Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

Interactive approaches to the solution of a class of combinatorial problems

PhD ThesisThis thesis considers the usefulness of interaction between a human and a powerful computer in attempting to solve a class of discrete optimization problems. Some typical problems are described in chapters 1 and 2 and the effectiveness of their exact solution by existing methods is assessed. Chapter 3 presents some heuristic techniques which produce good approximate solutions and the value of such methods is discussed. An alternative approach, that of providing a mechanism for manmachine interaction is proposed in chapter 4. A system for providing easy access to a range of algorithmic and heuristic techniques is described. The system, named IMPACT, was implemented by the author and its many features include the interruption, interrogation, adjustment and resumption of a process or algorithm. Some novel interactive tree-manipulation techniques and their usage are introduced in chapter 5. This chapter also describes extensions to certain other heuristics in order to improve their power when used interactively. Throughout the thesis a job-shop scheduling problem serves as a useful vehicle for illustrating ideas. This problem was investigated extensively and chapter 6 is devoted to the topic. The idea of a critical path of jobs through machines is introduced together with the slack time of a job upon a machine under a particular schedule. Branch-and-bound approaches to the problem have been proposed in the past. The performance of such an approach has been substantially improved, as is shown by new results. The improvement stems from two sources both of which were discovered interactively; i) a different branching procedure designed to exploit features of the job-shop scheduling problem, and ii) more realistic lower bounds than those originally proposed. The final chapter discusses the generality of the approach and illustrates the extendability of IMPACT. Other discrete optimization problems are discussed briefly and a branch-andbound formulation to one of them, an assignment problem~ is presented. An interactive approach by other authors to the travelling salesman problem is reviewed and features similar to those experienced in the job-shop scheduling investigation are remarked upon. To conclude, the advantages to be gained from an interactive approach are discussed

Two Combinatorial Optimization Problems at the Interface of Computer Science and Operations Research

Solving large combinatorial optimization problems is a ubiquitous task across multiple disciplines. Developing efficient procedures for solving these problems has been of great interest to both researchers and practitioners. Over the last half century, vast amounts of research have been devoted to studying various methods in tackling these problems. These methods can be divided into two categories, heuristic methods and exact algorithms. Heuristic methods can often lead to near optimal solutions in a relatively time efficient manner, but provide no guarantees on optimality. Exact algorithms guarantee optimality, but are often very time consuming. This dissertation focuses on designing efficient exact algorithms that can solve larger problem instances with faster computational time. A general framework for an exact algorithm, called the Branch, Bound, and Remember algorithm, is proposed in this dissertation. Three variations of single machine scheduling problems are presented and used to evaluate the efficiency of the Branch, Bound, and Remember algorithm. The computational results show that the Branch, Bound, and Remember algorithms outperforms the best known algorithms in the literature. While the Branch, Bound, and Remember algorithm can be used for solving combinatorial optimization problems, it does not address the subject of post-optimality selection after the combinatorial optimization problem is solved. Post-optimality selection is a common problem in multi-objective combinatorial optimization problems where there exists a set of optimal solutions called Pareto optimal (non-dominated) solutions. Post-optimality selection is the process of selecting the best solutions within the Pareto optimal solution set. In many real-world applications, a Pareto solution set (either optimal or near-optimal) can be extremely large, and can be very challenging for a decision maker to evaluate and select the best solution. To address the post-optimality selection problem, this dissertation also proposes a new discrete optimization problem to help the decision-maker to obtain an optimal preferred subset of Pareto optimal solutions. This discrete optimization problem is proven to be NP-hard. To solve this problem, exact algorithms and heuristic methods are presented. Different multi-objective problems with various numbers of objectives and constraints are used to compare the performances of the proposed algorithms and heuristics

Schedule Generation Schemes for Job Shop Problems with Fuzziness

We consider the job shop scheduling problem with fuzzy durations and expected makespan minimisation. We formally define the space of semi-active and active fuzzy schedules and propose and analyse different schedule-generation schemes (SGSs) in this fuzzy framework. In particular, we study dominance properties of the set of schedules obtained with each SGS. Finally, a computational study illustrates the great difference between the spaces of active and the semi-active fuzzy schedules, an analogous behaviour to that of the deterministic job shop.This research has been supported by the Spanish Government under research grants FEDER TIN2010-20976-C02-02 and MTM2010- 16051 and by the Principality of Asturias (Spain) under grants Severo Ochoa BP13106 and FC-13-COF13-03

Applying Iterative Flattening Search to the Job Shop Scheduling Problem with Alternative Resources and Sequence Dependent Setup Times

This paper tackles a complex version of the Job Shop Scheduling Problem (JSSP) that involves both the possibility to select alternative resources to activities and the presence of sequence dependent setup times. The proposed solving strategy is a variant of the known Iterative Flattening Search (IFS) metaheuristic. This work presents the following contributions: (1) a new constraint-based solving procedure produced by means of enhancing a previous JSSP-solving version of the same metaheuristic; (2) a new version of both the variable and value ordering heuristics, based on temporal flexibility, that capture the relevant features of the extended scheduling problem (i.e., the flexibility in the assignment of resources to activities, and the sequence dependent setup times); (3) a new relaxation strategy based on the random selection of the activities that are closer to the critical path of the solution, as opposed to the original approach based on a fully random relaxation. The performance of the proposed algorithm are tested on a new benchmark set produced as an extension of an existing well-known testset for the Flexible Job Shop Scheduling Problem by adding sequence dependent setup times to each original testset\u27s instance, and the behavior of the old and new relaxation strategies are compared

Job Shop Scheduling with Routing Flexibility and Sequence-Dependent Setup Times

This paper presents a meta-heuristic algorithm for solving a job shop scheduling problem involving both sequence dependent setup-times and the possibility of selecting alternative routes among the available machines. The proposed strategy is a variant of the Iterative Flattening Search (IFS ) schema. This work provides three separate results: (1) a constraint-based solving procedure that extends an existing approach for classical Job Shop Scheduling; (2) a new variable and value ordering heuristic based on temporal flexibility that take into account both sequence dependent setup-times and flexibility in machine selection; (3) an original relaxation strategy based on the idea of randomly breaking the execution orders of the activities on the machines with a activity selection criteria based on their proximity to the solution\u27s critical path. The efficacy of the overall heuristic optimization algorithm is demonstrated on a new benchmark set which is an extension of a well-known and difficult benchmark for the Flexible Job Shop Scheduling Problem

Project network models with discounted cash flows. A guided tour through recent developments.

The vast majority of the project scheduling methodologies presented in the literature have been developed with the objective of minimizing the project duration subject to precedence and other constraints. In doing so, the financial aspects of project management are largely ignored. Recent efforts have taken into account discounted cash flow and have focused on the maximalization of the net present value (npv) of the project as the more appropriate objective. In this paper we offer a guided tour through the important recent developments in the expanding field of research on deterministic and stochastic project network models with discounted cash flows. Subsequent to a close examination of the rationale behind the npv objective, we offer a taxonomy of the problems studied in the literature and critically review the major contributions. Proper attention is given to npv maximization models for the unconstrained scheduling problem with known cash flows, optimal and suboptimal scheduling procedures with various types of resource constraints, and the problem of determining both the timing and amount of payments.Scheduling; Models; Model; Discounted cash flow; Cash flow; Project scheduling; Project management; Management; Net present value; Value; Problems; Maximization; Optimal;