A transportation type aggregate production model with bounds on inventory and backordering

We consider a certain T period aggregate production planning model, where the two sources of production are regular and overtime. The model allows for time varying production, holding and backordering costs and includes bounds on inventory and backorders. We show that the problem has a rather interesting network structure and exploit this structure to develop a greedy algorithm to solve the problem. The procedure is easy to implement and has a computational complexity of O(T2). We report computational experience with the greedy procedure and demonstrate its superiority to a well known network simplex code, Gnet, implemented on the classical network formulation of the problem. © 1988

A Neurogenetic approach for the resource-constrained project scheduling problem

A variety of metaheuristic approaches have emerged in recent years for solving the resource-constrained project scheduling problem (RCPSP), a well-known NP-hard problem in scheduling. In this paper, we propose a Neurogenetic approach which is a hybrid of genetic algorithms (GA) and neural-network (NN) approaches. In this hybrid approach the search process relies on GA iterations for global search and on NN iterations for local search. The GA and NN search iterations are interleaved in a manner that allows NN to pick the best solution thus far from the GA pool and perform an intensification search in the solution's local neighborhood. Similarly, good solutions obtained by NN search are included in the GA population for further search using the GA iterations. Although both GA and NN approaches, independently give good solutions, we found that the hybrid approach gives better solutions than either approach independently for the same number of shared iterations. We demonstrate the effectiveness of this approach empirically on the standard benchmark problems of size J30, J60, J90 and J120 from PSPLIB. © 2010 Elsevier Ltd. All rights reserved

Metaheuristic methods

Given the NP—hard nature of the Resource Constrained Project Scheduling Problem (RCPSP), obtaining an optimal solution for larger instances of the problem becomes computationally intractable. Metaheuristic approaches are therefore commonly used to provide near—optimal solutions for larger instances of the problem. Over the past two decades, anumber of different metaheuristic approaches have been proposed and developed for combinatorial optimization problems in general and for the RCPSP in particular. In this chapter, we review the various metaheuristic approaches such as genetic algorithms, simulatedannealing, tabu search, scatter search, ant colonies, the bees algorithm, neural networks etc., that have been applied to the RCPSP. One metaheuristic approach called the NeuroGenetic approach is described in more detail. The NeuroGenetic approach is a hybrid of a neural—network based approach and the genetic algorithms approach.We summarize the best results in the literature for the various metaheuristic approaches on the standard benchmark problems J30, J60, J90, and J120 from PSPLIB (Kolisch and Sprecher, Eur J Oper Res 96:205-216, 1996). © Springer International Publishing Switzerland 2015

A Branch and Bound Procedure for the Resource Constrained Project Scheduling Problem with Discounted Cash Flows

Management of projects is complicated by the scarcity of resources required to execute them. Limited resources usually extend the project completion times beyond those determined by CPM/PERT. Several solution procedures have been developed for solving the resource constrained project scheduling problem. One objective commonly used for these problems is to complete the project as early as possible (minimize makespan). The problem considered in this paper is a resource constrained project scheduling problem, with the added features that there are cash flows associated with the project activities, and the objective is to schedule the project activities in such a way that the net present value of cash flows is maximized. With these features the problem becomes financially motivated and more realistic. We introduce a branch and bound procedure to solve the resource constrained project scheduling problem with discounted cash flows. Our procedure exploits the known fact that potential resource violations can be eliminated by introducing additional precedence relations between certain project activities. Specifically, we use the "minimal delaying alternatives" concept to resolve resource conflicts. The bounds in the branch and bound procedure are computed by solving Payment Scheduling Problems, which can be formulated as linear programs and by that are well-solvable. We test our procedure computationally on a set of 90 test problems from the literature and compare it with the only other exact procedure we know of.project scheduling, resource constraints, net present value

Branch and Bound Algorithm for the Separable Piecewise Linear Concave Cost Allocation Problem

This presentation was given at the Production and Operations Management Annual Conference (POMS)

Data Transmission Strategies over Networks with Different QoS Levels and All You Can Send Pricing

We investigate an optimization problem a firm faces when acquiring network capacity from multiple vendors. We define two types of tasks the firm performs using data networks, and show that the time, bandwidth and quality requirements of each type are quite different. We formulate the associated problem as a cost minimization problem subject to quality and capacity requirements and offer multiple solution approaches. We analyze how different prices, quality and task distribution affect the optimal behavior of the firm. We also implement Generalized Bender’s Decomposition to solve a relaxation of this problem

A Branch-and-Bound Algorithm for the Concave Cost Supply Problem

Effective supplier selection and allocation of order quantity among multiple suppliers are indispensable to the success of a manufacturing company. While companies have begun to turn into a comprehensive multi-criteria approach, most buyers still consider purchasing cost to be their primary concern in selecting their suppliers. In this paper, we consider the concave cost supply problem where a manufacturer seeks to select the suppliers and simultaneously procure the quantity of material/component required for production at the minimum total cost during a standard production period. We provide and validate an effective and efficient branch-and-bound algorithm that is finite and that finds the global optimal solution of the problem without any restrictions on the cost functions or on the set of input parameters used in the problem. Numerical experiments are conducted to evaluate the performance of the proposed algorithm