×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

### Create a StudySoup account

#### Be part of our community, it's free to join!

or

##### By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

## Linear Programming

by: Caleb Wearmouth

65

1

4

# Linear Programming BIT 3414

Caleb Wearmouth
Virginia Tech

### Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

### Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

## About this Document

Lineear Programming
COURSE
Operations and Supply Chain Management
PROF.
Dr. Laura Clark
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math
KARMA
25 ?

## Popular in Information System

This 4 page Class Notes was uploaded by Caleb Wearmouth on Tuesday March 22, 2016. The Class Notes belongs to BIT 3414 at Virginia Polytechnic Institute and State University taught by Dr. Laura Clark in Spring 2016. Since its upload, it has received 65 views. For similar materials see Operations and Supply Chain Management in Information System at Virginia Polytechnic Institute and State University.

×

## Reviews for Linear Programming

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 03/22/16
Aggregate Production Planning Reading Pages with Linear Programming 622 – middle 623 The optimal solution for an aggregate production plan can be found with a linear programming model. Model Formulation Decision Variables R = units produced w/ regular production in period t t O t units produced w/overtime production in period t S t units produced w/ subcontracted production in period t It = inventory at end of period t W t workforce size for period t H t = # hired for period t Ft = # fired for period t Objective Function Minimize cost Constraints Demand, Capacity, Production, Workforce Decision Variables Consider a Trial and Error table for a mixed strategy of Level Production, Overtime, and Subcontracting: Regular Overtime Subcontract Quarter Demand Production Production Production Inventory BIT 3414 Copyright 2015 p. 1 Given the following information: Regular Prod. Capacity = 2000 units/qtr Regular Prod. Cost = \$10/unit Quarter Demand 1 1200 Overtime Prod. Capacity = 500 units/qtr Overtime Prod. Cost = \$20/unit 2 3100 Subcontracting Capacity = 1000 units/qtr Subcontracting Cost = \$25/unit 3 2800 Inventory Capacity = 4000 units/qtr Inventory Cost = \$5/unit/qtr 4 900 Beginning Inventory = 100 units Backorder Cost = \$14/unit/qtr The company would like to determine the optimal mixture of the Level Production, Overtime, and Subcontracting strategies with a linear programming model. Decision Variables Objective Function Minimize Cost Z = + 25S + 25S + 25S + 25S 1 2 3 4 + 5I + 5I + 5I + 5I 1 2 3 4 Constraints Capacity Demand S: S 1 S 2 S ,3S ≤41000 3: R +3O + 3 + I 3 I 2 2803 I: I , I , I , I ≤ 4000 1 2 3 4 4: R +4O + 4 + I 4 I 3 9004 BIT 3414 Copyright 2015 p. 2 Given the following information: Hiring cost = \$200 / worker Firing cost = \$500 / worker Quarter Demand Regular Production Cost = \$2 / unit Spring 30,000 Summer 10,000 Inventory cost = \$0.50 / unit / quarter Production per employee = 1,000 units / quarter Fall 70,000 Winter 90,000 Beginning workforce = 50 workers Beginning inventory = 0 units The company would like to determine the optimal mixture of the Level Production and Chase Demand strategies with a linear programming model (assume no capacity limitations). Decision Variables Objective Function Minimize Cost Z = + 200H +1200H + 2002 + 200H 3 4 + 500F +1500F + 502F + 500F 3 4 Constraints Demand Production Workforce 3: R 3 I –2I =370,000 3: R –31000W = 0 3 3: W –3W – H2+ F =30 3 4: R 4 I –3I =490,000 4: R –41000W = 0 4 4: W –4W – H3+ F =40 4 BIT 3414 Copyright 2015 p. 3 Given the following information: Regular Prod. Capacity = 30,000 units/qtr Regular Prod. Cost = \$10/unit Quarter Demand Subcontracting Capacity = 20,000 units/qtr Subcontracting Cost = \$25/unit 1 30,000 2 60,000 Inventory Capacity = 10,000 units/qtr Inventory Cost = \$5/unit/qtr Beginning Inventory = 4,000 units Backorder Cost = \$10/unit/qtr 3 25,000 4 40,000 Production/employee = 2,000 units/qtr Hiring cost = \$1000/ worker Beginning workforce = 10 workers Firing cost = \$1500 / worker The company would like to determine the optimal mixture of the Level Production, Chase Demand, and Subcontracting strategies with a linear programming model. Decision Variables Objective Function Minimize Cost Z = 10R +110R + 102 + 10R 3 4 + 25S + 15S + 252 + 25S 3 4 + 5I 1 5I +25I + 3I 4 + 1000H + 1100H + 10002 + 1000H 3 4 + 1500F + 1500F + 15002 + 1500F 3 4 Constraints Capacity Production S: S 1 S 2 S 3 S 4 20,000 I: I1, 2 ,3I 4 I ≤ 10,000 2: R 2 2000W = 0 2 3: R – 2000W = 0 Demand 3 3 4: R 4 2000W = 0 4 Workforce 2: R + S + I – I = 60,000 2 2 1 2 3: R 3 S +3I – I2= 23,000 2: W –2W – H1+ F =20 2 4: R 4 S +4I – 3 = 44,000 3: W –3W – H2+ F =30 3 BIT 3414 Copyright 2015 4: W –4W – H3+ F =40 4 p. 4

×

×

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

×

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Jim McGreen Ohio University

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Amaris Trozzo George Washington University

#### "I made \$350 in just two days after posting my first study guide."

Steve Martinelli UC Los Angeles

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.