Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

Exact and suboptimal reactive strategies for resource-constrained project scheduling with uncertain resource availabilities.

In order to cope with the uncertainty inherent in practical project management, proactive and/or reactive strategies can be used. Proactive strategies try to anticipate future disruptions by incorporating slack time or excess resource availability into the schedule, whereas reactive strategies react after a disruption happened and try to revert to a feasible schedule. Traditionally, reactive approaches have focused on obtaining a good schedule with respect to the original objective function or a schedule that deviates as little as possible from the baseline schedule. In this paper, we present various approaches, exact as well as heuristic, for optimizing the latter objective and thus encouraging schedule stability. Furthermore, in contrast to traditional rescheduling algorithms, we present a new heuristic that also takes future uncertainty into account when repairing the schedule. We consider a variant of the resource- constrained project scheduling problem in which the uncertainty is modeled by means of unexpected resource breakdowns. The results of an extensive computational experiment are given to compare the performance of the proposed strategies.Schedule stability; Stability; Algorithms; Heuristic; Uncertainty; Project scheduling; Scheduling; Performance; Strategy; Order; Project management; Management; Time;

The single machine earliness and tardiness scheduling problem: lower bounds and a branch-and-bound algorithm

This paper addresses the single machine scheduling problem with a common due date aiming to minimize earliness and tardiness penalties. Due to its complexity, most of the previous studies in the literature deal with this problem using heuristics and metaheuristics approaches. With the intention of contributing to the study of this problem, a branch-and-bound algorithm is proposed. Lower bounds and pruning rules that exploit properties of the problem are introduced. The proposed approach is examined through a computational comparative study with 280 problems involving different due date scenarios. In addition, the values of optimal solutions for small problems from a known benchmark are provided.Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP[06/03496-3]""Conselho Nacional de Desenvolvimento Cientifico e Tecnologico"" - CNPq[486124/2007-0]""Conselho Nacional de Desenvolvimento Cientifico e Tecnologico"" - CNPq[307399/2006-0

A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem

We consider the single-machine total weighted tardiness problem (TWT) where a set of n jobs with general weights w_1,…, w_n, integer processing times p_1,…, p_n, and integer due dates d_1,…, d_n has to be scheduled non-preemptively. If C_j is the completion time of job j then T_j = max(0, C_j - d_j) denotes the tardiness of this job. The objective is to find a schedule S^{*}_{WT} that minimizes the weighted sum of the tardiness costs of all jobs computed as \sum_{j=1}^{n} w_j T_j. This problem is known to be unary NP-hard. Our goal is to design a constructive heuristic for this problem that yields excellent feasible solutions in short computational times by exploiting the structural properties of a preemptive relaxation

Minimizing total inventory cost on a single machine in just-in-time manufacturing

The just-in-time concept decrees not to accept ordered goods before their due dates in order to avoid inventory cost. This bounces the inventory cost back to the manufacturer: products that are completed before their due dates have to be stored. Reducing this type of storage cost by preclusion of early completion conflicts with the traditional policy of keeping work-in-process inventories down. This paper addresses a single-machine scheduling problem with the objective of minimizing total inventory cost, comprising cost associated with work-in-process inventories and storage cost as a result of early completion. The cost components are measured by the sum of the job completion times and the sum of the job earlinesses. This problem differs from more traditional scheduling problems, since the insertion of machine idle time may reduce total cost. The search for an optimal schedule, however, can be limited to the set of job sequences, since for any sequence there is a clear-cut way to insert machine idle time in order to minimize total inventory cost. We apply branch-and-bound to identify an optimal schedule. We present five approaches for lower bound calculation, based upon relaxation of the objective function, of the state space, and upon Lagrangian relaxation. Key Words and Phrases: just-in-time manufacturing, inventory cost, work-in-process inventory, earliness, tardiness, machine idle time, branch-and-bound algorithm, Lagrangian relaxation