JOB RELEASE CONTROL USING A CYCLIC SCHEDULE*

In just‐in‐time inventory management in any manufacturing setting, the general idea has been to release jobs as late as possible (to reduce inventory costs) while still having them arrive at bottleneck machines in time to maintain the desired throughput (by not starving a bottleneck machine). When a cyclic schedule is employed, the throughput is determined by a cyclic sequence of operations known as the cyclic critical path. These operations are not, in general, all performed on a single bottleneck machine. We present an algorithm for releasing jobs that treats this cyclic critical path as the bottleneck. Although this algorithm has the somewhat complex task of not delaying any of these operations on the cyclic critical path, it is greatly simplified by being able to take advantage of the fixed sequence of the cyclic schedule. The result is that the algorithm is relatively simple to implement. Although it uses a simulation‐based analysis, this analysis can all be done and the necessary results stored in advance of its use. We test the algorithm in a job shop environment with stochastic operation times. This algorithm is shown to be effective at reducing inventory while avoiding decreases in throughput.     

On single machine scheduling with resource constraint

The single machine scheduling with resource constraint is a nonlinear combinatorial optimization problem in cloud computing applications. Given a set of jobs and certain resource, the problem is to find a permutation of jobs and a distribution of resource to optimize certain objective function. The processing time of each job is a nonlinear function with respect to the resource assigned to it. In this paper, we propose a naive algorithm and study a subproblem in the algorithm that suppose the permutation of jobs is also given, how to find a resource distribution to minimize the total weighted flow time. We found a polynomial-time optimal solution for a special case and an approximation solution in general case.     

Bottleneck management: theory and practice

Advocates of TOC believe that bottleneck resource restricts an operation's ability to make money, and the best way to maximise income is to fully exploit the bottleneck resource. Almost all TOC literature focuses on situations where 100% bottleneck utilisation is applied. Based on the implementation experience, the finding is that the optimal level of bottleneck utilisation should be less than 100% and any attempt to increase utilisation beyond the optimal level brings disastrous results for a door manufacturing plant. In order to improve and maintain the performance of the plant effective bottleneck management is critical. The experience provides a deeper understanding of how to design such plants, which could be beneficial for practising managers and academics working with TOC concepts.     

A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling

In the multiprocessor scheduling problem to minimize the total job completion time, an optimal schedule can be obtained by the shortest processing time rule and the completion time of each job in the schedule can be used as a guarantee for scheduling revenue. However, in practice, some jobs will not arrive at the beginning of the schedule but are delayed and their delayed arrival times are given to the decision-maker for possible rescheduling. The decision-maker can choose to reject some jobs in order to minimize the total operational cost that includes three cost components: the total rejection cost of the rejected jobs, the total completion time of the accepted jobs, and the penalty on the maximum tardiness for the accepted jobs, for which their completion times in the planned schedule are their virtual due dates. This novel rescheduling problem generalizes several classic NP-hard scheduling problems. We first design a pseudo-polynomial time dynamic programming exact algorithm and then, when the tardiness can be unbounded, we develop it into a fully polynomial time approximation scheme. The dynamic programming exact algorithm has a space complexity too high for truthful implementation; we propose an alternative to integrate the enumeration and the dynamic programming recurrences, followed by a depth-first-search walk in the reschedule space. We implemented the alternative exact algorithm in C and conducted numerical experiments to demonstrate its promising performance.

     

An investigation of output flow control,bottleneck flow control and dynamic flow control mechanisms in various simple lines scenarios

Flow control mechanisms have been a topic of academic research for several years. With the growth of business-wide information systems such as enterprise resource planning and supply chain, better planning, scheduling and control of the business transformation process is required in order to achieve increased throughput, reduced inventories, shorter lead times and reduced tardiness. This research compares two new approaches to flow control, output flow control and bottleneck flow control to a real-time flow control system, dynamic flow control. Both output and bottleneck flow control mechanisms are much simpler to implement and manage than dynamic flow control in that they do not require continual feedback and rescheduling. Line characteristics, such as location of breakdowns with respect to the bottleneck, the location of the bottleneck when breakdowns occur, and the impact of variability of processing times on the performance measures (output, WIP level, lateness, and number of tardy jobs) for these three flow control mechanisms are compared. Both output and bottleneck flow control mechanisms perform favourably (particularly bottleneck) under different scenarios and warrant further study across a wider range of scenarios (mixed models, job shops, etc.).     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Hierarchical Multi‐skill Resource Assignment in the Telecommunications Industry

We formulate a discrete time Markov decision process for a resource assignment problem for multi‐skilled resources with a hierarchical skill structure to minimize the average penalty and waiting costs for jobs with different waiting costs and uncertain service times. In contrast to most queueing models, our application leads to service times that are known before the job is actually served but only after it is accepted and assigned to a server. We formulate the corresponding Markov decision process, which is intractable for problems of realistic size due to the curse of dimensionality. Using an affine approximation of the bias function, we develop a simple linear program that yields a lower bound for the minimum average costs. We suggest how the solution of the linear program can be used in a simple heuristic and illustrate its performance in numerical examples and a case study.     

Approximate versus Exact Equilibria in Dynamic Economies

This paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms that compute prices and allocations for which agents' first‐order conditions are approximately satisfied (“approximate equilibria”), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. We give a simple example to illustrate that approximate equilibria might be very far from exact equilibria. We then interpret approximate equilibria as equilibria for close‐by economies; that is, for economies with close‐by individual endowments and preferences. We present an error analysis for two models that are commonly used in applications, an overlapping generations (OLG) model with stochastic production and an asset pricing model with infinitely lived agents. We provide sufficient conditions that ensure that approximate equilibria are close to exact equilibria of close‐by economies. Numerical examples illustrate the analysis.     

Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

     

基于TrTS取样的股票收益率RV测度的改进

由于噪声的存在使得高频数据的分析过程存在着诸多困难,本文探讨了高频数据情况下的金融资产收益率已实现波动率的估计问题。在离散化的跳跃模型基础上,通过混合泊松分布而非传统的连续扩散模型来描述价格过程,并进一步提出了不同于以往文献研究的噪声假设,即在独立同分布的噪声假设基础上放松约束条件,保持噪声的独立性,但是允许噪声强度随时间变化,以此改善了传统的固定时间间隔取样模式。为了进一步改善估计效果,我们结合了TrTS(Transaction Time Sampling)以及一阶偏误修正的RV(realized variance)估计方式RVAC(1) (first-order AutoCorrelation to RV)。对来自两个交易所不同板块股票的价格数据进行的实证研究结果表明,本文的估计方式虽然对于个别股票价格数据会产生与实际背离潜在真实价格参数,但整体上对于已实现波动率的估计效果是比较稳健的。     

Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance

We consider the problem of scheduling a set of jobs with different processing times and sizes on a single bounded parallel-batch machine with periodic maintenance. Because the machine is in batch-processing model and the capacity is fixed, several jobs can be processed simultaneously in a batch provided that the total size of the jobs in the batch doesn’t exceed the machine capacity. And the processing time of a batch is the largest processing time of the jobs contained in the batch. Meanwhile, the production of each batch is non-resumable, that is, if a batch cannot be completed processing before some maintenance, that batch needs to be processed anew once the machine returns available. Our goal is to minimize the makespan. We first consider two special cases where the jobs have the same sizes or the same processing times, both of which are strongly NP-hard. We present two different approximation algorithms for them and show that these two algorithms have the same tight worst-case ratio of 2. We then consider the general case where the jobs have the arbitrary processing times and arbitrary sizes, for which we propose a 17/5-approximation algorithm.

     

The Maximum Throughput on a Golf Course

We develop stochastic models to help manage the pace of play on a conventional 18‐hole golf course. These models are for group play on each of the standard hole types: par‐3, par‐4, and par‐5. These models include the realistic feature that k−2 groups can be playing at the same time on a par‐k hole, but with precedence constraints. We also consider par‐3 holes with a “wave‐up” rule, which allows two groups to be playing simultaneously. We mathematically determine the maximum possible throughput on each hole under natural conditions. To do so, we analyze the associated fully loaded holes, in which new groups are always available to start when the opportunity arises. We characterize the stationary interval between the times successive groups clear the green on a fully loaded hole, showing how it depends on the stage playing times. The structure of that stationary interval evidently can be exploited to help manage the pace of play. The mean of that stationary interval is the reciprocal of the capacity. The bottleneck holes are the holes with the least capacity. The bottleneck capacity is then the capacity of the golf course as a whole.     

A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs,financial budget,and resource constraint in multiple manufacturers

We study a coordinated serial-batching scheduling problem that features deteriorating jobs, financial budget, resource constraints, resource-dependent processing times, setup times, and multiple manufacturers simultaneously. A unique feature but also a significant challenge in this problem is the dual constraints on resources, i.e., financial budget and resource quantity. Some key structural properties are first identified for the setting where the jobs and resources are already assigned to each manufacturer, which enables us to develop the optimal resource allocation scheme. Then, a polynomial-time scheduling rule is proposed to search for the optimal solution for each manufacturer in this setting. Then, a hybrid BA-VNS algorithm combining Bat algorithm (BA) and variable neighborhood search (VNS) is proposed to tackle the studied problem, and the optimal scheduling rule is implemented in its encoding procedure. Finally, computational experiments are conducted to test the performance of the proposed algorithm, and the efficiency and improvements are compared with those of BA, VNS, and Particle Swarm Optimization (PSO), with respect to convergence speed as well as computational stability.     

Balancing Production and Distribution in Paper Manufacturing

A paper manufacturing plant minimizes its production cost by using long production runs that combine the demands from its various customers. As jobs are completed, they are released to distribution for delivery. Deliveries are made by railcars, each of which is dedicated to one customer. Long production runs imply that maximizing railcar utilization requires holding the cars over several days or holding completed jobs within the loading facility. Each of these methods imposes a cost onto the distribution function. We find how distribution can minimize its cost, given production's schedule. We then consider the problem of minimizing the company's overall cost of both production and distribution. A computational study using general data illustrates that the distribution cost is reduced by 25.80% through our proposed scheme, and that the overall cost is reduced an additional 4.40% through our coordination mechanism. An optimal algorithm is derived for a specific plant's operations.     

Release of maintenance jobs in a decentralized multi-stage production/maintenance system with continuous condition monitoring

Condition-based maintenance is analyzed for multi-stage production with a separate maintenance department. It is assumed that the conditions of the machines deteriorate as a function of multiple production parameters and that the task of maintenance is to keep up predefined operational availabilities of the individual machines. In this context the problem of determining the optimal machine condition that triggers the release of a preventive maintenance job and the problem of scheduling maintenance jobs at the maintenance department arise. Existing approaches to solve these problems either assume a monolithic production/maintenance system or concentrate on a decentralized system in which the information flow and resource transfer do not cause delays. With our paper we aim at (1) deriving a triggering mechanism that is able to cope with relaxed assumptions and at (2) developing specific priority rules for scheduling maintenance jobs. Therefore, in this paper a specific continuous condition monitoring and a suitable information exchange protocol are developed, factors determining the release situation are operationalized, impacts of choosing the triggering conditions are identified and the components of specific priority rules for scheduling maintenance jobs are clearly elaborated. Finally the performance of the resulting solution approach is analyzed by simulations. Thereby, relevant characteristics of the production/maintenance system, the maintenance task and relevant priority rules are varied systematically. This research contributes answers to the questions on how the exchange of local information can be structured, the parameters of condition-based maintenance can be set and on what maintenance-specific priority rules can be applied in case of incomplete information about deterioration in a decentralized multistage production/maintenance system.     

Preventing and Diagnosing Colorectal Cancer with a Limited Colonoscopy Resource

This paper explores how the capacity of colonoscopy services should be allocated for screening and diagnosis of colorectal cancer to improve health outcomes. Both of these services are important since screening prevents cancer by removing polyps, while diagnosis is required to start treatment for cancer. This paper first presents a basic compartmental model to illustrate the trade‐off between these two analytically. Further, a more realistic population dynamics model with resource constraints is introduced for colorectal cancer screening and analyzed numerically. The best resource allocation decisions are investigated with the objectives of minimizing mortality or incidence rates. We provide a sensitivity analysis with respect to policy and disease‐related parameters. We conclude that to minimize mortality, the capacity should be rationed to ensure that the wait for diagnosis is at reasonable levels. When the relevant performance measure is the incidence rate, screening is allocated more capacity compared to the case with mortality rate measure. We also show that benefits from increasing compliance to screening programs can only be realized if there is sufficient service capacity.     

INTERPERSONAL SENSEMAKING AND THE MEANING OF WORK

In this paper, we present a model of interpersonal sensemaking and describe how this process contributes to the meaning that employees make of their work. The cues employees receive from others in the course of their jobs speak directly to the value ascribed by others to the job, role, and employee. We assert that these cues are crucial inputs in a dynamic process through which employees make meaning of their own jobs, roles, and selves at work. We describe the process through which interpersonal cues and the acts of others inform the meaning of work, and present examples from organizational research to illustrate this process. Interpersonal sensemaking at work as a route to work meaning contributes to theories of job attitudes and meaning of work by elaborating the role of relational cues and interpretive processes in the creation of job, role and self-meaning.     

Prices,Markups, and Trade Reform

This paper examines how prices, markups, and marginal costs respond to trade liberalization. We develop a framework to estimate markups from production data with multi‐product firms. This approach does not require assumptions on the market structure or demand curves faced by firms, nor assumptions on how firms allocate their inputs across products. We exploit quantity and price information to disentangle markups from quantity‐based productivity, and then compute marginal costs by dividing observed prices by the estimated markups. We use India's trade liberalization episode to examine how firms adjust these performance measures. Not surprisingly, we find that trade liberalization lowers factory‐gate prices and that output tariff declines have the expected pro‐competitive effects. However, the price declines are small relative to the declines in marginal costs, which fall predominantly because of the input tariff liberalization. The reason for this incomplete cost pass‐through to prices is that firms offset their reductions in marginal costs by raising markups. Our results demonstrate substantial heterogeneity and variability in markups across firms and time and suggest that producers benefited relative to consumers, at least immediately after the reforms.     

Online scheduling of equal length jobs on unbounded parallel batch processing machines with limited restart

We consider the online scheduling of equal length jobs on unbounded parallel batch processing machines to minimize makespan with limited restart. In the problem \(m\) identical unbounded parallel batch processing machines are available to process the equal length jobs arriving over time. The processing batches are allowed limited restart. Here, “restart” means that a running task may be interrupted, losing all the work done on it, and the jobs in the interrupted task are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that only a running batch that contains no restarted jobs can be restarted. For this problem, we present a best possible online algorithm.     

COMPETITION AND RELATIONAL CONTRACTS: THE ROLE OF UNEMPLOYMENT AS A DISCIPLINARY DEVICE

Abstract When workers are faced with the threat of unemployment, their relationship with a particular firm becomes valuable. As a result, a worker may comply with the terms of a relational contract that demands high effort even when performance is not enforceable by a third party. But can relational contracts motivate high effort when workers can easily find alternative jobs? We examine how competition for labor affects the emergence of relational contracts and their effectiveness in overcoming moral hazard in the labor market. We show that effective relational contracts do emerge in a market with excess demand for labor. Long‐term relationships turn out to be less frequent when there is excess demand for labor than they are in a market characterized by exogenous unemployment. However, stronger competition for labor does not impair labor market efficiency: higher wages induced by competition lead to higher effort out of concerns for reciprocity.