Non‐greedy heuristics and augmented neural networks for the open‐shop scheduling problem

In this paper we propose some non‐greedy heuristics and develop an Augmented‐Neural‐Network (AugNN) formulation for solving the classical open‐shop scheduling problem (OSSP). AugNN is a neural network based meta‐heuristic approach that allows integration of domain‐specific knowledge. The OSSP is framed as a neural network with multiple layers of jobs and machines. Input, output and activation functions are designed to enforce the problem constraints and embed known heuristics to generate a good feasible solution fast. Suitable learning strategies are applied to obtain better neighborhood solutions iteratively. The new heuristics and the AugNN formulation are tested on several benchmark problem instances in the literature and on some new problem instances generated in this study. The results are very competitive with other meta‐heuristic approaches, both in terms of solution quality and computational times. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Optimization of schedule stability and efficiency under processing time variability and random machine breakdowns in a job shop environment

The ability to cope with uncertainty in dynamic scheduling environments is becoming an increasingly important issue. In such environments, any disruption in the production schedule will translate into a disturbance of the plans for several external activities as well. Hence, from a practical point of view, deviations between the planned and realized schedules are to be avoided as much as possible. The term stability refers to this concern. We propose a proactive approach to generate efficient and stable schedules for a job shop subject to processing time variability and random machine breakdowns. In our approach, efficiency is measured by the makespan, and the stability measure is the sum of the variances of the realized completion times. Because the calculation of the original measure is mathematically intractable, we develop a surrogate stability measure. The version of the problem with the surrogate stability measure is proven to be NP‐hard, even without machine breakdowns; a branch‐and‐bound algorithm is developed for this problem variant. A tabu search algorithm is proposed to handle larger instances of the problem with machine breakdowns. The results of extensive computational experiments indicate that the proposed algorithms are quite promising in performance. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Multiproduct dynamic lot-sizing model with coordinated replenishments

In this article we consider a multiproduct dynamic lot-sizing model. In addition to a separate setup cost for each product ordered, a joint setup cost is incurred when at least one product is ordered. We formulate the model as a concave minimization problem over a compact polyhedral set and present a finite branch and bound algorithm for finding an optimal ordering schedule. Superiority of the branch and bound algorithm to the existing exact procedures is demonstrated. We report computational experience with problems whose dimensions render the existing procedures computationally infeasible.     

The interactive fixed charge linear programming problem

In many decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm.     

A branch and bound algorithm for solving a class of nonlinear integer programming problems

This article presents a branch and bound method for solving the problem of minimizing a separable concave function over a convex polyhedral set where the variables are restricted to be integer valued. Computational results are reported.     

Some branch-and-bound procedures for fixed-cost transportation problems

In this article we present three properties that will improve the performance of branch-and-bound algorithms for fixed-cost transportation problems. By applying Lagrangian relaxation we show that one can develop stronger up and down penalties than those traditionally used and also develop a strengthened penalty for nonbasic variables. We also show that it is possible to “look ahead” of a particular node and determine the solution at the next node without actually calculating it. We present computational evidence by comparing our developments with existing procedures.     

Modeling multiple stage manufacturing systems with generalized costs and capacity issues

This study introduces one modeling methodology that describes a broad range of multiple stage production planning issues, including multiple limited resources with setup times and joint fixed cost relationships. An existing production system is modeled in this fashion, creating a new set of 1350 highly generalized benchmark problems. A computational study is conducted with the 1350 benchmark problems introduced in this paper and 2100 benchmark problems, with more restrictive assumptions, from the existing literature. The relative merits of a decomposition‐based algorithm and a neighborhood search technique known as NIPPA, or the Non‐sequential Incremental Part Period Algorithm, are assessed. NIPPA is generally the more successful of the two techniques, although there are specific instances in which the decomposition‐based algorithm displayed a distinct advantage. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005