حل مسيله‌ي موازنه هزينه ـ زمان و كيفيت پروژه با استفاده از برنامه ريزي تصادفي چندهدفه

SOLVING TIME COST AND QUALITY TRADE OFF PROJECT PROBLEM USING MULTI OBJECTIVE STOCHASTIC PROGRAMMING

مسيله‌ي موازنه‌ي هزينه‌ـ زمان در پروژه‌ها از مباحث مهمي است كه مورد توجه محققين زيادي بوده است، اما تعداد اندكي از اين تحقيقات محيط هاي تصادفي را مورد توجه قرار داده اند. از طرف ديگر، كيفيت پروژه نيز يكي از مواردي است كه مديران پروژه به آن علاقه مندند كه در تحقيقات مورد توجه چنداني قرار نگرفته است. در اين نوشتار مسيله‌ي موازنه‌ي هزينه ـ زمان با در نظر گرفتن عامل كيفيت پروژه به‌عنوان يكي از اركان پروژه با پارامتر تصادفي تاخير در فعاليت هاي پروژه در هنگام فشرده‌سازي مورد بررسي واقع مي‌شود. در اين راستا ابتدا يك مدل تصادفي موازنه‌ي هزينه ـ زمان و كيفيت پروژه توسعه داده مي‌شود، آنگاه براي حل مدل از مفهوم برنامه ريزي سازشي مقيد‌شده‌ي تصادفي استفاده مي‌شود و در نهايت براي تشريح مدل و حصول نتايج، كاربرد آن در يك پروژه‌ي واقعي در زمينه‌ي استقرار مخازن گاز مايع مورد بررسي قرار مي گيرد. نتايج بيان‌گر كاربردي بودن مدل ما در مسايل واقعي‌اند.

The crashing of project times is not a new topic in the project management area and its history returns to CPM and PERT network development. New views and methods have been presented about the time-cost trade off in recent years. Generally, the completion time of projects could be shortened by reviewing project network logic or crashing the activities through expending more cost. Note that any reduction in the duration of activities could affect their quality. In other words, crashing could decrease the closeness rate of project deliverables from the employer or customer expectation levels. Ambiguity is an unavoidable factor in most activity duration estimates, and uncertainty is another problem that always goes along with project scheduling. By reviewing the literature, it was found that researchers often try to optimize a specific objective function, while, in real world problems, a project might have several objectives simultaneously. In this paper, we try to study the project scheduling problem in a multi-objective stochastic state. On the other hand, it might be an unpredictable lag that occurs for each activity which affects successor scheduling and the delivery date of the project, finally. This fact increases the importance of scheduling lags and the necessity of compensation or their avoidance. When project managers decide to shorten activities by expending cost, this problem becomes more important. So, it is necessary to consider the stochastic lags of each activity, which might occur after crashing, in project scheduling and the time-cost trade off problem. Since the duration time of these lags is not determined, we can consider them stochastic. Hence, applying stochastic objective functions in these problems is another innovation of this study, which could help to realize better than ever results. In this paper, the time-cost trade off problem, with quality (TCQTP) as a key element of the projects, is discussed, while crashing with stochastic lags is occurred in activities. First, a stochastic time-cost-quality model has been developed, and then, we use Chance Constrained Compromise Programming (CCCP) to solve it. Eventually, the ability of the proposed model is illustrated through a real case study in a Liquid Gas Tank Establishment (LGTE) project. The results demonstrate the applicability of our model in real world problems.