Adm2302 Assignment 3

Presentation on theme: "Transportation Assignment and Transshipments Problems"— Presentation transcript:

1 Transportation Assignment and Transshipments Problems
ADM2302 /Rim Jaber

2 IntroductionProblems belong to a special class of LP problems called Network Flow ProblemsCan be solved using the Simplex methodThere are specialized algorithms that are more efficient (northwest corner rule, minimum cost method, and stepping stone method, Hungarian Method)ADM2302 /Rim Jaber

3 ApproachIllustrate each problem with a specific example (application):Develop a graphical representation, called network of the problemShow how each can be formulated and solved as a LP using excel solver (that uses the simplex method)ADM2302 /Rim Jaber

4 Transportation Model Characteristics
Transportation of goods and services from a number of sources (supply points) to a number of destinations (demand points) at a minimum cost (objective)Each source is able to supply a fixed number of units of the goods or services, and each destination has a fixed demand for the goods or servicesADM2302 /Rim Jaber

5 Transportation Model: Objective
Most common objective of transportation problem is to schedule shipments from sources to destinations so that total production and transportation costs are minimizedADM2302 /Rim Jaber

6 Transportation Model (cont’d)
Parameters of the model:SuppliesDemandsUnit CostsAll the parameter of the model are included in a parameter table (summarizes the formulations of a transportation problem by giving all the unit costs, suppliers, and demands)ADM2302 /Rim Jaber

7 ExampleWheat is harvested in the Midwest and stored in grain elevators in three different cities – Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding one ton of wheat.The cost of shipping one ton of wheat from each grain elevator to each mill, the demand of wheat per month for each mill, and the number of tons that each grain elevator is able to supply to the mills on a monthly basis are shown in the parameters table:ADM2302 /Rim Jaber

8 Grain Elevator A. Chicago B. St. Louis C. Cincinnati Supply (Supplier)
Parameter TableMill (destination)Grain Elevator A. Chicago B. St. Louis C. Cincinnati Supply(Supplier)1. Kansas City $2. Omaha3. Des MoinesDemandADM2302 /Rim Jaber

9 Example (cont’d)Determine how many tons of wheat to transport form each grain elevator to each mill on a monthly basis in order to minimize the total cost of transportationGoalSelect the shipping routes and units to be shipped to minimize total transportation costADM2302 /Rim Jaber

10 Network Representation
Each supplier (si,i= 1,2, …,m) and demand (dj, j =1,2,…,n) point is represented by a node (circle)Each possible shipping route is represented by an arc (represent the amounts shipped)Direction of the flow is indicated by the arrows: Origin to DestinationThe goods shipped from origin to destination represent flow of the networkAmount of the supply is written next to the origin node (si)Amount of the demand is written next to the destination node (dj)ADM2302 /Rim Jaber

11 Network Representation
Supplier (origin)Demand (destination)123ABC68107114512150175275200100300Total = 600ADM2302 /Rim Jaber

12 LP Model FormulationDecision VariablesThe amount of goods or item to be transported from a numbers of origins to a number of destinationsApply this definition to our ExampleXij: The amount of tons of wheat transported from grain elevator i (where i= 1, 2, 3), to mill j (where j = A,B,C)General Form:Xij:: number of units shipped from origin i to destination j. (where i = 1, 2,…, m and j = 1, 2, …, n)The number of decision variables = numbers of arcsADM2302 /Rim Jaber

13 LP Model Formulation (cont’d)
Objective FunctionMinimize total transportation cost for all shipmentsThe sum of the individual shipping costs from each Grain Elevator to Each Mill:min Z = $ 6x1A + 8x1B + 10x1c + 7x2A+ 11x2B + 11x2C + 4x3A + 5x3B + 12x3CADM2302 /Rim Jaber

14 LP Model Formulation (cont’d)
ConstraintsDeal with the capacities at each origin (origin has a limited supply)Deal with the requirements at each destinations (destination has specific demands)Six constraints: One for each Elevator’s supply and one for each Mill’s demandWe write a constraint for each node in the networkADM2302 /Rim Jaber

15 LP Model Formulation (cont’d)
Xij: The amount of tons of wheat transported from grain elevator i (where i= 1, 2, 3), to mill j (where j = A,B,C)min Z = $ 6x1A + 8x1B + 10x1c + 7x2A+ 11x2B + 11x2C + 4x3A + 5x3B + 12x3CSubject tox1A + x1B + x1C = 150x2A + x2B + x2C = 175x3A + x3B + x3C = 275Supply constraintsx1A + x2A+ x3A = 200x1B+ x2B + x3B = 100x1C + x2C + x3C = 300xij ≥ 0Demand constraintsADM2302 /Rim Jaber

16 LP Model Formulation: Comments
In a balanced transportation model, supply equals demand such that all constraints are equalities (=)In an unbalanced model, supply does not equal demand and one set of constraints is <=ADM2302 /Rim Jaber

17 SolutionExcel solver uses the simplex method to solve any kind of linear programming problemRefer to the Transportation_Problem.xsl fileADM2302 /Rim Jaber

18 Total shipping cost is $4,525.
The Optimum SolutionSHIP:150 tons of wheat from Kansas to Cincinnati,25 tons of wheat from Omaha to Chicago,150 tons of wheat from Omaha to Cincinnati,175 tons from Des Moines to Chicago,and 100 tons of wheat Des Moines to St. Louis.Total shipping cost is $4,525.ADM2302 /Rim Jaber

19 More than one Optimal solution?
Discussed in classADM2302 /Rim Jaber

20 Problem Variations Total supply does not equal to total demand
Maximization objective functionRoute capacities or route minimumUnacceptable routesADM2302 /Rim Jaber

21 Total supply not equal to total demand
Total Supply > Total Demand:“<=“ used in the supply constraints instead of “=“Excess supply will appear as slack (unused supply or amount not shipped from the origin) in the LP solutionExample: refer to “Transportation_Promblem.xsl”Total Supply < Total Demand:“<=“ used in the demand constraints instead of “=“Some destinations will experience a shortfall or unsatisfied demandExample: Change the demand at Cincinnati to 350 tonsADM2302 /Rim Jaber

22 Maximization objective function
Objective: Maximize total transportation profitSolve as a maximization LP rather than minimization LPThe constraints are not affectedADM2302 /Rim Jaber

23 Route capacities or route minimum
Constraints need to be addedMaximum route capacity, Lij:Xij <= LijMinimum Route capacity, Mij:Xij >=MijADM2302 /Rim Jaber

24 Unacceptable routes Drop the corresponding arc from the network
Remove the corresponding variable from the linear programming formulationIf you want to keep the corresponding variable:make the variables that correspond to unacceptable routes equal zero (Xij = 0 if the route from i to j is not possible)ADM2302 /Rim Jaber

25 Example 2 (Midterm/Fall 01)
The U.S. government is auctioning off oil leases at two sites: 1 and 2. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 40% of the total land being auctioned.Cliff has bid $1000/acre for site 1 land and $2000/acre for site 2 land.Blake has bid $900/acre for site 1 land and 2200/acre for site 2 land.Alexis has bid $1100 /acre for site 1 land and $1900/acre for site 2 land.ADM2302 /Rim Jaber

26 Example 2 (cont’d)Draw the transportation network model that corresponds to the problem.Formulate the linear programming (LP) model to maximize the government’s revenue. (Don’t forget to define the decision variables).ADM2302 /Rim Jaber

27 Assignment ProblemsA special form of transportation problem where all supply and demand values equal oneInvolve assigning jobs to machines, agents to tasks, sales personnel to sales territories, contracts to bidders etc…Objective: minimize cost, minimize time, or maximize profits etc…ADM2302 /Rim Jaber

28 Parameters of the Model
Assignees (e.g. agents, jobs…)Tasks (e.g. shifts, machines…)Cost table (gives the cost for each possible assignment of an assignee to a task)ExampleADM2302 /Rim Jaber

29 Example 3Fowle Marketing Research has just received requests for market research studies from three new clients. The company faces the task of assigning a project leader (agent) to each client (task). Currently, three individuals have no other commitments and are available for the project leader assignments.Fowle’s management realizes, however, that the time required to complete each study depend on the experience and ability of the project leader assigned. The three projects have approximately the same priority.

30 The company wants to assign project leaders to minimize the total number of days required to complete all three projects. If the project leader is to be assigned to one client only, what assignments should be made? The estimated project completion times in days (cost table) is:ClientProject Leader1 2 31. Terry9 18 52. Carle6 14 33. McClymondsADM2302 /Rim Jaber

31 Network Representation
NodesProject leaders and clientsArcsPossible assignments of project leaders to clientsThe supply at each origin node and the demand at each destination node are 1Cost of assigning a project leader to a clientTime it takes that project leader to complete the client’s taskADM2302 /Rim Jaber

32 LP Model FormulationVariable for each arc and a constraint for each nodeUse of Double-subscripted decision variablesObjective functionConstraintsADM2302 /Rim Jaber

33 SolutionSolved with a special purpose optimization method called Hungarian algorithm.Application of this algorithm requires thatnumber of assignees = number of tasks.(Balanced Model)Refer to Excel(assignment_problems.xsl)Excel Solver uses the simplex methodADM2302 /Rim Jaber

34 Problem Variations Parallel those for the transportation Problem:
Total number of agents (supply) not equal to the total number of tasks (demand)A maximization objective functionUnacceptable assignmentsADM2302 /Rim Jaber

35 Example 4: Employee Scheduling Application
The Department head of a management science department at a major Midwestern university will be scheduling faculty to teach courses during the coming autumn term. Four core courses need to be covered. The four courses are at the UG, MBA, MS, and Ph.D. levels. Four professors will be assigned to the courses, with each professor receiving one of the courses. Student evaluations of professors are available from previous terms. Based on a rating scale of 4 (excellent), 3 (very good), 2 (average), 1(fair), and 0(poor), the average student evaluations for each professor are shown:ADM2302 /Rim Jaber

36 Professor D does not have a Ph. D
Professor D does not have a Ph.D. and cannot be assigned to teach the Ph.D.-level course. If the department head makes teaching assignments based on maximizing the student evaluation ratings over all four courses, what staffing assignments should be made?CourseProfessorUGMBAMSPh.D.A2.82.23.33.0B3.23.03.63.6C3.33.23.53.5D3.22.82.5-ADM2302 /Rim Jaber

37 Example 4 (cont’d) Formulation: is discussed in class if time permits
Solution: Refer to “assignment_problems.xsl” for the solutionRecommendation/analysis of the Solution:Assign Prof. A to the MS course, Prof. B to the Ph.D course, Prof. C to the MBA course, and Prof. D to the UG courseADM2302 /Rim Jaber

38 Transshipment Problems
Extension of transportation problem is called transshipment problem in which a point can have shipments that both arrive as well as leave.Example would be a warehouse where shipments arrive from factories and then leave for retail outlets.ADM2302 /Rim Jaber

39 Transshipment Problems
If total flow into a node is equal to total flow out from node, node represents a pure transshipment point.Flow balance equation will have a zero RHS value.It may be possible for firm to achieve cost savings (economies of scale) by consolidating shipments from several factories at warehouse and then sending them together to retail outlets.ADM2302 /Rim Jaber

40 Example 5Five Star Manufacturing Company makes compressors for air conditioners. The compressors are produced in 3 plants, then shipped on to 4 heating, ventilation and air conditioning (HVAC) contractors.A network model is shown on the next slide. Develop a LP model that five Star can solve to minimize the cost of shipping compressors from the plants through the warehouses and on to the HVAC contractors.ADM2302 /Rim Jaber

41 Per unit shipping Costs Plant Capacities (suppliers) Contractor Demand
62591217555011104911132835551015125913113945258Per unit shippingCostsTotal =Total =ADM2302 /Rim Jaber

42 Example 5 (cont’d) Formulation: is discussed in class if time permits
Solution: Refer to “Transhipment_Problem.xsl” for the solutionADM2302 /Rim Jaber

43 Summary Three network flow models were presented:
Transportation model deals with distribution of goods from several supplier to a number of demand points.Transshipment model includes points that permit goods to flow both in and out of them.Assignment model deals with determining the most efficient assignment of issues such as people to projects.ADM2302 /Rim Jaber

BUSINESS DECISION MODELS ADM2302 D Fall 2014 Professor Wojtek Michalowski Office Desmarais Building, DMS6130 Telephone 613-562-5800, ext. 4955 E-Mail wojtek@telfer.uottawa.ca Office Hours By appointment only Class Location Desmarais Building, DMS1120 Class Hours Monday 19:00 – 22:00 Prerequisite(s) CSI 1306 or ITI1120, MAT 1302 Program of study B.Com. core course Course Deliverable Assignments (4) Midterm exam Final exam Michalowski 2014 Due Date Due at a beginning of class, as follows: Assignment 1: September 29; Assignment 2: October 27; Assignment 3: November 17; Assignment 4: December 1 Weight on Final Grade 20% Saturday, October 25 starting at 13:00 (location to be announced) 30% Final exam date, time and location to be determined as per the published University schedule 50% Fall BUSINESS DECISION MODELS ADM2302 Section D, Fall 2014 Course Description This course provides an overview of the nature and application of decision models and business analytics using management science (MS)/operations research (OR) methods with emphasis on applications in different areas of business. Students will be introduced to the field by examining a survey of practical problems that are resolved using the methods of business analytics to be presented in this course. The scientific method of problem solving will be presented, with emphasis on the elements of problem formulation, modeling, and analysis of results. Quantitative, “deterministic” models for allocation of resources will be examined in detail, including techniques most commonly used in modern business: linear, integer and goal programming, as well as an introduction to the class of “nondeterministic” problems using the techniques of project management and decision analysis. Emphasis is on (i) the formulation of practical quantitative problems, (ii) the solution of problems using basic algorithms with the aid of Microsoft Excel Solver add-in, and (iii) the interpretation of results of model solutions as one would do as manager of an enterprise. Course Contribution to Program Learning Goals This course contributes to the attainment of several of the B.Com Learning Goals including, as follows, the identified course related activities: Goa l LG1 LG2 LG3 LG4 LG5 Description Link to ADM2302 Understand, Apply and Integrate Core Management Disciplines Demonstrate Critical Thinking and Decision Making Skills Demonstrate Leadership, Interpersonal and Communications Skills Identifying and structuring problems in organization (Weeks 2-4) Problem formulation, decision making in linear applications (Weeks 1-11) Presentation of individual assignments, and participation in classroom and out of class activities (all weeks) Preparation of individual and group work assignments (Weeks 4,6,10,12) Participation in group assignments, and in the large class atmosphere (all weeks) Apply high standards of Integrity, Ethics and Social Responsibility Demonstrate the Ability to Perform in a Culturally Diverse Environment Course Learning Objectives Michalowski 2014 Fall The objective of this course is to learn the fundamental approach to solving problems in organizations known as the “scientific method of problem solving”. Students will learn to apply this method including the logical formulation, mathematical model construction, testing and validation of results, and sensitivity analysis processes involved in problem resolution. Students will be required to formulate and analyze quantitative problems, interpret the results of specific mathematical models presented in class, and improve their communication skills for identifying, structuring, and recommending solutions to business problems. Regular assignments and minicases will be the means by which students will apply the techniques learned in class, and communicate problem resolutions. Course Organization Classes for Section D will be held weekly during the Fall 2014 semester on Mondays 19:00 – 22:00 in the Desmarais Building, Room DMS1120. It is expected that students come to class prepared, having read the appropriate reading materials, and completed all assignments before each lecture. Students are responsible for submitting the assignments, for preparing for the Midterm and Final exams, and for solving suggested problem sets that will be presented in the weekly lab tutorials sessions. The Mid-term Exam will be held outside regularly scheduled class on Saturday, October 25 from 13:00 to 15:30. The weekly course schedule included in this course outline contains the detailed list of readings from the text, as well as the suggested problem sets for the weekly lab tutorials sessions from material covered in class. Student Course Performance Evaluation Item 1 2 3 Deliverable Assignments (A) Mid-Term Exam (MT) Final Exam (F) Total Value 20% 30% 50% 100% Exams Note: To pass the course students must achieve a combined passing grade of 50% on the Midterm and Final exams (i.e., MT+F must be at least 40% out of total value of 80%). Students who do not meet this requirement will receive a failing grade in the course. Attendance at the Mid-Term and Final Exams is compulsory. Early departures will not be accepted as a reason for not attending the Final Exam at its regularly scheduled time. The Midterm and the Final exams are closed book exams, however, a calculator and a one-page review sheet (8.5x11, double-sided) will be allowed for both exams. The Final Exam will be comprehensive, covering all topics including those for the Mid-Term Exam. Assignments Michalowski 2014 Fall There are four (4) assignments deliverables throughout the semester that may be submitted in groups (up to 3 students in a group). All assignments are to be submitted electronically as a single PDF file. Front page of the PDF document has to include title of the assignment and names and student numbers of all members of a group. Second page is the Statement of Integrity signed by all members of a group. Electronic submission must be made prior to the start of the Monday class when the assignments are due (see also the Weekly Course Schedule below). Assigned exercises and cases emphasize all aspects of the course material. Students will be notified of texts of the assignments in class. Submitted assignments must be neat, readable, and well organized. Assignment marks will be adjusted for sloppiness, poor grammar and spelling, as well as for technical errors. Each assignment is valued equally at 10 points each. Assignment without all signatures on the Statement of Integrity will not be marked. The corresponding Personal Ethics Agreements documents are attached to this course outline. Students are asked to read the statement: “Beware of Academic Fraud” attached to this course outline and to consult and familiarize themselves with the University of Ottawa Academic Integrity website: http://web5.uottawa.ca/mcs-smc/academicintegrity/home.php. Structure and Format of the Assignment Assignment 1 asks for answering a number of questions. Assignments 2, 3, and 4 are submitted in the form of a “Report to Management”. There is no strict standard form for such a report, but presentation, organization, grammar and neatness are particularly important here. Keep in mind that the manager/decision maker—who may know little about the principles of decision models and business analytics—needs to address a problem and it is your responsibility to communicate suggested solution in this regard. Be concise and to the point—longer is usually NOT better. Consider the following logical report structure: Header - state to whom the report is addressed, and from whom it is coming, the date, and a relevant title identifying the problem (top of page 1). Introduction - present a brief statement of the problem including all options available (where applicable). Maximum length: 1 page. Recommendations - specify (in words) the recommendations with a brief and unequivocal supporting argument. Maximum length: 1 page. Analysis and Data - present the detailed data and analysis, including computations and calculations in support of the recommendations given above, e.g., Excel LP output tables go here. Organize the data and analysis in a logical fashion. Use tables and charts where convenient. Maximum length: 4 pages. Blackboard Learn Course Website Class presentations, additional course problem sets, sample exams and additional readings for course material will be made available in electronic form on the Course Website. The course Website for ADM2302 is found at the University of Ottawa’s Blackboard Learn website: Michalowski 2014 Fall https://uottawa.blackboard.com. Registered ADM2302 students are required to identify themselves via Infoweb to enter this Website and select the ADM2302D course Home Site. Class notes are in the form of PowerPoint presentations (.ppt) files, Excel spreadsheets (.xls) files and Adobe Acrobat (.pdf) files. Files of course material will be available for downloading from the Blackboard Learn course website. Supplementary materials to the text are available to students on the student Online Learning Centre http://highered.mcgraw-hill.com/sites/0078024064/information_center_view0/. The Student Edition Online Learning Centre includes a number of resources for student self-study including Excel spreadsheet tutorials and templates useful for assisting in solving the course assignment and lab problems. Students will be required to become familiar with operating business and management science software such as spreadsheets (e.g., Excel), presentation (e.g., PowerPoint) and word processing (e.g., Word) packages, as well as specialized management science software (e.g., Excel Solver, TreePlan, MS Project) and the interpretation of computergenerated results. Students registered through the Registrar’s Office in ADM2302 Section D for the Fall 2014 are pre-registered to the Blackboard Learn website. This registration allows students to contribute to the course discussion areas, view posted grades, receive internal email postings, and join in real-time chat session between the course instructor and students. Students are encouraged to use the Blackboard Learn course website “Discussion Area” for questions (viewed by all) related to assignments or course materials. Textbook/Course Package A custom textbook Business Decision Models ADM2302, ISBN 9781259259104 is a required text for the course. It is a customized version of Hillier, Frederick S., and Mark S. Hillier. 2014. Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets, 5/e. McGraw-Hill. ISBN: 0078024064. The Custom textbook can be purchased from the University of Ottawa bookstore. Also, access to the course eBook for the 4th edition (available at the time of preparation) may be found on the Web for students who wish to purchase the abridged and annotated course text using a credit card. The Web address for purchasing the 4th edition eBook is https://create.mheducation.com/shop/#/catalog/details/?isbn=9781121922129. The student Online Learning Centre noted above at URL: http://highered.mcgrawhill.com/sites/0078024064/information_center_view0/ also contains information about the textbook and supplementary material for each chapter of the textbook. Additional References (see also www.biblio.uottawa.ca/mrt/) 1. Anderson, D., D. Sweeney, and T. Williams, 2008. Management Science: Quantitative Approaches to Decision Making (12th ed.), South-Western College Publishing. 772p. + appendices. 2. Hillier, Frederick S., Mark S. Hillier 2003. Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets. (2nd ed.) McGraw-Hill. 845p. + appendices Michalowski 2014 Fall 3. Render, B., and R.M. Stair, Jr. 2009. Quantitative Analysis for Management (10th ed.). Prentice-Hall, Inc.: Upper Saddle River, New Jersey. 718p. + appendices. 4. Stevenson, William J., Ozgur, Ceyhun, and Nsakanda, A. L. 2009. Introduction to Management Science with Spreadsheets (Canadian edition). McGraw-Hill/Ryerson. 671p. + appendices. 5. Taylor, B.W. III 2007. Introduction to Management Science. (9th ed.) Prentice-Hall, Upper Saddle River, New Jersey. 771p. + appendices. Discussion Groups Weekly problem solving sessions have been established for each of the five (5) sections of ADM2302 offered in the Fall 2014 semester. Schedules and locations are provided in the University of Ottawa’s Course Timetable for ADM2302 at: https://web30.uottawa.ca/v3/SITS/timetable/Course.aspx?code=ADM2302&session=20149 Students may attend any one of the four weekly sessions of their choice and convenience according to their personal availability. Discussion Group materials (e.g., see also the column of “Discussion Group Problems” in the Weekly Course Schedule) follow the schedule of the material presented in class. Teaching Assistants will lead these Discussion Groups to answer students’ questions about the course problems, and will be prepared to discuss the solutions to the “Discussion Group Problems” each week. Students are advised to review questions and present them to the Teaching Assistant in the Discussion Group for consideration. Attendance at the weekly Discussion Group sessions is not compulsory. Michalowski 2014 Fall ADM2302 Section D: Weekly Course Schedule Week Lecture Topics 1 Sept. 8 2 Sept. 15 Course Organization; Origins of MS/OR Chap 1,pp. 9-25 None Discussion Group Problems None Introduction to Linear Programming (LP) Solving LP Chap 2, pp.32-63 Suppl. Chap 2, pp.75-91 None Chap 1, #1, 3, 4, 5, 7 3 Sept. 22 4 Sept. 29 LP Solutions: Excel Spreadsheets; LP Formulation and Applications I LP Formulation and Applications II 5 Oct. 6 What-If / Sensitivity Analysis for LP Oct. 13 6 Oct. 20 Oct. 25 7 Oct. 27 Special Case LPs: Transportation and Assignment Problems MID-TERM EXAM on Saturday Oct. 25 13:00-15:30 Integer and Binary Programming I Textbook Readings* Chap 3, pp. 98-128 Chap 4, pp.172-193 Chap 3, pp.98-128 Appendix A, pp. 631-636 Chap 5, pp. 200-251 Chap 2, #2, 3, 5, 6, 9, 12, 17 None Chap 3, #1, 3, 7, 10, 12, 16, 18 Chap 4, #2, 7, 10 Study Week Break (no classes) Chap 3, pp.129-136 Assignment 2: LP and Chap 6, pp.252-260 Sensitivity Analysis Chap 15, pp.447-513 Due: Mon., October 27 Chaps 1-6, 15 pp. 9-260, 447-513 Chap 7, pp. 296-357 None Integer and Binary Programming Goal Programming Chap 17, pp.597-629 9 Nov. 10 Decision Analysis I Tables and Trees 10 Nov. 17 Decision Analysis II (continued) Value of Information Project Management: Chap 9, pp.358-366; pp.366-369 Suppl. Chap 9, pp. 425-439 Chap 9, pp. 369-386 Michalowski 2014 Assignment 1: Graphical LP Due: Mon., September 29 None 8 Nov. 3 11 Nov. 24 Homework Chap 16, pp. 515564 Assignment 3: Integer, Binary, and Goal LP Due: Mon., November 17 None Assignment 4: Decision Analysis Due: Mon., December 1 None Chap 5, #1, 2, 5, 7, 8, 11 Chap 3, #17, 27 Chap 6, #2, 4 Chap 15, #2, 3, 4, 6, 7, 15, 17, 20 Chap 7, #2, 3, 11, 17 Chap 17, #2, 4, 5, 17 Chap 9, #1, 2, 3, 4, 9, 22, 23 Chap 9, #24, 25, 26 Chap 16, #4, 5, 9, 11 Chap 16, #13, Fall 12 Dec. 1 Final Review All chapters None 17, 19a; Course Review * Note: Page numbers refer to Custom Text top of page number. Michalowski 2014 Fall Pour les étudiants ayant besoin d’un soutien à l’apprentissage Les étudiants qui ont besoin d’accommodements d’examen ou autre soutien scolaire en raison d’une condition physique, d’un trouble d’apprentissage ou de toute autre condition qui affecte leur capacité d’apprendre, sont invités à s’inscrire au SERVICE D’ACCÈS : En personne : UCU 339 Par téléphone : 562-5976 ATS : 562-5214 Par courriel : adapt@uottawa.ca Par Internet : www.sass.uottawa.ca Les étudiants pourront par la suite rencontrer un spécialiste du Service d’accès pour déterminer leurs besoins individuels ainsi que les interventions pertinentes. DATES IMPORTANTES À SE RAPPELER Demande d’accommodement pour tout examen de mi-session : Toute demande doit être présentée au Service d’accès au moins 7 jours (excluant le jour de l’examen et tout congé férié) avant la date de l’examen, du test, du quiz ou autres évaluations écrites. Demande d’accommodement pour tout examen final : En session d’automne: avant le 15 novembre En session d’hiver: avant le 15 mars En session printemps/été: 7 jours avant la date de l’examen (excluant le jour de l’examen et tout congé férié) ************************** For students in need of learning supports Students who require accommodations or academic support because of a physical or learning disability, or any condition that affects their ability to learn, are invited to register with ACCESS SERVICE: In person: UCU 339 Telephone: 562-5976 TTY: 562-5214 E-mail: adapt@uottawa.ca Web: www.sass.uottawa.ca Students can then meet with an Access Service specialist to identify their individual needs and to discuss appropriate interventions. IMPORTANT DATES TO REMEMBER For requesting accommodations for a mid-term examination: Requests must be submitted at least 7 days (not including the day of the exam nor any statutory holiday) prior to the writing date of mid-terms, tests, quizzes or other forms of written evaluations. For requesting accommodations for final exams: Fall Semester: before 15 November Winter Semester: before 15 March Michalowski 2014 Fall Spring/Summer Semester: 7 days prior to the exam (not including the day of the exam nor any statutory holiday) Michalowski 2014 Fall Beware of Academic Fraud Academic fraud is an act committed by a student to distort the marking of assignments, tests, examinations and other forms of academic evaluation. Academic fraud is neither accepted nor tolerated by the University. Anyone found guilty of academic fraud is liable to severe academic sanctions. Here are a few examples of academic fraud: • engaging in any form of plagiarism or cheating; • presenting falsified research data; • handing in an assignment that was not authored, in whole or in part, by the student; • submitting the same assignment in more than one course, without the written consent of the professors concerned In recent years, the development of the Internet has made it much easier to identify academic plagiarism. The tools available to your professors allow them to trace the exact origin of a text on the Web, using just a few words. In cases where students are unsure whether they are at fault, it is their responsibility to consult the University’s Web site at the following address, where you will find resources, tips and tools tools for writing papers and assignments: http://web5.uottawa.ca/mcs-smc/academicintegrity/home.php Persons who have committed or attempted to commit (or have been accomplices to) academic fraud will be penalized. Here are some examples of the academic sanctions, which can be imposed: • a grade of “F” for the assignment or course in question; • an additional program requirement of between three and thirty credits; • suspension or expulsion from the School. Please be advised that professors have been formally advised to report every suspected case of academic fraud. In most cases of a first offence of academic fraud, the sanction applied to students who have been found guilty is an “F” for the course with an additional three credits added to their program requirements. Repeat offenders are normally expulsed from the School of Management. Finally, The Telfer School of Management asks that students sign and submit with their deliverables the Personal Ethics Agreement form. Two versions of this form exist: one for individual assignments, and one for group submissions. Assignments will not be accepted or marked if this form is not submitted and signed by all authors of the work. We hope that by making this personal commitment, all students will understand the importance the School places Michalowski 2014 Fall on maintaining the highest standards of academic integrity. The forms are accessible on docdepot: En français: http://doc-depot.gestion.uottawa.ca/ (et suivez le lien ‘Intégrité Académique’). In English: http://doc-depot.management.uottawa.ca/ (then click on ‘Academic Integrity’). Personal Ethics Agreement Concerning University Assignments By signing this Statement, I am attesting to the fact that I have reviewed not only my own work, but the work of my colleagues, in its entirety. I attest to the fact that my own work in this project meets all of the rules of quotation and referencing in use at the Telfer School of Management at the University of Ottawa, as well as adheres to the fraud policies as outlined in the Academic Regulations in the University’s Undergraduate Studies Calendar. I further attest that I have knowledge of and have respected the “Beware of Plagiarism” brochure (https://www.uottawa.ca/about/sites/www.uottawa.ca.about/files/plagiarism.pdf). To the best of my knowledge, I also believe that each of my group colleagues has also met the rules of quotation and referencing aforementioned in this Statement. I understand that if my group assignment is submitted without a signed copy of this Personal Ethics Statement from each group member, it will be interpreted by the Telfer School of Management that the missing student(s) signature is confirmation of non-participation of the aforementioned student(s) in the required work. ________________________________ Signature _______________ Date ________________________________ Last Name (print), First Name (print) _______________ Student Number ________________________________ Signature _______________ Date ________________________________ Last Name (print), First Name (print) _______________ Student Number ________________________________ Signature _______________ Date ________________________________ _______________ Michalowski 2014 Fall Last Name (print), First Name (print) Michalowski 2014 Student Number Fall

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