Project Scheduling with Modular Project Completion on a Bottleneck Resource

Abstract

Abstract. In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project in order to maximize the expected profit when the activities have a probability of failure and when an activity's failure can cause its module and thereby the overall project to fail. A module succeeds when at least one of its constituent activities is successfully executed. All activities are scheduled on a scarce resource that is modeled as a single machine. We describe various policy classes, establish the relationship between the classes, develop exact algorithms to optimize over two different classes (one dynamic program and one branch-and-bound algorithm), and examine the computational performance of the algorithms on two randomly generated instance sets.Key words. scheduling, uncertainty, research and development, activity failures, modular precedence network AMS subject classifications. 90B35, 90B36, 90C27, 68M201. Introduction. Activities in a practical project are typically subject to many uncertainties; the most frequently studied types of uncertainty are resource breakdowns and duration variability. In research and development (R&D), activities may also fail altogether, for instance because the new technology under study does not perform as anticipated or because a toxicity test is not passed (in case of drug development). We model an R&D project as consisting of several modules, with each module containing one or more activities that pursue a homogeneous target, for instance representing repeated trials or technological alternatives. Each activity has a cost, a duration and a probability of success. A module is successful when at least one of its included activities succeeds. The successful completion of the whole project requires the successful completion of all the modules; project success equates with receiving a project payoff (cash inflow). This setup is subsequently referred to as 'modular project completion'. The objective is to schedule the activities in such a way that a maximum expected profit is attained. A solution to this scheduling problem is a policy, which is a dynamic decision rule that decides which activities are to be started at which time. We examine the scheduling of the project activities on a single machine, representing a scarce or bottleneck resource. Examples of such scarce resources are specialized equipment, or departments or individuals with specific areas of expertise (see Kavadias and Loch [14] for a similar motivation in a slightly different setting).The main contributions of this paper are fivefold: (1) we introduce and formulate a generic model for optimally scheduling R&D projects with modular completion; (2) we describe various scheduling policy classes and examine the relationship between the classes; (3) we provide an analysis of a number of properties; (4) we develop exact algorithms to optimize over two different classes (one dynamic program and o...

A fast greedy heuristic for scheduling modular projects

“…This problem has been proved to be NP-hard, even for certain restrictive special cases (Coolen et al 2014). This means that, unless P = NP, no exact polynomial-time algorithm exists, which motivates our search for an efficient heuristic that provides good solutions to MP1 instances in polynomial time.…”

“…Finally, the transitions from a given state and selected action at a decision epoch to the state at the next decision epoch are determined by the success and failure probabilities of the jobs. Coolen et al (2014) propose a backward stochastic dynamic-programming algorithm with state space as described in this paragraph. The value function can be computed recursively by choosing at each state the best allowable action based on the best allowable actions determined at previously computed states in the dynamic-programming algorithm.…”

“…Various classes of scheduling policies are presented in Coolen et al (2014); the definitions below mainly draw from that source. We will restrict our solution space to only one class, namely the 'elementary module-sequence policies.…”

“…Projects such as those described above will be referred to as modular projects. Exact scheduling algorithms for this type of projects have recently been developed by Coolen et al (2014). Ranjbar and Davari (2013) propose exact algorithms for a special case of this problem with only one module, but the cash flows are discounted.…”

“…The main contribution of this paper is the development of a heuristic that produces 'good' schedules for such projects, i.e., schedules with a high expected profit, while requiring only very limited CPU time and computer memory. We compare the results to the optimal solutions obtained by the algorithms described in Coolen et al (2014).…”