Modeling and analysis of a mixed‐model assembly line with stochastic operation times

We consider a mixed‐model assembly line (MMAL) comprised a set of workstations and a conveyor. The workstations are arranged in a serial configuration. The conveyor moves at a constant speed along the workstations. Initial units belonging to different models are successively fed onto the conveyor, and they are moved by the conveyor to pass through the workstations to gradually generate final products. All assembling tasks are manually performed with operation times to be stochastic. An important performance measure of MMALs is overload times that refer to uncompleted operations for operators within their work zones. This paper establishes a method to analyze the expected overload times for MMALs with stochastic operation times. The operation processes of operators form discrete time nonhomogeneous Markov processes with continuous state spaces. For a given daily production schedule, the expected overload times involve in analyzing the Markov processes for finite horizon. Based on some important properties of the performance measure, we propose an efficient approach for calculating the expected overload times. Numerical computations show that the results are very satisfactory. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The stochastic U‐line balancing problem

A U‐line arranges tasks around a U‐shaped production line and organizes them into stations that can cross from one side of the line to the other. In addition to improving visibility and communication between operators on the line, which facilitates problem‐solving and quality improvement, U‐lines can reduce the total number of operators required on the line and make rebalancing the line easier compared to the traditional, straight production line. This paper studies the (type 1) U‐line balancing problem when task completion times are stochastic. Stochastic completion times occur when differences between operators cause completion times to vary somewhat and when machine processing times vary. A recursive algorithm is presented for finding the optimal solution when completion times have any distribution function. An equivalent shortest path network is also presented. An improvement for the special case of normally distributed task completion times is given. A computational study to determine the characteristics of instances that can be solved by the algorithms shows that they are able to solve instances of practical size (like the 114 Japanese and U.S. U‐lines studied in a literature review paper). © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

A sequential dynamic pricing model and its applications

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Sojourn times in a two‐stage queueing network with blocking

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines. The main feature of our model is blocking, i.e., as soon as the second waiting line reaches a certain upper limit, the first line is blocked. The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type. Our objective is to study the sojourn time distribution under the first‐come‐first‐serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi‐birth‐and‐death processes and continuous‐time Markov chains. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Integrated scheduling of loading and transportation with tractors and semitrailers separated

Motivated by some practical applications, we study a new integrated loading and transportation scheduling problem. Given a set of jobs, a single crane is available to load jobs, one by one, onto semitrailers with a given capacity. Loaded semitrailers are assigned to tractors for transportation tasks. Subject to limited resources (crane, semitrailers, and tractors), the problem is to determine (1) an assignment of jobs to semitrailers for loading tasks, (2) a sequence for the crane to load jobs onto semitrailers, (3) an assignment of loaded semitrailers to tractors for transportation tasks, and (4) a transportation schedule of assigned tractors such that the completion time of the last transportation task is minimized. We first formulate the problem as a mixed integer linear programming model (MILPM) and prove that the problem is strongly NP‐hard. Then, optimality properties are provided which are useful in establishing an improved MILPM and designing solution algorithms. We develop a constructive heuristic, two LP‐based heuristics, and a recovering beam search heuristic to solve this problem. An improved procedure for solutions by heuristics is also presented. Furthermore, two branch‐and‐bound (B&B) algorithms with two different lower bounds are developed to solve the problem to optimality. Finally, computational experiments using both real data and randomly generated data demonstrate that our heuristics are highly efficient and effective. In terms of computational time and the number of instances solved to optimality in a time limit, the B&B algorithms are better than solving the MILPM. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 416–433, 2015     

Radar pulse interleaving for multi‐target tracking

In a multifunction radar, the maximum number of targets that can be managed or tracked is an important performance measure. Interleaving algorithms developed to operate radars exploit the dead‐times between the transmitted and the received pulses to allocate new tracking tasks that might involve transmitting or receiving pulses, thus increasing the capacity of the system. The problem of interleaving N targets involves a search among N! possibilities, and suboptimal solutions are usually employed to satisfy the real‐time constraints of the radar system. In this paper, we present new tight 0–1 integer programming models for the radar pulse interleaving problem and develop effective solution methods based on Lagrangian relaxation techniques. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Scheduling recurrent construction

A problem we call recurrent construction involves manufacturing large, complex, expensive products such as airplanes, houses, and ships. Customers order configurations of these products well in advance of due dates for delivery. Early delivery may not be permitted. How should the manufacturer determine when to purchase and release materials before fabrication, assembly, and delivery? Major material expenses, significant penalties for deliveries beyond due dates, and long product makespans in recurrent construction motivate choosing a release timetable that maximizes the net present value of cash flows. Our heuristic first projects an initial schedule that dispatches worker teams to tasks for the backlogged products, and then solves a series of maximal closure problems to find material release times that maximize NPV. This method compares favorably with other well‐known work release heuristics in solution quality for large problems over a wide range of operating conditions, including order strength, cost structure, utilization level, batch policy, and uncertainty level. Computation times exhibit near linear growth in problem size. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

The cyclic separation scheduling problem

This paper deals with the problem of scheduling items (tasks, employees, equipment, etc.) over a finite time horizon so as to minimize total cost expenditures while maintaining a predefined separation between certain items. The problem is cyclic, because the same schedule will be repeated over several consecutive time periods of equal length. Thus, requirements are present to maintain the separation of items not only within the individual time periods considered, but also between items in adjoining periods. A special purpose branch-and-bound algorithm is developed to solve this scheduling problem by taking advantage of its cyclic nature. Computational results are given.     

Flow‐shop batch scheduling with identical processing‐time jobs

In many practical situations of production scheduling, it is either necessary or recommended to group a large number of jobs into a relatively small number of batches. A decision needs to be made regarding both the batching (i.e., determining the number and the size of the batches) and the sequencing (of batches and of jobs within batches). A setup cost is incurred whenever a batch begins processing on a given machine. This paper focuses on batch scheduling of identical processing‐time jobs, and machine‐ and sequence‐independent setup times on an m‐machine flow‐shop. The objective is to find an allocation to batches and their schedule in order to minimize flow‐time. We introduce a surprising and nonintuitive solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

The (s,Q) inventory model with Erlang lead time and deterministic demand

We develop a simple, approximately optimal solution to a model with Erlang lead time and deterministic demand. The method is robust to misspecification of the lead time and has good accuracy. We compare our approximate solution to the optimal for the case where we have prior information on the lead‐time distribution, and another where we have no information, except for computer‐generated sample data. It turns out that our solution is as easy as the EOQ's, with an accuracy rate of 99.41% when prior information on the lead‐time distribution is available and 97.54–99.09% when only computer‐generated sample information is available. Apart from supplying the inventory practitioner with an easy heuristic, we gain insights into the efficacy of stochastic lead time models and how these could be used to find the cost and a near‐optimal policy for the general model, where both demand rate and lead time are stochastic. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A unified model incorporating yield,burn‐in,and reliability

The correlated improvement in yield and reliability has been observed in the case studies on integrated circuits and electronic assemblies. This paper presents a model that incorporates yield and reliability with the addition of a burn‐in step to explain their correlated improvement. The proposed model includes as special cases several yield and reliability models that have been previously published and thus provides a unifying framework. The model is used to derive a condition for which yield functions can be multiplied to obtain the overall yield. Yield and reliability are compared as a function of operation time, and an analytical condition for burn‐in to be effective is also obtained. Finally, Poisson and negative binomial defects models are further considered to investigate how reliability is based on yield. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

On‐line algorithms for minimizing makespan on batch processing machines

We consider problem of scheduling jobs on‐line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on‐line algorithms with worst‐case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst‐case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on‐line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001     

Due‐window assignment with unit processing‐time jobs

In due‐window assignment problems, jobs completed within a designated time interval are regarded as being on time, whereas early and tardy jobs are penalized. The objective is to determine the location and size of the due‐window, as well as the job schedule. We address a common due‐window assignment problem on parallel identical machines with unit processing time jobs. We show that the number of candidate values for the optimal due‐window starting time and for the optimal due‐window completion time are bounded by 2. We also prove that the starting time of the first job on each of the machines is either 0 or 1, thus introducing a fairly simple, constant‐time solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Production scheduling with history‐dependent setup times

We consider a parallel‐machine scheduling problem with jobs that require setups. The duration of a setup does not depend only on the job just completed but on a number of preceding jobs. These setup times are referred to as history‐dependent. Such a scheduling problem is often encountered in the food processing industry as well as in other process industries. In our model, we consider two types of setup times—a regular setup time and a major setup time that becomes necessary after several “hard‐to‐clean” jobs have been processed on the same machine. We consider multiple objectives, including facility utilization, flexibility, number of major setups, and tardiness. We solve several special cases assuming predetermined job sequences and propose strongly polynomial time algorithms to determine the optimal timing of the major setups for given job sequences. We also extend our analysis to develop pseudopolynomial time algorithms for cases with additional objectives, including the total weighted completion time, the total weighted tardiness, and the weighted number of tardy jobs. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Analysis of algorithms for two‐stage flowshops with multi‐processor task flexibility

In this article we introduce a 2‐machine flowshop with processing flexibility. Two processing modes are available for each task: namely, processing by the designated processor, and processing simultaneously by both processors. The objective studied is makespan minimization. This production environment is encountered in repetitive manufacturing shops equipped with processors that have the flexibility to execute orders either individually or in coordination. In the latter case, the product designer exploits processing synergies between two processors so as to execute a particular task much faster than a dedicated processor. This type of flowshop environment is also encountered in labor‐intensive assembly lines where products moving downstream can be processed either in the designated assembly stations or by pulling together the work teams of adjacent stations. This scheduling problem requires determining the mode of operation of each task, and the subsequent scheduling that preserves the flowshop constraints. We show that the problem is ordinary NP‐complete and obtain an optimal solution using a dynamic programming algorithm with considerable computational requirements for medium and large problems. Then, we present a number of dynamic programming relaxations and analyze their worst‐case error performance. Finally, we present a polynomial time heuristic with worst‐case error performance comparable to that of the dynamic programming relaxations. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Limiting behavior of the stochastic sequential assignment problem

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Capacitated lot‐sizing and scheduling with parallel machines,back‐orders,and setup carry‐over

We address the capacitated lot‐sizing and scheduling problem with setup times, setup carry‐over, back‐orders, and parallel machines as it appears in a semiconductor assembly facility. The problem can be formulated as an extension of the capacitated lot‐sizing problem with linked lot‐sizes (CLSPL). We present a mixed integer (MIP) formulation of the problem and a new solution procedure. The solution procedure is based on a novel “aggregate model,” which uses integer instead of binary variables. The model is embedded in a period‐by‐period heuristic and is solved to optimality or near‐optimality in each iteration using standard procedures (CPLEX). A subsequent scheduling routine loads and sequences the products on the parallel machines. Six variants of the heuristic are presented and tested in an extensive computational study. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Higher‐order Markov chain models for categorical data sequences*

In this paper we study higher‐order Markov chain models for analyzing categorical data sequences. We propose an efficient estimation method for the model parameters. Data sequences such as DNA and sales demand are used to illustrate the predicting power of our proposed models. In particular, we apply the developed higher‐order Markov chain model to the server logs data. The objective here is to model the users' behavior in accessing information and to predict their behavior in the future. Our tests are based on a realistic web log and our model shows an improvement in prediction. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Designing acceptance sampling schemes for life testing with mixed censoring

Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time‐consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Resourcing for defense: Solving the roles and missions puzzle

One of the most important issues facing the post‐Cold War U.S. defense establishment concerns the future allocation of combat tasks and responsibilities among different branches of the armed forces. The challenge is to reduce unnecessary redundancy across roles and missions when resources are highly constrained, without compromising military effectiveness. Defining the policy problem as one of resource allocation rather than operational effectiveness, we develop a methodology for allocating roles and missions. Our methodology focuses at the highest level of force aggregation and uses a mathematical programming model to produce cross‐service cross‐mission trade‐offs that will yield the best total force combat and non‐combat potential within resource consumption constraints.