. Clearly, |S| = k. To show S is a clique, consider some edge (v, w) ∈ E'. Then, if (v, w) ∈ E', either v ∈ S', w ∈ S', or both. By contrapositive, if v ∉ S' and w ∉ S', then (v, w) ∈ E; thus, S is a clique in G.

Vertex Cover ≤ SET COVER

Given a black box that solves instances of SET-COVER, let G = (V, E) and k be an instance of VERTEX-COVER. Create a SET-... Continue reading "Complexity Theory: Reductions and NP-Completeness Proofs" »

1. Many business owners spend years trying to get their enterprise started.

2. At the rate we are going, we are lucky to break even at year's end.

3. The world's biggest stock exchange is in New York.

4. Every employee has shares in the company.

5. The stock market rose 20% today. Brokers were euphoric!

6. The dip in the market caused some investors concern.

7. There was a dramatic rise in the share price at the end of the week.

8. Dividend is the part of the company's profits which is paid to shareholders.

9. One of the most difficult parts of running a restaurant is keeping the cashflow which can be variable.

10. House prices have increased by 5%. It is too expensive to buy now.

11. Demand for this product has fallen recently. We won't manufacture... Continue reading "Understanding Business and Stock Market Terminology" »

Queueing Models

M/M/s: Exponential arrival and service with more than one server. These models are needed in the economic analysis of the system.

M/G/1: Exponential arrival with general service time.

M/D/1: Exponential arrival with deterministic (fixed) service time. Because of lower variability in service time, performance measures are better than M/M/1.

Queues with priority: Performance measures will improve for high-priority customers and worsen for low-priority customers. However, performance measures averaged across all customers (high AND low priority) will remain the same as before.

Distinguish between the number of servers and the number of queues:

1. An M/M/2 queue with two servers but a single queue of waiting customers.
2. Two M/M/1 queues where

Accounting Concepts: Real Value Recording

Cost Concept: To record the real value and not the estimated value.

Cost Accounting and Budgeting Fundamentals

• FOH Allocation: Single Plantwide, Departmental, and Activity-Based Rates
• Advantages of Departmental FOH Rates: It doesn't assign other costs such as depreciation.
• Characteristics of Unit, Batch, Facility, and Product Level
• Activity-Based Costing and the Importance of Activity Drivers
• Importance of ABC Costing
• Importance of Matching Strategic Planning with Pricing, Market Penetration, and Expansion
• Contribution Margin Formula: Sales - Variable Costs (VC)
• Fixed Cost and Variable Cost Behavior
• Break-Even Point Concept and Formula: Level of sales at which contribution margin matches fixed expenses, expressed in dollars.
• Direct Labor (DL) Cost per Unit: Given two different levels of production
• Differences Between

Revoking Public Privileges

To identify and revoke public privileges, use the following query:

SQL> SELECT table_name FROM dba_tab_privs WHERE owner='SYS' AND privilege = 'EXECUTE' AND grantee='PUBLIC' AND table_name LIKE 'UTL%';

Users with DBA Role

SQL> SELECT grantee FROM dba_role_privs WHERE granted_role = 'DBA';

Users with SYSDBA and SYSOPER Privileges

SQL> SELECT * FROM V$PWFILE_USERS;

Audit Parameters and Session Auditing

Check the current audit parameters:

SHOW PARAMETER AUDIT_FILE_DEST || AUDIT_SYS_OPERATIONS || AUDIT_TRAIL;

Common Audit Commands:

• SQL> AUDIT session;
• SQL> AUDIT session by user;
• SQL> AUDIT TABLE BY hr WHENEVER NOT SUCCESSFUL;
• SQL> AUDIT DROP ANY TABLE BY hr BY SESSION;
• SQL> AUDIT UPDATE ON hr.employees BY ACCESS;

The Production Volume Variance

Represents the difference between budgeted (incurred) and actual (allocated) fixed manufacturing costs.

When a greater proportion of costs are fixed costs, then

when demand is low the risk of loss is high

FALSE?

Gross Margin will always be greater than contribution margin.

Given a constant contribution margin per unit and constant fixed costs, the period-to-period change in operating income under variable costing is driven solely by:

changes in the quantity of units actually sold

In CVP analysis, the amount of units to be sold for the company to break even:

Increases when the contribution margin per unit decreases, all other things being equal

FALSE?

Nonmanufacturing costs are expensed in the future under variable costing.... Continue reading "Understanding Production Volume Variance and Costing Methods" »

Ch 12 Anova

Goal/purpose: Evaluate mean difference between 2 or more treatments

• Factor: The IV that designates the groups being compared
• Levels: Individual conditions or values that make up a factor
• Factorial design: A study that combines two or more factors

The Logic:

• Between treatment variance
  • Variability results from general differences between the treatment conditions
  • Variance between treatments measures differences among sample means
• Within treatments variance
  • Variability within each sample
  • Individual scores are not the same within each sample

Notations:
k= # of treatment condition
T= sum of squares for each treatment
G= grand total of all scores in study
N= total number of scores
kn= when all samples are same size
n1,n2= # of scores in each treatment

Post

What is the COUNTIF Formula?

The COUNTIF function counts cells that meet a single criterion.

When to Use the COUNTIF Formula

The COUNTIF function can be used to count cells with dates, numbers, and text that match specific criteria.

COUNTIF Logical Operators and Wildcards

The COUNTIF function supports logical operators (>, <, <>, =) and wildcards (*, ?, "") for partial matching.

Principal Purpose of COUNTIF

To count cells that match specified criteria.

COUNTIF Return Value

A number representing the count of cells.

How the COUNTIF Formula Works

COUNTIF counts the number of cells in the specified range that contain numeric values less than a given 'X' and returns the result as a number.

Complete the Statements: COUNTIF Syntax & Arguments

• Syntax: