Lectures 20 and 21
Lectures 20 and 21 CEE 270
Popular in System Analysis and Economic Civil Engineering
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This 3 page Class Notes was uploaded by Nathaniel Bautz on Friday April 10, 2015. The Class Notes belongs to CEE 270 at University of Massachusetts taught by Bernd Schliemann in Spring2015. Since its upload, it has received 90 views. For similar materials see System Analysis and Economic Civil Engineering in Civil and Environmental Engineering at University of Massachusetts.
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Date Created: 04/10/15
O 90 O 90 LECTURE 20 TRANSPORTATION AND TRANSSHIPMENT Transportation Problem gt A set of m sources from which a good is shipped Source i can supply at most si units gt A set of 11 destinations to which a good is shipped Destination j must receive at least dj units gt Each unit produced at source i and shipped to destination j incurs a unit cost of cij gt Objective is to satisfy the LP and minimize cost or maximize revenue Applications Transportation of goods Power distribution Water supply Production scheduling Work scheduling Distribution centers do not use The Prototype Example gt Three canneries produce canned peas supply gt Four warehouses receive peas from canneries demand gt Shipping cost per truckload between canneries and warehouse depends on distance labor costs and etc Notation gt m sources in row i where i 1 2 m gt 11 destinations in column j where j 1 2n gt cij cost per unit distributed gt u shadow price for supply constraint gt v shadow price for demand constraint Assumptions gt Requirements assumption fixed and balanced supply as well as demand gt Cost assumption total shipping cost is directly proportional to the number of units shipped gt Integer solutions assumption if si and dj are integers all basic variables will be integers Streamlined Simplex Steps gt 1 Initialization I Build transportation simplex tableau Find initial BF solution mn 1 using NW corner rule gt 2 Optimality Test I Basic cij ui vj Nonbasic cij ui vj 2 0 Iteration Select entering basic variable most negative I Determine leaving basic variable chain reaction I Determine new BF solution gt 4 Return to step 2 Transportation Issues VVVVVV V m O 90 gt Big M method gt Dummy source destination gt Basic variables can take on a value of 0 gt Degeneracy Transshipment Problem gt Shipments allowed between sources and destinations gt Distribution centers permitted transshipment points LECTURE 21 CRITICAL PATH METHOD 0 9 Projects amp Project Management gt Project goals I Complete on time or before I Not exceed budget I Meet specifications to customer satisfaction gt Define scope time frame resources gt Select the project manager team structure gt CPM PERT network or Gantt Chart Network Diagrams gt Precedent relationships determine the sequence for undertaking activities gt Activity times must be estimated using historical information statistical analysis learning curves or informed estimates gt In the activityonnode approach AON nodes represent activities and arcs represent the relationships between activities Develop a Project Network gt Iterative draft on scratch paper gt Keep writing out nodes and arcs gt Rearrange to remove intersecting arcs gt Don t forgot two special nodes I START I FINISH Scheduling Activities Forward Pass ES Earliest start time of an activity when there is no delay anywhere EF Earliest finish time of an activity when there is no delay anywhere d duration of an activity EF ES d Go forwards through the project network ES largest EF of immediate predecessors cheduling Activities Backward Pass LS Latest start time of an activity without delaying the project LF Latest finish time of an activity without delaying the project d duration of an activity LS LF d Go backwards through the project network WVVVVVV VVVVV gt LF smallest LS of immediate successors Slack gt A measure of how much an activity can be delayed without delaying the whole project gt SlackLS ES LF EF gt Slack 0 on the critical path Questions to be Answered gt Total time required to finish gt When to start and finish each activity gt Which are critical bottlenecks gt For other activities how much delay can be tolerated Crashing Activities gt Taking measures to reduce activity duration 39 Overtime I Temporary help 39 Special equipment I More costly materials e g finished lumber Marginal Analysis Iterative Method gt 1 Start from the critical paths gt 2 Pick an activity or a combination of activities with the lowest crash cost per week AND positive allowed reduction time that will reduce the length of the critical path by one week gt 3 Reduce each picked activity duration by one week gt 4 Reduce the allowed reduction time of each crashed activity by one week gt 5 Recalculate the critical path Go back to Step 2 gt 6 Stop when the desired project duration is reached For Multiple Critical Paths gt 1 Check activities on all critical paths gt 2 Find the least expensive way of shortening ALL critical paths by one week Note only when all critical paths are reduced by one week will the project duration be reduced by one week gt 3 Can crash one activity or a number of activities gt 4 Can be very complicated as the number of options can be large