# ISE 204 OR II. Chapter 8 The Transportation and Assignment Problems. Asst. Prof. Dr. Deniz TÜRSEL ELİİYİ

Save this PDF as:

Size: px
Start display at page:

Download "ISE 204 OR II. Chapter 8 The Transportation and Assignment Problems. Asst. Prof. Dr. Deniz TÜRSEL ELİİYİ"

## Transcription

1 ISE 204 OR II Chapter 8 The Transportation and Assignment Problems Asst. Prof. Dr. Deniz TÜRSEL ELİİYİ 1

2 The Transportation and Assignment Problems Transportation Problems: A special class of Linear Programming Problems. Assignment: Special Case of Transportation Problems Most of the constraint coefficients (a ij ) are zero. Thus, it is possible to develop special streamlined algorithms. 2

3 The Transportation Problem P&T Company producing canned peas. Peas are prepared at three canneries, then shipped by truck to four distributing warehouses. Management wants to minimize total transportation cost. 3

4 The Transportation Problem Objective: minimum total shipping cost. Decisions: Determine the assignments (shipments from canneries to warehouses), i.e. How much to ship from each cannery to each warehouse. 4

5 The Transportation Problem Network representation Arcs (arrows, branches) show possible routes for trucks, numbers on arcs are unit cost of shipment on that route. Square brackets show supply (output) and demand (allocation) at each node (circle, vertex) 5

6 The Transportation Problem Linear programming problem of the transportation problem type. 6

7 The Transportation Problem The problem has a special structure of its constraint coefficients. This structure distinguishes this problem as a transportation problem. 7

8 The Transportation Problem Generally, a transportation problem is concerned with distributing any commodity from any group of supply centers (sources) to any group of receiving centers (destinations) in a way to minimize the total transportation cost. 8

9 The Transportation Problem There needs to be a balance between the total supply and total demand in the problem. 9

10 The Transportation Problem 10

11 The Transportation Problem When the problem is unbalanced, we reformulate the problem by defining a dummy source or a dummy destination for taking up the slack. Cost assumption: Costs in the model are unit costs. Any problem that can be described as in the below table, and that satisfies the requirements assumption and cost assumption is a transportation problem. The problem may not actually involve transportation of commodities. 11

12 The Transportation Problem General Mathematical Model 12

13 The Transportation Problem General Network Representation 13

14 The Transportation Problem 14

15 The Transportation Problem Dummy Destination Example NORTHERN AIRLINE produces airplanes. Last stage in production: Produce jet engines and install them in the completed airplane frame. The production of jet engines for planes should be scheduled for the next four months at total minimum cost. 15

16 The Transportation Problem Dummy Destination Example One way to formulate: Define x j : jet engines produced in month j, j=1,2,3,4 But this will not be a transportation type formulation, therefore will be harder to solve. Transportation formulation: 16

17 The Transportation Problem Dummy Destination Example 17

18 The Transportation Problem Dummy Destination Example We don t know the exact supplies (exact production quantities for each month), but we know what can be upper bounds on the amount of supplies for each month. To convert these equalities into equalities, we use slack variables. These are allocations to a single dummy destination that represent total unused production capacity. The demand of this destination: 18

19 The Transportation Problem Dummy Destination Example 19

20 The Transportation Problem Dummy Source Example METRO WATER DISTRICT : An agency that handles water distribution in a large geographic region. Sources of water: Colombo, Sacron and Calorie rivers. Destinations: Berdoo, Los Devils, San Go, Hollyglass. No water should be distributed to Hollyglass from Claorie river. Allocate all available water to at least meet minimum needs at minimum cost. 20

21 The Transportation Problem Dummy Source Example After allocating the minimum amounts for other cities, how much extra can we supply for Hollyglass? (Upper bound) Define a dummy source to send the extra demand. The supply quantity of this source should be: 21

22 The Transportation Problem Dummy Source Example 22

23 The Transportation Problem Dummy Source Example How can we take the minimum need of each city into account? Los Devils: Minimum=70 =Requested=70. All should be supplied from actual sources. Put M cost in dummy sources row. San Go: Minimum=0, Requested=30. No water needs to be supplied from actual sources. Put 0 cost in dummy sources row. Hollyglass: Minimum=10, Requested (UB)=60. Since the dummy source s supply is 50, at least 10 will be supplied from actual sources anyway. Put 0 cost in dummy sources row. Berdoo: Minimum=30, Requested=50. Split Berdoo into two destinations, one with a demand of 30, one with 20. Put M and 0 in the dummy row for these two destinations. 23

24 The Transportation Problem Dummy Source Example 24

25 Transportation Simplex Recall: Mathematical Model 25

26 Transportation Simplex Traditional simplex tableau for a transportation problem: Convert the objective function to minimization Introduce artificial variables for = constraints Entities not shown are zeros. 26

27 Transportation Simplex At any iteration of traditional simplex: u i and v i : dual variables representing how many times the corresponding rows are multiplied and subtracted from row 0. If x ij is nonbasic, (c ij -u i -v j ) is the rate at which Z will change as x ij is increased. 27

28 Regular Simplex: Transportation Simplex Find an initial BFS by introducing artificial variables Test for optimality Determine the entering variable Determine the leaving variable Find the new BFS Transportation Simplex No artificial variables needed to find an initial BFS The current row can be calculated by calculating the current values of u i and v j The leaving variable can be identified in a simple way The new BFS can be identified without any algebraic manipulations on the rows of the tableau. 28

29 Transportation Simplex 29

30 Transportation Simplex: Initialization In an LP with n variables and m constraints : Number of basic variables = m+n In a transportation problem with n destinations and m sources: Number of basic variables = m+n-1 This is because one constraint is always redundant in a transportation problem, i.e. if all m-1 constraints are satisfied, the remaining constraint will be automatically satisfied. Any BF solution on the transportation tableau will have exactly m+n-1 circled nonnegative allocations (BVs), where the sum of the allocations for each row or column equals its supply or demand. 30

31 Transportation Simplex Initial BFS 1. From the rows and columns still under consideration, select the next BV according to some criterion. 2. Allocate as much as possible considering the supply and demand for the related column and row. 3. Eliminate necessary cells from consideration (column or row). If both the supply and demand is consumed fully, arbitrarily select the row. Then, that column will have a degenerate basic variable. 4. If only one row or column remains, complete the allocations by allocating the remaining supply or demand to each cell. Otherwise return to Step 1. 31

32 The Transportation Problem Metro Water District Problem 32

33 Transportation Simplex Initial BFS Alternative Criteria 1. Northwest Corner Rule: Start by selecting x 11 (the northwest corner of the tableau). Go on with the one neighboring cell. 33

34 Transportation Simplex Initial BFS Alternative Criteria 2. Vogel s Approximation Method (VAM): I. Calculate penalty costs for each row (and column) as the difference between the minimum unit cost and the next minimum unit cost in the row (column). II. III. Select the row or column with the largest penalty. Break ties arbitrarily. Allocate as much as possible to the smallest-cost-cell in that row or column. Break ties arbitrarily. IV. Eliminate necessary cells from consideration. Return to Step I. 34

35 Transportation Simplex Initial BFS Alternative Criteria - VAM 35

36 Transportation Simplex Initial BFS Alternative Criteria - VAM 36

37 Transportation Simplex Initial BFS Alternative Criteria - VAM 37

38 Transportation Simplex Initial BFS Alternative Criteria 3. Russell s Approximation Method (RAM): I. For each source row still under consideration, determine its u i as the largest unit cost (c ij ) remaining in that row. II. III. For each destination column still under consideration, determine its v j as the largest unit cost (c ij ) remaining in that column. For each variable not previously selected in these rows and columns, calculate: ij cij ui v j IV. Select the variable having the most negative delta value. Break ties arbitrarily. Allocate as much as possible. Eliminate necessary cells from consideration. Return to Step I. 38

39 The Transportation Problem RAM Metro Water District 39

40 Transportation Simplex Initial BFS Alternative Criteria - RAM 40

41 Transportation Simplex Initial BFS Alternative Criteria - RAM 41

42 Comparison: Transportation Simplex Initial BFS Alternative Criteria I. Northwest: Quick and easy, usually far from optimal. II. III. VAM: Popular, easy to implement by hand, yields nice solutions considering penalties. RAM: Still easy by computer, frequently better than VAM. Which is better on the average is unclear. For this problem VAM gave the optimal solution. For a large problem, use all to find the best initial BFS. Let s use the RAM BFS to start transportation simplex. 42

43 Transportation Simplex Initial BFS 43

44 Transportation Simplex 44

45 Transportation Simplex 45

46 Transportation Simplex Compute cij ui v j Step 1: Negative, not optimal Select x 25 as entering 46

47 Transportation Simplex There is always one chain reaction. 47

48 Transportation Simplex 48

49 Transportation Simplex 49

50 Transportation Simplex 50

51 Transportation Simplex 51

52 Transportation Simplex 52

53 The Assignment Problem Special type of LP, in fact a special type of Transportation prob. Assignees (workers, processors, machines, vehicles, plants, time slots) are being assigned to tasks (jobs, classrooms, people). 53

54 The Assignment Problem Example The JOB SHOP company has 3 new machines. There are 4 available locations in the shop where a machine could be installed, but m/c 2 cannot be installed at location 2. Objective: Assign machines to the locations to minimize total handling cost. 54

55 The Assignment Problem Example Introduce a dummy m/c for the extra location with zero costs. Assign cost M to the assignment of m/c 2 to location 2. 55

56 The Assignment Problem Mathematical Model (IP) Introduce a binary decision variable. 56

57 The Assignment Problem Mathematical Model (IP) 57

58 The Assignment Problem Mathematical Model (LP) Hence, change binary decision variables to continuous variables. Solve the resulting problem as an LP. xij 1, 58

59 The Assignment Problem Network Representation 59

60 The Assignment Problem Applying transportation simplex to this tableau, you get: 60

61 The Assignment Problem The solution with transportation simplex will have too many degenerate variables. m=n (number of sources = number of destinations) m+n-1 basic variables only n variables will take nonzero values (assignments) (2n-1) n = n-1 degenerate basic variables. Wasted iterations in transportation simplex. An even more efficient method for solving an assignment problem: The Hungarian Algorithm (or Assignment Algorithm) 61

62 The Assignment Problem: Example BETTER PRODUCTS Co. The company starts the production of 4 new products. Production will be in 3 plants, Plant 2 cannot make Product 3. Two options: 1. Permit product splitting, same product can be produced in more than one plant Transportation problem 2. Do not permit product splitting Assignment Problem 62

63 Example continued Option 1: Splitting allowed Transportation formulation 63

64 Example continued Option 2: Splitting not allowed Assignment formulation 64

65 Assignment formulation. Example continued 65

66 The Assignment Problem The Hungarian Method The algorithm operates on the cost table of the problem. Convert costs into opportunity costs: 1. Subtract the minimum element in each row from all elements of that row. (Row reduction) 2. If the table does not have a zero element in each row and each column, subtract the minimum element in each column from all elements of that column. (Column reduction) 3. The new table will have a zero in each row and column. 4. If these zero elements provide a complete set of assignments, we are done; the solution is optimal. Idea: One can add or subtract any constant from every element of a row or column of the cost table without really changing the 66 problem.

67 The Assignment Problem Consider JOB SHOP Co: 3 The Hungarian Method Row reduction: M (D) Column reduction (No need): The optimal solution: Assignment 1-4 Cost: 11 Assignment 2-3 Cost: 13 Assignment 3-1 Cost: 5 Assignment 4-2 Cost: 0 Total Cost = M (D)

68 The Assignment Problem The Hungarian Method Iteration 1 Consider BETTER PRODUCT Co: Every row (but one) already has zero element. Let s start with column reduction: a b a M b M M Every row and column has at least one zero No need for row reduction. But, can we make a complete assignment? 68

69 The Assignment Problem The Hungarian Method Iteration 1 We CANNOT make a complete assignment, we can only make 3. To see this, draw the minimum number of lines through rows or columns to cover all zeros in the table a b a M b M M 69

70 The Assignment Problem The Hungarian Method Iteration 1 Three lines mean 3 assignments, but we need to make 5. The minimum number of lines Number of rows (columns) a b a M b M M 70

71 The Assignment Problem The Hungarian Method Iteration 2 The minimum number of lines Number of rows (columns) Find the minimum element not crossed out. Subtract it from the entire table. Add it to each row and column crossed out. Equivalently: Subtract the element from elements not crossed out, and add it to elements crossed out twice a b a M b M M 71

72 The Assignment Problem The Hungarian Method Iteration 2 Draw the minimum number of lines through rows or columns to cover all zeros in the table a b a M b M M 72

73 The Assignment Problem The Hungarian Method Iteration 2 Four lines mean 4 assignments, we need 5. We should repeat a b a M b M M 73

74 The Assignment Problem The Hungarian Method Iteration 3 Repeat steps of previous iterations a b a M b M M 74

75 The Assignment Problem The Hungarian Method Iteration 3 Draw the minimum number of lines through rows or columns to cover all zeros in the table a b a 0 30 M b 0 30 M M 75

76 The Assignment Problem The Hungarian Method Iteration 3 Minimum five lines are needed to cover all zeros. We are done! a b a 0 30 M b 0 30 M M 76

77 The Assignment Problem The Hungarian Method Iteration 3 Make the assignments. Red zeros are one set of assignments, blue zeros show an alternative optimal solution. The purple zero is common to both solutions a b a 0 30 M b 0 30 M M Z = = 3290 (from the original cost table) for red zeros Exercise: Check for the blue ones! 77

### The Transportation and Assignment Problems. Hillier &Lieberman Chapter 8

The Transportation and Assignment Problems Hillier &Lieberman Chapter 8 The Transportation and Assignment Problems Two important special types of linear programming problems The transportation problem

### The Transportation and Assignment Problems. Chapter 9: Hillier and Lieberman Chapter 7: Decision Tools for Agribusiness Dr. Hurley s AGB 328 Course

The Transportation and Assignment Problems Chapter 9: Hillier and Lieberman Chapter 7: Decision Tools for Agribusiness Dr. Hurley s AGB 328 Course Terms to Know Sources Destinations Supply Demand The Requirements

### Transportation problem

Transportation problem Operations research (OR) are concerned with scientifically deciding how to best design and operate people machine systems, usually under conditions requiring the allocation of scarce

### TRANSPORTATION PROBLEM AND VARIANTS

TRANSPORTATION PROBLEM AND VARIANTS Introduction to Lecture T: Welcome to the next exercise. I hope you enjoyed the previous exercise. S: Sure I did. It is good to learn new concepts. I am beginning to

### 3. Transportation Problem (Part 1)

3 Transportation Problem (Part 1) 31 Introduction to Transportation Problem 32 Mathematical Formulation and Tabular Representation 33 Some Basic Definitions 34 Transportation Algorithm 35 Methods for Initial

### The Study of Using LP to Solve Flower Transport Problem

The Study of Using LP to Solve Flower Transport Problem 1 Chung-Hsin Liu, 2 Le Le Trung 1 Department of Computer Science & Information Engineering, Chinese Culture University, Taiwan, R.O.C. liu3.gold@msa.hinet.net

### International Journal of Mathematics Trends and Technology (IJMTT) Volume 44 Number 4 April 2017

Solving Transportation Problem by Various Methods and Their Comaprison Dr. Shraddha Mishra Professor and Head Lakhmi Naraian College of Technology, Indore, RGPV BHOPAL Abstract: The most important and

### Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras

Operation and supply chain management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture - 37 Transportation and Distribution Models In this lecture, we

### Transportation Problems

C H A P T E R 11 Transportation Problems Learning Objectives: Understanding the feature of Assignment Problems. Formulate an Assignment problem. Hungarian Method Unbalanced Assignment Problems Profit Maximization

### Balancing a transportation problem: Is it really that simple?

Original Article Balancing a transportation problem: Is it really that simple? Francis J. Vasko a, * and Nelya Storozhyshina b a Mathematics Department, Kutztown University, Kutztown, Pennsylvania 19530,

### Application of Transportation Linear Programming Algorithms to Cost Reduction in Nigeria Soft Drinks Industry

Application of Transportation Linear Programming Algorithms to Cost Reduction in Nigeria Soft Drinks Industry A. O. Salami Abstract The transportation problems are primarily concerned with the optimal

### Optimal Solution of Transportation Problem Based on Revised Distribution Method

Optimal Solution of Transportation Problem Based on Revised Distribution Method Bindu Choudhary Department of Mathematics & Statistics, Christian Eminent College, Indore, India ABSTRACT: Transportation

### An Alternative Method to Find Initial Basic Feasible Solution of a Transportation Problem

Annals of Pure and Applied Mathematics Vol., No. 2, 2, 3-9 ISSN: 2279-087X (P), 2279-0888(online) Published on 6 November 2 www.researchmathsci.org Annals of An Alternative Method to Find Initial Basic

### Techniques of Operations Research

Techniques of Operations Research C HAPTER 2 2.1 INTRODUCTION The term, Operations Research was first coined in 1940 by McClosky and Trefthen in a small town called Bowdsey of the United Kingdom. This

### A New Technique for Solving Transportation Problems by Using Decomposition-Based Pricing and its Implementation in Real Life

Dhaka Univ. J. Sci. 64(1): 45-50, 2016 (January) A New Technique for Solving Transportation Problems by Using Decomposition-Based Pricing and its Implementation in Real Life Sajal Chakroborty and M. Babul

### TRANSPORTATION MODEL IN DELIVERY GOODS USING RAILWAY SYSTEMS

TRANSPORTATION MODEL IN DELIVERY GOODS USING RAILWAY SYSTEMS Fauziah Ab Rahman Malaysian Institute of Marine Engineering Technology Universiti Kuala Lumpur Lumut, Perak, Malaysia fauziahabra@unikl.edu.my

### Statistical Investigation of Various Methods to Find the Initial Basic Feasible Solution of a Transportation Problem

Statistical Investigation of Various Methods to Find the Initial Basic Feasible Solution of a Transportation Problem Ravi Kumar R 1, Radha Gupta 2, Karthiyayini.O 3 1,2,3 PESIT-Bangalore South Campus,

### OPERATIONS RESEARCH Code: MB0048. Section-A

Time: 2 hours OPERATIONS RESEARCH Code: MB0048 Max.Marks:140 Section-A Answer the following 1. Which of the following is an example of a mathematical model? a. Iconic model b. Replacement model c. Analogue

### B.1 Transportation Review Questions

Lesson Topics Network Models are nodes, arcs, and functions (costs, supplies, demands, etc.) associated with the arcs and nodes, as in transportation, assignment, transshipment, and shortest-route problems.

### ISE480 Sequencing and Scheduling

ISE480 Sequencing and Scheduling INTRODUCTION ISE480 Sequencing and Scheduling 2012 2013 Spring term What is Scheduling About? Planning (deciding what to do) and scheduling (setting an order and time for

### Linear Programming Applications. Structural & Water Resources Problems

Linear Programming Applications Structural & Water Resources Problems 1 Introduction LP has been applied to formulate and solve several types of problems in engineering field LP finds many applications

### 56:171 Homework Exercises -- Fall 1993 Dennis Bricker Dept. of Industrial Engineering The University of Iowa

56:7 Homework Exercises -- Fall 99 Dennis Bricker Dept. of Industrial Engineering The University of Iowa Homework # Matrix Algebra Review: The following problems are to be found in Chapter 2 of the text,

### Linear Programming and Applications

Linear Programming and Applications (v) LP Applications: Water Resources Problems Objectives To formulate LP problems To discuss the applications of LP in Deciding the optimal pattern of irrigation Water

### A Particle Swarm Optimization Algorithm for Multi-depot Vehicle Routing problem with Pickup and Delivery Requests

A Particle Swarm Optimization Algorithm for Multi-depot Vehicle Routing problem with Pickup and Delivery Requests Pandhapon Sombuntham and Voratas Kachitvichayanukul Abstract A particle swarm optimization

### A comparative study of ASM and NWCR method in transportation problem

Malaya J. Mat. 5(2)(2017) 321 327 A comparative study of ASM and NWCR method in transportation problem B. Satheesh Kumar a, *, R. Nandhini b and T. Nanthini c a,b,c Department of Mathematics, Dr. N. G.

### WAYNE STATE UNIVERSITY Department of Industrial and Manufacturing Engineering May, 2010

WAYNE STATE UNIVERSITY Department of Industrial and Manufacturing Engineering May, 2010 PhD Preliminary Examination Candidate Name: 1- Sensitivity Analysis (20 points) Answer ALL Questions Question 1-20

### Modeling Using Linear Programming

Chapter Outline Developing Linear Optimization Models Decision Variables Objective Function Constraints Softwater Optimization Model OM Applications of Linear Optimization OM Spotlight: Land Management

### The Efficient Allocation of Individuals to Positions

The Efficient Allocation of Individuals to Positions by Aanund Hylland and Richard Zeckhauser Presented by Debreu Team: Justina Adamanti, Liz Malm, Yuqing Hu, Krish Ray Hylland and Zeckhauser consider

### A Minimum Spanning Tree Approach of Solving a Transportation Problem

International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: 2321 4767 P-ISSN: 2321-4759 Volume 5 Issue 3 March. 2017 PP-09-18 A Minimum Spanning Tree Approach of Solving a Transportation

### Assignment Technique for solving Transportation Problem A Case Study

Assignment Technique for solving Transportation Problem A Case Study N. Santosh Ranganath Faculty Member, Department of Commerce and Management Studies Dr. B. R. Ambedkar University, Srikakulam, Andhra

### DIS 300. Quantitative Analysis in Operations Management. Instructions for DIS 300-Transportation

Instructions for -Transportation 1. Set up the column and row headings for the transportation table: Before we can use Excel Solver to find a solution to C&A s location decision problem, we need to set

### 1.224J/ESD.204J TRANSPORTATION OPERATIONS, PLANNING AND CONTROL: CARRIER SYSTEMS

1.224J/ESD.204J TRANSPORTATION OPERATIONS, PLANNING AND CONTROL: CARRIER SYSTEMS Professor Cynthia Barnhart Professor Nigel H.M. Wilson Fall 2003 1.224J/ ESD.204J Outline Sign-up Sheet Introductions Carrier

### The Transportation Problem

The Transportation Problem Stages in solving transportation problems Steps for Stage 1 (IBFS) 1) If problem is not balanced, introduce dummy row/column to balance it. [Note: Balancing means ensuring that

### INDIAN INSTITUTE OF MATERIALS MANAGEMENT Post Graduate Diploma in Materials Management PAPER 18 C OPERATIONS RESEARCH.

INDIAN INSTITUTE OF MATERIALS MANAGEMENT Post Graduate Diploma in Materials Management PAPER 18 C OPERATIONS RESEARCH. Dec 2014 DATE: 20.12.2014 Max. Marks: 100 TIME: 2.00 p.m to 5.00 p.m. Duration: 03

### Supply Chain Location Decisions Chapter 11

Supply Chain Location Decisions Chapter 11 11-01 What is a Facility Location? Facility Location The process of determining geographic sites for a firm s operations. Distribution center (DC) A warehouse

### TAKING ADVANTAGE OF DEGENERACY IN MATHEMATICAL PROGRAMMING

TAKING ADVANTAGE OF DEGENERACY IN MATHEMATICAL PROGRAMMING F. Soumis, I. Elhallaoui, G. Desaulniers, J. Desrosiers, and many students and post-docs Column Generation 2012 GERAD 1 OVERVIEW THE TEAM PRESENS

### OPERATIONS RESEARCH TWO MARKS QUESTIONS AND ANSWERS

OPERATIONS RESEARCH TWO MARKS QUESTIONS AND ANSWERS 1.when does degenaracy happen in transportation problem? In transportation problem with m orgins and n destinations, if a IBFS has less than m+n-1 allocations,

### Optimizing Product Transportation At Frito Lay

Spring 11 Optimizing Product Transportation At Frito Lay Javier González Fernando G. Sada Marcelo G. Sada Southern Methodist University Table of Contents 2. Background and Description of the Problem...

### The Time Window Assignment Vehicle Routing Problem

The Time Window Assignment Vehicle Routing Problem Remy Spliet, Adriana F. Gabor June 13, 2012 Problem Description Consider a distribution network of one depot and multiple customers: Problem Description

### Transportation Logistics Part I and II

Transportation Logistics Part I and II Exercise Let G = (V,E) denote a graph consisting of vertices V = {,2,3,4,5,6,,8} and arcs A = {(,2),(,3),(2,4),(3,2),(4,3),(4,5),(4,6),(5,3),(5,),(6,8),(,4),(,6),(,8)}.

### Container Sharing in Seaport Hinterland Transportation

Container Sharing in Seaport Hinterland Transportation Herbert Kopfer, Sebastian Sterzik University of Bremen E-Mail: kopfer@uni-bremen.de Abstract In this contribution we optimize the transportation of

### Modeling of competition in revenue management Petr Fiala 1

Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize

### Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras

Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture - 24 Sequencing and Scheduling - Assumptions, Objectives and Shop

### LECTURE 41: SCHEDULING

LECTURE 41: SCHEDULING Learning Objectives After completing the introductory discussion on Scheduling, the students would be able to understand what scheduling is and how important it is to high volume

### Getting Started with OptQuest

Getting Started with OptQuest What OptQuest does Futura Apartments model example Portfolio Allocation model example Defining decision variables in Crystal Ball Running OptQuest Specifying decision variable

### UNIT 7 TRANSPORTATION PROBLEM

UNIT 7 TRNSPORTTION PROLEM Structure 7.1 Introduction Objectives 2 asic Feasible Solution of a Transportation Problem 7. Modified Distribution (MODI) Method 7.4 Stepping Stone Method 7.5 Unbalanced Transportation

### Transshipment and Assignment Models

March 31, 2009 Goals of this class meeting 2/ 5 Learn how to formulate transportation models with intermediate points. Learn how to use the transportation model framework for finding optimal assignments.

### A Log-Truck Scheduling Model Applied to a Belgian Forest Company. Jean-Sébastien Tancrez 1

A Log-Truck Scheduling Model Applied to a Belgian Forest Company Jean-Sébastien Tancrez 1 Louvain School of Management, Université catholique de Louvain, Mons, Belgium {js.tancrez@uclouvain.be} Abstract.

### Multi-depot Vehicle Routing Problem with Pickup and Delivery Requests

Multi-depot Vehicle Routing Problem with Pickup and Delivery Requests Pandhapon Sombuntham a and Voratas Kachitvichyanukul b ab Industrial and Manufacturing Engineering, Asian Institute of Technology,

Advances in Production Engineering & Management 4 (2009) 3, 127-138 ISSN 1854-6250 Scientific paper LOADING AND SEQUENCING JOBS WITH A FASTEST MACHINE AMONG OTHERS Ahmad, I. * & Al-aney, K.I.M. ** *Department

### AFRREV STECH An International Journal of Science and Technology Bahir Dar, Ethiopia Vol.1 (3) August-December, 2012:54-65

AFRREV STECH An International Journal of Science and Technology Bahir Dar, Ethiopia Vol.1 (3) August-December, 2012:54-65 ISSN 2225-8612 (Print) ISSN 2227-5444 (Online) Optimization Modelling for Multi-Objective

### Each location (farm, slaughterhouse or slaughtering company) is identified with a production

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Appendix Section A: Transport data Each location (farm, slaughterhouse or slaughtering company) is identified with a production place number

### Solving Scheduling Problems in Distribution Centers by Mixed Integer Linear Programming Formulations

Solving Scheduling Problems in Distribution Centers by Mixed Integer Linear Programming Formulations Maria Pia Fanti Gabriella Stecco Walter Ukovich Department of Electrical and Electronic Engineering,

### Topics in Supply Chain Management. Session 3. Fouad El Ouardighi BAR-ILAN UNIVERSITY. Department of Operations Management

BAR-ILAN UNIVERSITY Department of Operations Management Topics in Supply Chain Management Session Fouad El Ouardighi «Cette photocopie (d articles ou de livre), fournie dans le cadre d un accord avec le

### Chapter 3 Formulation of LP Models

Chapter 3 Formulation of LP Models The problems we have considered in Chapters 1 and 2 have had limited scope and their formulations were very straightforward. However, as the complexity of the problem

### Routing and Scheduling in Tramp Shipping - Integrating Bunker Optimization Technical report

Downloaded from orbit.dtu.dk on: Jan 19, 2018 Routing and Scheduling in Tramp Shipping - Integrating Bunker Optimization Technical report Vilhelmsen, Charlotte; Lusby, Richard Martin ; Larsen, Jesper Publication

### Unit 1: Introduction. Forest Resource Economics

Unit : Introduction Scope of Forest Resource Economics Economics is the science which deals with allocating scarce resources among competing means to satisfy the wants of mankind. Forest could be regarded

### Distributed Algorithms for Resource Allocation Problems. Mr. Samuel W. Brett Dr. Jeffrey P. Ridder Dr. David T. Signori Jr 20 June 2012

Distributed Algorithms for Resource Allocation Problems Mr. Samuel W. Brett Dr. Jeffrey P. Ridder Dr. David T. Signori Jr 20 June 2012 Outline Survey of Literature Nature of resource allocation problem

### INTEGER PROGRAMMING BASED SEARCH

INTEGER PROGRAMMING BASED SEARCH A Thesis Presented to The Academic Faculty by Michael R Hewitt In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Industrial

### Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray)

Gebauer/Matthews: MIS 213 Hands-on Tutorials and Cases, Spring 2015 111 Excel Solver Tutorial: Wilmington Wood Products (Originally developed by Barry Wray) Purpose: Using Excel Solver as a Decision Support

### a) Measures are unambiguous quantities, whereas indicators are devised from common sense understandings

Chapter-1: QUANTITATIVE TECHNIQUES Self Assessment Questions 1. An operational definition is: a) One that bears no relation to the underlying concept b) An abstract, theoretical definition of a concept

### SYLLABUS Class: - B.B.A. IV Semester. Subject: - Operations Research

SYLLABUS Class: - B.B.A. IV Semester Subject: - Operations Research UNIT I Definition of operations research, models of operations research, scientific methodology of operations research, scope of operations

### Technical Bulletin Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations

Technical Bulletin 2009-06-03 Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations June 15, 2009 Comparison of Lossy versus Lossless Shift Factors in the ISO Market Optimizations

### An Optimization Algorithm for the Inventory Routing Problem with Continuous Moves

An Optimization Algorithm for the Inventory Routing Problem with Continuous Moves Martin Savelsbergh Jin-Hwa Song The Logistics Institute School of Industrial and Systems Engineering Georgia Institute

### Chapter 11. Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool

Chapter 11 Decision Making and Relevant Information Linear Programming as a Decision Facilitating Tool 1 Introduction This chapter explores cost accounting for decision facilitating purposes It focuses

### The vehicle routing problem with demand range

DOI 10.1007/s10479-006-0057-0 The vehicle routing problem with demand range Ann Melissa Campbell C Science + Business Media, LLC 2006 Abstract We propose and formulate the vehicle routing problem with

### INTEGRATING VEHICLE ROUTING WITH CROSS DOCK IN SUPPLY CHAIN

INTEGRATING VEHICLE ROUTING WITH CROSS DOCK IN SUPPLY CHAIN Farshad Farshchi Department of Industrial Engineering, Parand Branch, Islamic Azad University, Parand, Iran Davood Jafari Department of Industrial

### CROSS-DOCKING: SCHEDULING OF INCOMING AND OUTGOING SEMI TRAILERS

CROSS-DOCKING: SCHEDULING OF INCOMING AND OUTGOING SEMI TRAILERS 1 th International Conference on Production Research P.Baptiste, M.Y.Maknoon Département de mathématiques et génie industriel, Ecole polytechnique

### A Heuristic on Risk Management System in Goods Transportation Model Using Multi-Optimality by MODI Method

Open Journal of Applied Sciences, 16, 6, -1 Published Online August 16 in SciRes. http://www.scirp.org/journal/ojapps http://dx.doi.org/.26/ojapps.16.6 A Heuristic on Risk Management System in Goods Transportation

### The Blending Model. Example Example 2.2.2

2.1. The Blending Model. Example 2.2.1. To feed her stock a farmer can purchase two kinds of feed. He determined that the herd requires 60, 84, and 72 units of the nutritional elements A,B, and C, respectively,

### APPLIED A NEW METHOD FOR MULTI-MODE PROJECT SCHEDULING

project, project scheduling, resource-constrained project scheduling, project-driven manufacturing, multi-mode, heuristic, branch and bound scheme, make-to-order Iwona PISZ Zbigniew BANASZAK APPLIED A

### Heuristic Techniques for Solving the Vehicle Routing Problem with Time Windows Manar Hosny

Heuristic Techniques for Solving the Vehicle Routing Problem with Time Windows Manar Hosny College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia mifawzi@ksu.edu.sa Keywords:

### Managing Low-Volume Road Systems for Intermittent Use

224 TRANSPORTATION RESEARCH RECORD 1291 Managing Low-Volume Road Systems for Intermittent Use JERRY ANDERSON AND JOHN SESSIONS In some areas of the United States, particularly in gentle topography, closely

### MGSC 1205 Quantitative Methods I

MGSC 1205 Quantitative Methods I Class Seven Sensitivity Analysis Ammar Sarhan 1 How can we handle changes? We have solved LP problems under deterministic assumptions. find an optimum solution given certain

### Timber Management Planning with Timber RAM and Goal Programming

Timber Management Planning with Timber RAM and Goal Programming Richard C. Field Abstract: By using goal programming to enhance the linear programming of Timber RAM, multiple decision criteria were incorporated

### Solving Business Problems with Analytics

Solving Business Problems with Analytics New York Chapter Meeting INFORMS New York, NY SAS Institute Inc. December 12, 2012 c 2010, SAS Institute Inc. All rights reserved. Outline 1 Customer Case Study:

### Application of a Capacitated Centered Clustering Problem for Design of Agri-food Supply Chain Network

www.ijcsi.org 300 Application of a Capacitated Centered Clustering Problem for Design of Agri-food Supply Chain Network Fethi Boudahri 1, Mohamed Bennekrouf 2, Fayçal Belkaid 1, and Zaki Sari 1 1 MELT

### Scheduling of Maintenance Tasks and Routing of a Joint Vessel Fleet for Multiple Offshore Wind Farms

Journal of Marine Science and Engineering Article Scheduling of Maintenance Tasks and Routing of a Joint Vessel Fleet for Multiple Offshore Wind Farms Nora Tangen Raknes 1, Katrine Ødeskaug 1, Magnus Stålhane

### Production Activity Control

Production Activity Control Here the progress of manufacturing operations in the workshop is recorded. Also the material transactions tied to the Open WO s are entered. Open Work Order Maintenance Window

### SELECTED HEURISTIC ALGORITHMS FOR SOLVING JOB SHOP AND FLOW SHOP SCHEDULING PROBLEMS

SELECTED HEURISTIC ALGORITHMS FOR SOLVING JOB SHOP AND FLOW SHOP SCHEDULING PROBLEMS A THESIS SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENT OF THE DEGREE OF BACHELOR OF TECHNOLOGY IN MECHANICAL

### Tutorial Segmentation and Classification

MARKETING ENGINEERING FOR EXCEL TUTORIAL VERSION v171025 Tutorial Segmentation and Classification Marketing Engineering for Excel is a Microsoft Excel add-in. The software runs from within Microsoft Excel

### Modeling a Four-Layer Location-Routing Problem

Modeling a Four-Layer Location-Routing Problem Paper 018, ENG 105 Mohsen Hamidi, Kambiz Farahmand, S. Reza Sajjadi Department of Industrial and Manufacturing Engineering North Dakota State University Mohsen.Hamidi@my.ndsu.edu,

### Enhancing Pendulum Nusantara Model in Indonesian Maritime Logistics Network

Enhancing Pendulum Nusantara Model in Indonesian Maritime Logistics Network Komarudin System Engineering, Modeling Simulation (SEMS) Laboratory, Department of Industrial Engineering, Universitas Indonesia,

### Optimizing capital investments under technological change and deterioration: A case study on MRI machine replacement

The Engineering Economist A Journal Devoted to the Problems of Capital Investment ISSN: 0013-791X (Print) 1547-2701 (Online) Journal homepage: http://www.tandfonline.com/loi/utee20 Optimizing capital investments

### 36106 Managerial Decision Modeling Revenue Management

36106 Managerial Decision Modeling Revenue Management Kipp Martin University of Chicago Booth School of Business October 5, 2017 Reading and Excel Files 2 Reading (Powell and Baker): Section 9.5 Appendix

### Multi-Period Vehicle Routing with Call-In Customers

Multi-Period Vehicle Routing with Call-In Customers Anirudh Subramanyam, Chrysanthos E. Gounaris Carnegie Mellon University Frank Mufalli, Jose M. Pinto Praxair Inc. EWO Meeting September 30 th October

### Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC

Konrad-Zuse-Zentrum fu r Informationstechnik Berlin Takustraße 7 D-14195 Berlin-Dahlem Germany BENJAMIN HILLER SVEN O. KRUMKE JO RG RAMBAU Reoptimization Gaps versus Model Errors in Online-Dispatching

### LME POLICY ON THE APPROVAL AND OPERATION OF WAREHOUSES, REVISED [1 JUNE 2015]

LME POLICY ON THE APPROVAL AND OPERATION OF WAREHOUSES, REVISED [1 JUNE 2015] A) Warehouses 1. Applicants to be a Warehouse will be considered for approval and listing in an existing or new Delivery Point

### Power System Economics and Market Modeling

Power System Economics and Market Modeling 2001 South First Street Champaign, Illinois 61820 +1 (217) 384.6330 support@powerworld.com http://www.powerworld.com PowerWorld Simulator OPF and Locational Marginal

### Cost allocation in collaborative forest transportation

Cost allocation in collaborative forest transportation M. Frisk b M. Göthe-Lundgren c K. Jörnsten a M. Rönnqvist a a Norwegian School of Economics and Business Administration, Bergen, Norway b The Forestry

### Limits of Software Reuse

Technical Note Issued: 07/2006 Limits of Software Reuse L. Holenderski Philips Research Eindhoven c Koninklijke Philips Electronics N.V. 2006 Authors address: L. Holenderski WDC3-044; leszek.holenderski@philips.com

### We consider a distribution problem in which a set of products has to be shipped from

in an Inventory Routing Problem Luca Bertazzi Giuseppe Paletta M. Grazia Speranza Dip. di Metodi Quantitativi, Università di Brescia, Italy Dip. di Economia Politica, Università della Calabria, Italy Dip.

### Hadoop Fair Scheduler Design Document

Hadoop Fair Scheduler Design Document August 15, 2009 Contents 1 Introduction The Hadoop Fair Scheduler started as a simple means to share MapReduce clusters. Over time, it has grown in functionality to

### Global Supply Chain Planning under Demand and Freight Rate Uncertainty

Global Supply Chain Planning under Demand and Freight Rate Uncertainty Fengqi You Ignacio E. Grossmann Nov. 13, 2007 Sponsored by The Dow Chemical Company (John Wassick) Page 1 Introduction Motivation

### Balanced Billing Cycles and Vehicle Routing of Meter Readers

Balanced Billing Cycles and Vehicle Routing of Meter Readers by Chris Groër, Bruce Golden, Edward Wasil University of Maryland, College Park University of Maryland, College Park American University, Washington

### B O O K. WRITING AND SIMPLIFYING EXPRESSIONS AIMS Education Foundation

INTERACTIVE B O O K WRITING AND SIMPLIFYING EXPRESSIONS 57 011 AIMS Education Foundation Developed and Published by AIMS Education Foundation This book contains materials developed by the AIMS Education

### Hello and welcome to this overview session on SAP Business One release 9.1

Hello and welcome to this overview session on SAP Business One release 9.1 1 The main objective of this session is to provide you a solid overview of the new features developed for SAP Business One 9.1

### Modeling Linear Programming Problem Using Microsoft Excel Solver

Modeling Linear Programming Problem Using Microsoft Excel Solver ADEKUNLE Simon Ayo* & TAFAMEL Andrew Ehiabhi (Ph.D) Department of Business Administration, Faculty of Management Sciences, University of