Resource-Constrained Project Scheduling — Minimization of Project Duration

Abstract

Thus far, we have not taken account of the limited availability of resources which are required for carrying out the activities of a project. In what follows, we are going to take scarce resources into consideration. In practice, different types of resources may occur. Renewable resources (such as machines, equipment, manpower, or space) are available at each point in time or, if time is discrete, in each single time period during the execution of the project independently of their utilization formerly. Nonrenewable resources (e.g. money or energy) are depleted by use. Nonrenewable resources only affect the scheduling of activities if activities can be carried out in alternative modes which differ, for example, in duration and amount of resources needed. We then speak of multi-mode project scheduling problems in contrast to single-mode problems. Doubly-constrained resources are restricted at each point in time (or in each time period if time is discrete) during the execution of the project and for the whole project (for example, money with restricted cash flow per period and limited amount of capital available). A doubly-constrained resource can be replaced by a combination of a renewable and a nonrenewable resource. Cumulative or storage resources represent stock-keeping facilities. They can store a single or several different products and have a prescribed minimum and maximum inventory, where the inventory is generally depleted and replenished over time. Sometimes, the activities are divided into families containing activities with similar properties. Synchronizing resources process the activities from such a family batchwise, where all activities in a batch must be started at the same time. Examples of synchronizing resources are furnaces or autoclaves in process industries. In literature, additional resource types have been discussed: partially renewable resources (cf. Böttcher et al., 1999), whose capacity refers to sets of time periods, and spatial resources (see de Boer, 1998, and Demeulemeester and Herroelen, 2002, Ch. 2, Subsect. 2.2.5), for which resource requirements refer to activity families instead of individual activities and resource units are occupied from the start of the first up to the completion of the last activity of the family.