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     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

The continuous‐time single‐sourcing problem with capacity expansion opportunities

This paper develops a new model for allocating demand from retailers (or customers) to a set of production/storage facilities. A producer manufactures a product in multiple production facilities, and faces demand from a set of retailers. The objective is to decide which of the production facilities should satisfy each retailer's demand, in order minimize total production, inventory holding, and assignment costs (where the latter may include, for instance, variable production costs and transportation costs). Demand occurs continuously in time at a deterministic rate at each retailer, while each production facility faces fixed‐charge production costs and linear holding costs. We first consider an uncapacitated model, which we generalize to allow for production or storage capacities. We then explore situations with capacity expansion opportunities. Our solution approach employs a column generation procedure, as well as greedy and local improvement heuristic approaches. A broad class of randomly generated test problems demonstrates that these heuristics find high quality solutions for this large‐scale cross‐facility planning problem using a modest amount of computation time. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A nested benders decomposition approach for telecommunication network planning

Despite its ability to result in more effective network plans, the telecommunication network planning problem with signal‐to‐interference ratio constraints gained less attention than the power‐based one because of its complexity. In this article, we provide an exact solution method for this class of problems that combines combinatorial Benders decomposition, classical Benders decomposition, and valid cuts in a nested way. Combinatorial Benders decomposition is first applied, leading to a binary master problem and a mixed integer subproblem. The subproblem is then decomposed using classical Benders decomposition. The algorithm is enhanced using valid cuts that are generated at the classical Benders subproblem and are added to the combinatorial Benders master problem. The valid cuts proved efficient in reducing the number of times the combinatorial Benders master problem is solved and in reducing the overall computational time. More than 120 instances of the W‐CDMA network planning problem ranging from 20 demand points and 10 base stations to 140 demand points and 30 base stations are solved to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

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     

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     

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     

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     

Simultaneous price,location, and capacity decisions on a line of time‐sensitive customers

Consider a monopolist who sells a single product to time‐sensitive customers located on a line segment. Customers send their orders to the nearest distribution facility, where the firm processes (customizes) these orders on a first‐come, first‐served basis before delivering them. We examine how the monopolist would locate its facilities, set their capacities, and price the product offered to maximize profits. We explicitly model customers' waiting costs due to both shipping lead times and queueing congestion delays and allow each customer to self‐select whether she orders or not, based on her reservation price. We first analyze the single‐facility problem and derive a number of interesting insights regarding the optimal solution. We show, for instance, that the optimal capacity relates to the square root of the customer volume and that the optimal price relates additively to the capacity and transportation delay costs. We also compare our solutions to a similar problem without congestion effects. We then utilize our single‐facility results to treat the multi‐facility problem. We characterize the optimal policy for serving a fixed interval of customers from multiple facilities when customers are uniformly distributed on a line. We also show how as the length of the customer interval increases, the optimal policy relates to the single‐facility problem of maximizing expected profit per unit distance. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Dual‐ascent and primal heuristics for production‐assembly‐distribution system design

This article proposes two dual‐ascent algorithms and uses each in combination with a primal drop heuristic embedded within a branch and bound framework to solve the uncapacitated production assembly distribution system (i.e., supply chain) design problem, which is formulated as a mixed integer program. Computational results indicate that one approach, which combines primal drop and dual‐ascent heuristics, can solve instances within reasonable time and prescribes solutions with gaps between the primal and dual solution values that are less than 0.15%, an efficacy suiting it for actual large‐scale applications. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

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     

The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

The single and multi‐item transshipment problem with fixed transshipment costs

This article deals with supply chain systems in which lateral transshipments are allowed. For a system with two retailers facing stochastic demand, we relax the assumption of negligible fixed transshipment costs, thus, extending existing results for the single‐item case and introducing a new model with multiple items. The goal is to determine optimal transshipment and replenishment policies, such that the total centralized expected profit of both retailers is maximized. For the single‐item problem with fixed transshipment costs, we develop optimality conditions, analyze the expected profit function, and identify the optimal solution. We extend our analysis to multiple items with joint fixed transshipment costs, a problem that has not been investigated previously in the literature, and show how the optimality conditions may be extended for any number of items. Due to the complexity involved in solving these conditions, we suggest a simple heuristic based on the single‐item results. Finally, we conduct a numerical study that provides managerial insights on the solutions obtained in various settings and demonstrates that the suggested heuristic performs very well. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 637–664, 2014     

An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines

We consider the multitasking scheduling problem on unrelated parallel machines to minimize the total weighted completion time. In this problem, each machine processes a set of jobs, while the processing of a selected job on a machine may be interrupted by other available jobs scheduled on the same machine but unfinished. To solve this problem, we propose an exact branch‐and‐price algorithm, where the master problem at each search node is solved by a novel column generation scheme, called in‐out column generation, to maintain the stability of the dual variables. We use a greedy heuristic to obtain a set of initial columns to start the in‐out column generation, and a hybrid strategy combining a genetic algorithm and an exact dynamic programming algorithm to solve the pricing subproblems approximately and exactly, respectively. Using randomly generated data, we conduct numerical studies to evaluate the performance of the proposed solution approach. We also examine the effects of multitasking on the scheduling outcomes, with which the decision maker can justify making investments to adopt or avoid multitasking.     

Algorithms for the multi‐item multi‐vehicles dynamic lot sizing problem

We consider a two‐stage supply chain, in which multi‐items are shipped from a manufacturing facility or a central warehouse to a downstream retailer that faces deterministic external demand for each of the items over a finite planning horizon. The items are shipped through identical capacitated vehicles, each incurring a fixed cost per trip. In addition, there exist item‐dependent variable shipping costs and inventory holding costs at the retailer for items stored at the end of the period; these costs are constant over time. The sum of all costs must be minimized while satisfying the external demand without backlogging. In this paper we develop a search algorithm to solve the problem optimally. Our search algorithm, although exponential in the worst case, is very efficient empirically due to new properties of the optimal solution that we found, which allow us to restrict the number of solutions examined. Second, we perform a computational study that compares the empirical running time of our search methods to other available exact solution methods to the problem. Finally, we characterize the conditions under which each of the solution methods is likely to be faster than the others and suggest efficient heuristic solutions that we recommend using when the problem is large in all dimensions. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

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     

The one-period,N-location distribution problem

This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.     

Route optimization for multiple searchers

We consider a discrete time‐and‐space route‐optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. This article formulates a novel convex mixed‐integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target‐ and location‐dependent search effectiveness. We present two solution approaches, one based on the cutting‐plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting‐plane approach solves many realistically sized problem instances in a few minutes, while existing branch‐and‐bound algorithms fail. A specialized cut improves solution time by 50[percnt] in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting‐plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

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     

A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017