Time Stochastic Processes Research Articles

Properties of Optimal-Weighted Flowtime Policies with a Makespan Constraint and Set-up Times

We characterize optimal policies for the problem of allocating a single server to a set of jobs from N families. Each job is an instance of demand for an item and is associated with a family, a holding cost rate, and a mean processing time. Set-up times are required to switch from one family to another, but are not required to switch within a family. We consider the case in which the order of jobs within the family is unconstrained, and a variation in which the order is fixed. The optimization is with respect to the weighted flowtime, and we treat problems both with and without a makespan-constraint. Practical examples based on this model are described. We partially characterize an optimal policy by means of a Gittins rewardrate index and a similar switching index derived from multi-armed bandit theory. For deterministic problems with a makespan constraint, we present an optimization algorithm for the special case of two families and at most three set-ups . Without a makespan constraint and without preemption, we prove that our analysis of a deterministic model extends to stochastic set-up and processing times without loss of optimality. Managerial insights based on our technical results are provided.

BIOPOLITICS AND INTUITIVE ALGEBRA IN THE MATHEMATIZATION OF CRYPTOLOGY? A REVIEW OF SHANNON'S “A MATHEMATICAL THEORY OF CRYPTOGRAPHY” FROM 1945

Communication theory of secrecy systems as well as information theory in terms of Claude E. Shannon not only explains the solvability but also explores the theoretical secrecy of cryptograms by modeling information sources in higher order statistics, so-called a priori transition probabilities. In order to understand messages as stochastic processes in time, the mathematical theory of communication is historically traced back to World War II and into two fields of knowledge: biopolitics and intuitive algebra.

The effect of sudden material handling system breakdown on the performance of a JIT system

In this paper we explore the impact of sudden breakdown of the material handling system on the performance of a traditional kanban system (TKS). TKS, which is an element of the just-in-time system, is designed to operate in an ideal environment such as constant processing times and uninterrupted processing. However, in a real life environment, the TKS could be subjected to various unpredictable factors including stochastic processing times and process interruption due to equipment failure. These factors would seriously strain the performance of TKS. We consider a TKS in which some stations are dependent on a material handling system to move parts between them. We study the effect of a sudden breakdown of such a material handling system on the performance of the TKS. In addition, we also study a newly developed kanban system (which dynamically and systematically manipulates the number of kanbans in order to offset the blocking and starvation caused by these factors during a production cycle) under the same conditions. We refer to the new system as the 'flexible kanban system' (FKS). We compare the overall performances of the TKS and FKS by considering a variety of cases. We present the solution procedure, results and discussion for these cases.

A Weak Ordering of Positive Dependence Structure of Stochastic Processes

In this paper we introduce a new concept of more weakly quadrant dependence of hitting times of stochastic processes. This concept is weaker than the more positively quadrant dependence and it is closed under some statistical operations of weakly positive quadrant dependence (WPQD) ordering.

Adapting just-in-time manufacturing systems to preventive maintenance interruptions

The just-in-time (JIT) system is designed to operate in an ideal environment such as with constant processing times, smooth and stable demand and uninterrupted processing. However, in a real-life environment, the JIT system is subjected to various uncertain factors including stochastic processing times, variable demand and process interruption due to planned preventive maintenance. These factors seriously compromise the performance of JIT. In this paper, we present a newly developed JIT system which uses an algorithm to dynamically and systematically manipulate the number of Kanbans in order to offset the blocking and starvation caused by the said factors during a production cycle. We refer to the new system as the flexible Kanban system (FKS). We provide steps of the algorithm and demonstrate the effectiveness of FKS using a case example. For the case example, we present the solution procedure, results and discussion.

Vibration control of super tall buildings subjected to wind loads

Excessive vibration due to wind loads is a major obstacle in design and construction of a super tall building. The authors recently introduced an innovative method for controlling the wind response of super tall buildings, which takes advantage of the so-called mega-sub structural configuration. Preliminary investigation was performed under the assumption that the wind load is a white noise and the building can be modeled as a shear structure. In this paper, a more reasonable tall building model (a cantilever beam) and a more realistic wind load model (a non-white stochastic process in time and space) are employed to design passive and hybrid mega-sub control systems and to examine the performance of such controlled buildings. Building vibration in both along-wind and across-wind directions is examined. The control parameters of the proposed systems, including the frequency ratio of the sub to the mega structures, the damping ratio of the sub structure, and the feedback gains of the actuator force, are studied and their optimal values are obtained. For comparison, a tall building without control and one with the conventional tuned-mass-damper control are also studied under the same load conditions. The significant cost-effectiveness of the proposed mega-sub systems is demonstrated in reducing the acceleration and deformation responses of tall buildings to wind loads, not only enhancing the safety of structure and its contents but also improving the comfort of occupants.

On Irregular, Nonlinear Waves in a Spread Sea

Abstract Optimal design and reassessment of offshore structures requires a good understanding of the ocean environment. The motion of the sea surface can be viewed as a three-dimensional, nonlinear stochastic process in time. In order to characterize the wave environment adequately, we need to model its random, nonlinear, and spread nature. In this paper, we address: • the expected shape of a wave near a crest or trough, • the expected shape of the ocean surface at one point, given a crest at a different point, • an efficient method to incorporate nonlinear effects within linear wave simulations, • the magnitude of wave nonlinearity as a function of wave amplitude. Detailed comparison of theory and full-scale offshore measurements at the Shell Expro Tern platform show good agreement.

An algorithm to dynamically adjust the number of Kanbans in stochastic processing times and variable demand environment

In a real-life environment, the just-in-time JIT system is subjected to various types of uncertainties such as stochastic processing times and variable demand. Since, JIT was only meant to operate in a deterministic environment, its performance is seriously affected by variations in processing times and demand. In this paper, a newly developed Kanban system is presented which uses an algorithm to dynamically and systematically manipulate the number of Kanbans in order to offset the blocking and starvation caused by the said uncertainties during a production cycle. The new system is termed a flexible Kanban system FKS . The steps of the algorithm are detailed and the effectiveness of FKS is demonstrated using an example model. For the example model, the solution procedure, results and a discussion are presented.

An evaluation of order release strategies in a remanufacturing environment

Remanufacturing is a process by which worn-out products are restored to like new condition. Remanufacturing operations are characterized by probabilistic recovery rates of parts from the cores, and stochastic routings and lead times, as well as stochastic processing times. These factors serve to complicate planning and control functions for firms in remanufacturing, an environment with a greater degree of variability than a traditional manufacturing environment. There is no literature to assist in deciding on scheduling/order release strategies in a remanufacturing environment. In this article various order release strategies are evaluated in conjunction with scheduling rules in a remanufacturing environment, using a simulation model of a Naval aviation depot's engine components work shops. The results indicate that a simple level order release strategy in conjunction with a due date based scheduling rule provides an efficient means of releasing and scheduling work in this environment.

The Dynamic and Stochastic Knapsack Problem with Deadlines

In this paper a dynamic and stochastic model of the well-known knapsack problem is developed and analyzed. The problem is motivated by a wide variety of real-world applications. Objects of random weight and reward arrive according to a stochastic process in time. The weights and rewards associated with the objects are distributed according to a known probability distribution. Each object can either be accepted to be loaded into the knapsack, of known weight capacity, or be rejected. The objective is to determine the optimal policy for loading the knapsack within a fixed time horizon so as to maximize the expected accumulated reward. The optimal decision rules are derived and are shown to exhibit surprising behavior in some cases. It is also shown that if the distribution of the weights is concave, then the decision rules behave according to intuition.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

The interface of buffer design and cyclic scheduling decisions in deterministic flow lines

In this paper, we address some issues on the interface of buffer design and cyclic scheduling decisions in a multi-product deterministic flow line. We demonstrate the importance of the above interface for the throughput performance of the flow line. In particular, we point out that the use of sequence-independent information, such as workload distribution and variability in processing times among stations, is not adequate to decide the optimal buffer configuration of the flow line. We formulate the buffer design problem for a fixed sequence of jobs as a general resource allocation problem, and suggest two effective heuristics for its solution. For the simultaneous buffer design and cyclic scheduling problem, we suggest an iterative scheme that builds on the effectiveness of the above heuristics. One of the side results of our extensive computational studies on this problem is that the general guidelines of buffer design in single-product flow lines with stochastic processing times are not directly transferable to the multiproduct deterministic flow line environment.

Stochastic assembly line balancing using simulated annealing

The problem of balancing assembly lines with stochastic task processing times is addressed. The size of the problems that can be solved by optimal methods is limited and hence many heuristics have been developed, which give sub-optimal solutions. An approach for solving the problem using the simulated annealing technique is presented here. The proposed approach tries to reach the global optimum by not getting trapped at the different local optimum points. Another feature of this method is the non-dependence of the final solution on the initial solution. Solutions for line balancing problems obtained using the above method compare favourably with the results of other greedy heuristics.

Turnpike Optimality of Smith's Rule in Parallel Machines Stochastic Scheduling

Consider scheduling a batch of jobs with stochastic processing times on parallel machines, with minimization of expected weighted flowtime as objective. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time, provides a natural heuristic for this problem. In a previous paper we have found an upper bound for the difference between the expected objective under Smith's Rule and under the optimal strategy. In this paper we find an upper bound on the expected number of times that Smith's rule differs from the optimal decision. Under some mild and reasonable assumptions these bounds remain constant when the number of jobs increases. Hence, under these conditions Smith's Rule is asymptotically optimal, and it has a Turnpike Optimality property, that is, Smith's Rule is optimal most of the time.

Scheduling jobs with stochastic processing times and due dates to minimize total tardiness

We study the optimality of expected earliest due date (EEDD) sequencing of n jobs on M parallel identical machines, to minimize the total tardiness. The processing times of the jobs are assumed to be identically distributed with distribution function F(χ), and the due date of job j, Dj, j = 1,…, n is assumed to be distributed with distribution function Gj. We give stochastic comparisons of the objective function when the due dates are comparable in different stochastic order relations. For a single processor, the results are extended to the case when the processing times are not identically distributed, but are compatible with the due dates.

Simulation modelling and analysis of a JIT production system

With a view to examine the effects of stochastic demand and processing times, and the number of Kanbans on system performance, we simulate a 9-workstation, sequential production line. To determine ...

Uniform Assembly Line Balancing with Stochastic Task Times in Just‐in‐time Manufacturing

Recognising the enormous potential of just‐in‐time (JIT) concepts for boosting productivity and quality, an increasing number of US and European firms consider adopting JIT concepts in manufacturing. However, the transfer of a manufacturing policy from traditional to JIT always requires radical structural changes in a production line design. One typical example of these changes is uniform assembly which does not allow high variability in the production schedules. Consequently, major hindrance to uniform assembly is a random fluctuation of task processing times in assembly line balancing. This article proposes a heuristic which takes into account stochastic task processing times and further develops a work assignment with the lowest expected total cost as well as an assignment with the highest work completion probability crucial for the success of JIT manufacturing.

Sequencing jobs on a single machine with a common due date and stochastic processing times

This paper presents a procedure for sequencing jobs on a single machine with jobs having a common due date and stochastic processing times. The performance measure to be optimized is the expected incompletion cost. Job processing times are normally distributed random variables, and the variances of the processing times are proportional to their means. The optimal sequences are shown to have a W- or V-shape. Based on this property computationally attractive solution methods are presented.

Approximation results in parallel machnies stochastic scheduling

We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We obtain a bound on the worst case difference between the expected weighted flow time under Smith's Rule and under an optimal policy. For a wide class of processing time distributions, this bound is of oderO(1) and does not increase with the number of jobs.