IJE TRANSACTIONS B: Applications Vol. 31, No. 5 (May 2018) 770-779    Article in Press

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H. R. Mollaei, R. Tavakkoli-Moghaddam and A. Toloie-Eshlaghy
( Received: October 23, 2017 – Accepted in Revised Form: January 04, 2018 )

Abstract    The purpose of this problem is to choose a set of project activities for crashing, in a way that the expected project time, cost and risk are minimized and the expected quality is maximized. In this problem, each project activity can be performed with a specific executive mode. Each executive mode is characterized with four measures, namely the expected time, cost, quality and risk. In this paper, linear relationships between time and cost, and between time and quality are omitted and the problem of the expected time-cost-quality tradeoff is considered in a probabilistic and discrete state. Then, to make the problem more real, the combination of four measures are considered as uncertain for each executive mode. It means that time, cost, quality or risk (or all of them) of each activity in each executive mode is considered as the expected numbers (probabilistic means). After modeling three objective problems, a test problem with nine activities is presented and solved by the NSGA-II algorithm. In order to improve the results and speed of the proposed algorithm in accessing Pareto solutions, a new hybrid algorithm, called MEM-NSGA, is presented that gives better solutions than the NSGA-II algorithm in the same conditions.


Keywords    Project scheduling; Risk based project planning; Discrete Time–Cost–Quality-risk Trade-off; Evolutionary algorithm.


چکیده    هدف از این مسئله ، انتخاب مجموعه‌اي از فعاليت‌هاي پروژه براي فشرده‌سازي است، بطوريکه هزينه مورد انتظار و مدت‌زمان اتمام مورد انتظار و ريسک پروژه کمينه و کيفيت کل مورد انتظار پروژه بيشينه شود. در اين مسئله هر فعاليت پروژه مي‌تواند با روشهاي اجرايي مشخص اجرا شود. هر روش اجرا با چهار مشخصهE(t)،E(c) ، E(q) و R بيان مي‌شود، که به ترتيب بيانگر زمان، هزينه و کيفيت مورد انتظار و ريسک کلي مربوط به هر مد اجرائي آن فعاليت است. در اين مقاله با حذف رابطه خطي بين زمان-هزينه و زمان-کيفيت، مسئله موازنه هزينه-زمان-کيفيت-ريسک را در حالت گسسته (DTCQRTP) و احتمالي بررسي مي‌کند و سپس براي واقعي‌تر کردن مسئله، ترکيب چهارتايي مشخصه هاي(t,c,q,r) را براي هر روش اجرايي به‌ صورت غيرقطعي مطرح مي‌کند. يعني اينکه زمان يا هزينه يا کيفيت يا ريسک ( يا هر چهار معيار) هر فعاليت در هر روش اجرايي ، به‌ صورت اعداد انتظاري(ميانگين احتمالي) خواهد بود. پس از مدلسازي مساله چهار هدفه، يک مساله کاربردي با نه فعاليت، ارائه شده و با الگوريتم NSGA-II کد نويسي و حل شده است و براي افزايش سرعت دسترسي به جوابهاي پارتو و بهبود جوابها، الگوريتم ترکيبي MEM-NSGA بصورت ابتکاري ارائه شده است، که در شرايط يکسان جوابهاي بهتري را نسبت به الگوريتم NSGA-II ارائه نموده است.


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