STOCHASTIC NETWORK PROJECT SCHEDULING WITH NON-CONSUMABLE LIMITED RESOURCES

This paper presents a newly developed resource constrained scheduling model for a PERT type project. Several non-consumable activity related resources, such as machines or manpower, are imbedded in the model. E ach activity in a project requires resources of various types with fix ed capacities. Each type of resource is in limited supply with a resou rce limit that is fixed at the same level throughout the project durat ion. For each activity, its duration is a random variable with given d ensity function. The problem is to determine starting lime values S-ij for each activity (i,j) entering the project, i.e., the timing of fee ding-in resources for that activity. Values S-ij. are not calculated b eforehand and are random values conditional on our decisions. The mode l's objective is to minimize the expected project duration. Determinat ion of values S-ij is carried out at decision points when at least one activity is ready to be operated and there are free available resourc es. If, at a certain point of time, more than one activity is ready to be operated but the available amount of resources is limited, a compe tition among the activities is carried out in order to choose those ac tivities which can be supplied by the resources and which have to be o perated first. We suggest carrying out the competition by solving a ze ro-one integer programming problem to maximize the total contribution of the accepted activities to the expected project duration. For each activity, its contribution is the product of the average duration of t he activity and its probability of being on the critical path in the c ourse of the project's realization. Those probability values are calcu lated via simulation. Solving a zero-one integer programming problem a t each decision point results in the following policy: the project man agement takes all measures to first operate those activities that, bei ng realized, have the greatest effect of decreasing the expected proje ct duration. Only afterwards, does the management take care of other a ctivities. A heuristic algorithm for resource constrained project sche duling is developed. A numerical example is presented.