Discrete equal‐capacity p‐median problem

This paper examines the discrete equal‐capacity p‐median problem that seeks to locate p new facilities (medians) on a network, each having a given uniform capacity, in order to minimize the sum of distribution costs while satisfying the demand on the network. Such problems arise, for example, in local access and transport area telecommunication network design problems where any number of a set of p facility units can be constructed at the specified candidate sites (hence, the net capacity is an integer multiple of a given unit capacity). We develop various valid inequalities, a separation routine for generating cutting planes that are specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for this class of problems. © 2000 John & Sons, Inc. Naval Research Logistics 47: 166–183, 2000.     

Repairable consecutive‐k‐out‐of‐n: F system with Markov dependence

In this article, a model for a repairable consecutive‐k‐out‐of‐n: F system with Markov dependence is studied. A binary vector is used to represent the system state. The failure rate of a component in the system depends on the state of the preceding component. The failure risk of a system state is then introduced. On the basis of the failure risk, a priority repair rule is adopted. Then the transition density matrix can be determined, and the analysis of the system reliability can be conducted accordingly. One example each of a linear and a circular system is then studied in detail to explain the model and methodology developed in this paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 18–39, 2000     

Optimal shift scheduling: A branch‐and‐price approach

We present a branch‐and‐price technique for optimal staff scheduling with multiple rest breaks, meal break, and break windows. We devise and implement specialized branching rules suitable for solving the set covering type formulation implicitly, using column generation. Our methodology is more widely applicable and computationally superior to the alternative methods in the literature. We tested our methodology on 365 test problems involving between 1728 and 86400 shift variations, and 20 demand patterns. In a direct comparison with an alternative method, our approach yields significant improvements both in cpu time and in the number of problem instances solved to optimality. The improvements were particularly marked for problems involving larger numbers of feasible shifts. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 185–200, 2000     

Partial equilibrium in risk‐based production decisions

Characteristically, a small subset of operational problems admit risk neutrality when contingent claims methodology were used in their analysis. That is, for the majority of manufacturing and production problems, operating cash flows are not directly linked to prices of traded assets. However, to the extent that correlations can be estimated, the methodology's applicability to a broader set of operational problems is supported. Our article addresses this issue with the objective of extending the use of contingent claims techniques to a larger set of operational problems. In broad terms, this objective entails a partial equilibrium approach to the problem of valuing uncertain cash flows. To this end, we assume risk aversion and cast our approach within Merton's intertemporal capital asset pricing model. In this context, we formulate a “generic” production valuation model that is framed as an exercise in stochastic optimal control. The model is versatile in its characterization and can easily be adapted to accommodate a wide‐ranging set of risk‐based operational problems where the underlying sources of uncertainty are not traded. To obtain results, the model is recast as a stochastic dynamic program to be solved numerically. The article addresses a number of fundamental issues in the analysis risk based decision problems in operations. First, in the approach provided, decisions are analyzed under a properly defined risk structure. Second, the process of analysis leads to suitably adjusted probability distributions through which, appropriately discounted expectations are derived. Third, through consolidating existing concepts into a standard and adaptable framework, we extend the applicability of contingent claims methodology to a broader set of operational problems. The approach is advantageous as it obviates the need for exogenously specifying utility functions or discount rates.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts

We consider in this paper the coordinated replenishment dynamic lot‐sizing problem when quantity discounts are offered. In addition to the coordination required due to the presence of major and minor setup costs, a separate element of coordination made possible by the offer of quantity discounts needs to be considered as well. The mathematical programming formulation for the incremental discount version of the extended problem and a tighter reformulation of the problem based on variable redefinition are provided. These then serve as the basis for the development of a primal‐dual based approach that yields a strong lower bound for our problem. This lower bound is then used in a branch and bound scheme to find an optimal solution to the problem. Computational results for this optimal solution procedure are reported in the paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 686–695, 2000     

Case‐based reasoning and improved adaptive search for project scheduling

Most scheduling problems are notoriously intractable, so the majority of algorithms for them are heuristic in nature. Priority rule‐based methods still constitute the most important class of these heuristics. Of these, in turn, parametrized biased random sampling methods have attracted particular interest, due to the fact that they outperform all other priority rule‐based methods known. Yet, even the “best” such algorithms are unable to relate to the full range of instances of a problem: Usually there will exist instances on which other algorithms do better. We maintain that asking for the one best algorithm for a problem may be asking too much. The recently proposed concept of control schemes, which refers to algorithmic schemes allowing to steer parametrized algorithms, opens up ways to refine existing algorithms in this regard and improve their effectiveness considerably. We extend this approach by integrating heuristics and case‐based reasoning (CBR), an approach that has been successfully used in artificial intelligence applications. Using the resource‐constrained project scheduling problem as a vehicle, we describe how to devise such a CBR system, systematically analyzing the effect of several criteria on algorithmic performance. Extensive computational results validate the efficacy of our approach and reveal a performance similar or close to state‐of‐the‐art heuristics. In addition, the analysis undertaken provides new insight into the behaviour of a wide class of scheduling heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 201–222, 2000     

Makespan minimization in the two‐machine flowshop batch scheduling problem

In this paper we consider a practical scheduling problem commonly arising from batch production in a flexible manufacturing environment. Different part‐types are to be produced in a flexible manufacturing cell organized into a two‐stage production line. The jobs are processed in batches on the first machine, and the completion time of a job is defined as the completion time of the batch containing it. When processing of all jobs in a batch is completed on the first machine, the whole batch of jobs is transferred intact to the second machine. A constant setup time is incurred whenever a batch is formed on any machine. The tradeoff between the setup times and batch processing times gives rise to the batch composition decision. The problem is to find the optimal batch composition and the optimal schedule of the batches so that the makespan is minimized. The problem is shown to be strongly NP‐hard. We identify some special cases by introducing their corresponding solution methods. Heuristic algorithms are also proposed to derive approximate solutions. We conduct computational experiments to study the effectiveness of the proposed heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 128–144, 2000     

A branch‐and‐price algorithm for a targeting problem

In this paper, we consider a new weapon‐target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model, but it can be transformed into a linear integer programming model. We present a branch‐and‐price algorithm for the problem employing the disaggregated formulation, which has exponentially many columns denoting the feasible allocations of weapon systems to each target. A greedy‐style heuristic is used to get some initial columns to start the column generation. A branching strategy compatible with the pricing problem is also proposed. Computational results using randomly generated data show this approach is promising for the targeting problem. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Asymptotically optimal linear time algorithms for two‐stage and three‐stage flexible flow shops

We consider two‐stage and three‐stage flexible flow shops with parallel machines in each stage and the minimum makespan objective. We develop linear time algorithms for these problems with absolute worst‐case bounds either sharper or no worse than the currently available ones and we accomplish this with lower complexity algorithms. We also demonstrate the asymptotic optimality of a class of algorithms for multistage flexible flow shop problems (which includes the proposed algorithms) under certain probabilistic assumptions on the job processing times. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 259–268, 2000     

A branch‐and‐price approach for the stochastic generalized assignment problem

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014     

Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

In this article, we propose a branch‐and‐price‐and‐cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time to carry out a job, that is, the routes of the scheduling subjects are dependent. The incorporation of the synchronization constraints increases the difficulty of the MRPSC significantly and makes the existing VRP exact algorithm inapplicable. Although there are many types of valid inequalities for the VRP or its variants, so far we can only adapt the infeasible path elimination inequality and the weak clique inequality to handle the synchronization constraints in our BPC algorithm. The experimental results at the root node of the branch‐and‐bound tree show that the employed inequalities can effectively improve the lower bound of the problem. Compared with ILOG CPLEX, our BPC algorithm managed to find optimal solutions for more test instances within 1 hour. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 138–171, 2016     

Optimal FCFS allocation rules for periodic‐review assemble‐to‐order systems

In Assemble‐To‐Order (ATO) systems, situations may arise in which customer demand must be backlogged due to a shortage of some components, leaving available stock of other components unused. Such unused component stock is called remnant stock. Remnant stock is a consequence of both component ordering decisions and decisions regarding allocation of components to end‐product demand. In this article, we examine periodic‐review ATO systems under linear holding and backlogging costs with a component installation stock policy and a First‐Come‐First‐Served (FCFS) allocation policy. We show that the FCFS allocation policy decouples the problem of optimal component allocation over time into deterministic period‐by‐period optimal component allocation problems. We denote the optimal allocation of components to end‐product demand as multimatching. We solve the multi‐matching problem by an iterative algorithm. In addition, an approximation scheme for the joint replenishment and allocation optimization problem with both upper and lower bounds is proposed. Numerical experiments for base‐stock component replenishment policies show that under optimal base‐stock policies and optimal allocation, remnant stock holding costs must be taken into account. Finally, joint optimization incorporating optimal FCFS component allocation is valuable because it provides a benchmark against which heuristic methods can be compared. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 158–169, 2015     

Managing components for assemble‐to‐order products with lead‐time‐dependent pricing: The full‐shipment model

We study a component inventory planning problem in an assemble‐to‐order environment faced by many contract manufacturers in which both quick delivery and efficient management of component inventory are crucial for the manufacturers to achieve profitability in a highly competitive market. Extending a recent study in a similar problem setting by the same authors, we analyze an optimization model for determining the optimal component stocking decision for a contract manufacturer facing an uncertain future demand, where product price depends on the delivery times. In contrast to our earlier work, this paper considers the situation where the contract manufacturer needs to deliver the full order quantity in one single shipment. This delivery requirement is appropriate for many industries, such as the garment and toy industries, where the economies of scale in transportation is essential. We develop efficient solution procedures for solving this optimization problem. We use our model results to illustrate how the different model parameters affect the optimal solution. We also compare the results under this full‐shipment model with those from our earlier work that allows for multiple partial shipments. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A branch and bound algorithm for computing optimal replacement policies in consecutive k‐out‐of‐n‐systems

This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete‐time, infinite‐horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k‐out‐of‐n systems. The objective is to minimize the long‐run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k‐out‐of‐n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n ≤ 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288–302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017     

A branch‐and‐bound‐based solution approach for dynamic rerouting of airborne platforms

This article is a sequel to a recent article that appeared in this journal, “An extensible modeling framework for dynamic reassignment and rerouting in cooperative airborne operations” [ 17 ], in which an integer programming formulation to the problem of rescheduling in‐flight assets due to changes in battlespace conditions was presented. The purpose of this article is to present an improved branch‐and‐bound procedure to solve the dynamic resource management problem in a timely fashion, as in‐flight assets must be quickly re‐tasked to respond to the changing environment. To facilitate the rapid generation of attractive updated mission plans, this procedure uses a technique for reducing the solution space, supports branching on multiple decision variables simultaneously, incorporates additional valid cuts to strengthen the minimal network constraints of the original mathematical model, and includes improved objective function bounds. An extensive numerical analysis indicates that the proposed approach significantly outperforms traditional branch‐and‐bound methodologies and is capable of providing improved feasible solutions in a limited time. Although inspired by the dynamic resource management problem in particular, this approach promises to be an effective tool for solving other general types of vehicle routing problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

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.     

On the polyhedral structure of two‐level lot‐sizing problems with supplier selection

In this article, we study a two‐level lot‐sizing problem with supplier selection (LSS), which is an NP‐hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet‐defining. We show numerically that incorporating these valid inequalities within a branch‐and‐cut framework leads to significant improvements in computation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 647–666, 2017     

Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems

Clustering problems are often difficult to solve due to nonlinear cost functions and complicating constraints. Set partitioning formulations can help overcome these challenges, but at the cost of a very large number of variables. Therefore, techniques such as delayed column generation must be used to solve these large integer programs. The underlying pricing problem can suffer from the same challenges (non‐linear cost, complicating constraints) as the original problem, however, making a mathematical programming approach intractable. Motivated by a real‐world problem in printed circuit board (PCB) manufacturing, we develop a search‐based algorithm (Rank‐Cluster‐and‐Prune) as an alternative, present computational results for the PCB problem to demonstrate the tractability of our approach, and identify a broader class of clustering problems for which this approach can be used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Chance‐constrained multi‐terminal network design problems

We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum‐cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose two scenario‐based Steiner cut formulations, study the strength of the proposed valid inequalities, and develop a branch‐and‐cut solution method. We also propose an LP‐based separation for the scenario‐based directed Steiner cut inequalities using Benders feasibility cuts, leveraging the success of the directed Steiner cuts for the deterministic Steiner tree problem. In our computational study, we test our branch‐and‐cut method on instances adapted from graphs in SteinLib Testdata Library with up to 100 nodes, 200 edges, and 17 terminals. The performance of our branch‐and‐cut method demonstrates the strength of the scenario‐based formulations and the benefit from adding the additional valid inequalities that we propose. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 321–334, 2015