The Analysis of Activity Networks Under Generalized Precedence Relations (GPRs)
We present a model for activity networks under generalized precedence relations (GPRs), discuss its temporal analysis and the issues that may arise relative to inconsistency among the specified relations and the activity durations. We also give more precise definition to the concept of criticality o...
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| Veröffentlicht in: | Management science 1992-09, Vol.38 (9), p.1245-1263 |
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| creator | Elmaghraby, Salah E Kamburowski, Jerzy |
| description | We present a model for activity networks under generalized precedence relations (GPRs), discuss its temporal analysis and the issues that may arise relative to inconsistency among the specified relations and the activity durations. We also give more precise definition to the concept of criticality of an activity, and introduce the new concept of flexibility of an activity which is akin to the traditional concept of activity floats in regular CPM, with the latter taking on different meaning from its common interpretation in standard CPM.
Issues of optimization are raised when one assumes, for each activity, a piecewise-linear time-cost function that permits positive and negative deviations from its least-cost duration between specified lower and upper bounds on that duration. We seek the optimal activity durations subject to the specified GPRs and a given due date . We also seek the construction of the complete project duration-cost function between the project minimum duration and its least-cost duration when the due date is interpreted, first, as a "deadline" and, second, as a "target date" with rewards for early, and penalties for late completion. The relations between the problems posed and the uncapacitated minimum cost flow problems are revealed and are utilized in the algorithmic solution of the problems. |
| doi_str_mv | 10.1287/mnsc.38.9.1245 |
| format | Article |
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Issues of optimization are raised when one assumes, for each activity, a piecewise-linear time-cost function that permits positive and negative deviations from its least-cost duration between specified lower and upper bounds on that duration. We seek the optimal activity durations subject to the specified GPRs and a given due date . We also seek the construction of the complete project duration-cost function between the project minimum duration and its least-cost duration when the due date is interpreted, first, as a "deadline" and, second, as a "target date" with rewards for early, and penalties for late completion. The relations between the problems posed and the uncapacitated minimum cost flow problems are revealed and are utilized in the algorithmic solution of the problems.</description><identifier>ISSN: 0025-1909</identifier><identifier>EISSN: 1526-5501</identifier><identifier>DOI: 10.1287/mnsc.38.9.1245</identifier><identifier>CODEN: MSCIAM</identifier><language>eng</language><publisher>Linthicum, MD: INFORMS</publisher><subject>activity networks ; Algorithms ; Applied sciences ; Arc length ; Cost efficiency ; Cost functions ; Critical path ; criticality ; Economic models ; Exact sciences and technology ; flexibility ; Flows in networks. Combinatorial problems ; generalized precedence ; Management science ; Mathematical minima ; Minimization of cost ; minimum cost flow ; Modeling ; Operational research and scientific management ; Operational research. Management science ; PERT ; Polynomials ; Salah ; Scheduling ; Statistical models ; time-cost trade-off</subject><ispartof>Management science, 1992-09, Vol.38 (9), p.1245-1263</ispartof><rights>Copyright 1992 The Institute of Management Sciences</rights><rights>1992 INIST-CNRS</rights><rights>Copyright Institute for Operations Research and the Management Sciences Sep 1992</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c476t-d9bfb7ca7d6e8abcc4adc260d8cf6e42c8397c9199789c5c650a044efddebb183</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2632632$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/mnsc.38.9.1245$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,780,784,803,3692,4008,27869,27924,27925,58017,58250,62616</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5545222$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/inmormnsc/v_3a38_3ay_3a1992_3ai_3a9_3ap_3a1245-1263.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Elmaghraby, Salah E</creatorcontrib><creatorcontrib>Kamburowski, Jerzy</creatorcontrib><title>The Analysis of Activity Networks Under Generalized Precedence Relations (GPRs)</title><title>Management science</title><description>We present a model for activity networks under generalized precedence relations (GPRs), discuss its temporal analysis and the issues that may arise relative to inconsistency among the specified relations and the activity durations. We also give more precise definition to the concept of criticality of an activity, and introduce the new concept of flexibility of an activity which is akin to the traditional concept of activity floats in regular CPM, with the latter taking on different meaning from its common interpretation in standard CPM.
Issues of optimization are raised when one assumes, for each activity, a piecewise-linear time-cost function that permits positive and negative deviations from its least-cost duration between specified lower and upper bounds on that duration. We seek the optimal activity durations subject to the specified GPRs and a given due date . We also seek the construction of the complete project duration-cost function between the project minimum duration and its least-cost duration when the due date is interpreted, first, as a "deadline" and, second, as a "target date" with rewards for early, and penalties for late completion. The relations between the problems posed and the uncapacitated minimum cost flow problems are revealed and are utilized in the algorithmic solution of the problems.</description><subject>activity networks</subject><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Arc length</subject><subject>Cost efficiency</subject><subject>Cost functions</subject><subject>Critical path</subject><subject>criticality</subject><subject>Economic models</subject><subject>Exact sciences and technology</subject><subject>flexibility</subject><subject>Flows in networks. Combinatorial problems</subject><subject>generalized precedence</subject><subject>Management science</subject><subject>Mathematical minima</subject><subject>Minimization of cost</subject><subject>minimum cost flow</subject><subject>Modeling</subject><subject>Operational research and scientific management</subject><subject>Operational research. 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We also give more precise definition to the concept of criticality of an activity, and introduce the new concept of flexibility of an activity which is akin to the traditional concept of activity floats in regular CPM, with the latter taking on different meaning from its common interpretation in standard CPM.
Issues of optimization are raised when one assumes, for each activity, a piecewise-linear time-cost function that permits positive and negative deviations from its least-cost duration between specified lower and upper bounds on that duration. We seek the optimal activity durations subject to the specified GPRs and a given due date . We also seek the construction of the complete project duration-cost function between the project minimum duration and its least-cost duration when the due date is interpreted, first, as a "deadline" and, second, as a "target date" with rewards for early, and penalties for late completion. The relations between the problems posed and the uncapacitated minimum cost flow problems are revealed and are utilized in the algorithmic solution of the problems.</abstract><cop>Linthicum, MD</cop><pub>INFORMS</pub><doi>10.1287/mnsc.38.9.1245</doi><tpages>19</tpages></addata></record> |
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| ispartof | Management science, 1992-09, Vol.38 (9), p.1245-1263 |
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| source | Informs; RePEc; Periodicals Index Online; EBSCOhost Business Source Complete; Jstor Complete Legacy |
| subjects | activity networks Algorithms Applied sciences Arc length Cost efficiency Cost functions Critical path criticality Economic models Exact sciences and technology flexibility Flows in networks. Combinatorial problems generalized precedence Management science Mathematical minima Minimization of cost minimum cost flow Modeling Operational research and scientific management Operational research. Management science PERT Polynomials Salah Scheduling Statistical models time-cost trade-off |
| title | The Analysis of Activity Networks Under Generalized Precedence Relations (GPRs) |
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