Morteza Davari

Two branch-and-bound algorithms for the robust parallel machine scheduling problem

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem of scheduling a given number of jobs on a specified number of identical parallel machines when the processing time of each job is stochastic. Our goal is to find a robust schedule that maximizes the customer service level, which is the probability of the makespan not exceeding the due date. We develop two branch-and-bound algorithms for finding an optimal solution; the two algorithms differ mainly in their branching scheme. We generate a set of benchmark instances and compare the performance of the algorithms based on this dataset.

An exact method for scheduling of the alternative technologies in R&D projects

A fundamental challenge associated with research or new product development projects is identifying that innovative activity that will deliver success. In such projects, it is typically the case that innovative breakthroughs can be achieved by any of several possible alternative technologies, some of which may fail due to the technological risks involved. In some cases, the project payoff is obtained as soon as any single technology is completed successfully. We refer to such a project as alternative-technologies project and in this paper we consider the alternative-technologies project scheduling problem. We examine how to schedule alternative R&D activities in order to maximize the expected net present value, when each technology has a cost and a probability of failure. Although a branch-and-bound algorithm has been presented for this problem in the literature, we reformulate the problem and develop a new and improved branch-and-bound algorithm. We show using computational results that the new algorithm is much more efficient and outperforms the previous one.

Exact algorithms for single-machine scheduling with time windows and precedence constraints

We study a single-machine scheduling problem that is a generalization of a number of problems for which computational procedures have already been published. Each job has a processing time, a release date, a due date, a deadline, and a weight representing the penalty per unit-time delay beyond the due date. The goal is to schedule all jobs such that the total weighted tardiness penalty is minimized and both the precedence constraints as well as the time windows (implied by the release dates and the deadlines) are respected. We develop a branch-and-bound algorithm that solves the problem to optimality. Computational results show that our approach is effective in solving medium-sized instances, and that it compares favorably with existing methods for special cases of the problem.

A novel branch-and-bound algorithm for the chance-constrained RCPSP

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a MILP formulation that solve the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. Since solving CC-RCPSP is computationally intractable, its sample average approximation counterpart is considered to be solved. The computational results suggest that the proposed branch-and-bound procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.

Important classes of reactions for the proactive and reactive resource-constrained project scheduling problem

The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2017), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a baseline schedule and a set of required transitions (reactions). In this research, we introduce two interesting classes of reactions, namely the class of selection-based reactions and the class of buffer-based reactions, the latter in fact being a subset of the class of selection-based reactions. We also discuss the theoretical relevance of these two classes of reactions. We run some computational results and report the contributions of the selection-based reactions and the buffer-based reactions in the optimal solution. The results suggest that although both selection-based reactions and buffer-based reactions contribute largely in the construction of the optimal PR-policy, the contribution of the buffer-based reactions is of much greater importance. These results also indicate that the contributions of non-selection-based reactions (reactions that are not selection-based) and selection-but-not-buffer-based reactions (selection-based reactions that are not buffer-based) are very limited.

The Proactive and Reactive Resource-Constrained Project Scheduling Problem: The Crucial Role of Buffer-Based Reactions

The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2016a), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a baseline schedule and a set of required transitions (reactions). In this research, we introduce two interesting classes of reactions, namely the class of selection-based reactions and the class of buffer-based reactions. We also discuss the theoretical relevance of these two classes of reactions. We run some computational results and report the contributions of the selection-based reactions and the buffer-based reactions in the optimal solution. The results suggest that although both selection-based reactions and buffer-based reactions contribute largely in the construction of the optimal PR-policy, the contribution of the buffer-based reactions is of much greater importance.

The Proactive and Reactive Resource-Constrained Project Scheduling Problem

Uncertainty has become an inevitable aspect of project scheduling. We study the resource-constrained project scheduling problem (RCPSP) with stochastic durations. One of the most studied approaches to deal with stochastic durations is that of proactive and reactive scheduling. In this paper, we formulate an integrated proactive and reactive scheduling problem with a combined cost function which includes a baseline schedule cost as well as costs of a series of reactions. We propose four dynamic programming based models (Models 1-4) that solve the problem until optimality over different classes of policies. We compare our models with each other and with a combination of a traditional proactive solution (STC) and a reactive solution (RP SGS). Computational results show that Model 2 outperforms the traditional solution only when reaction costs are greater than zero. Moreover, Model 3 and Model 4 clearly outperform Model 1 and Model 2 in all settings and the traditional solution in most of the settings.