Total Backlog Research Articles

Use of validated community-based trachoma trichiasis (TT) case finders to measure the total backlog and detect when elimination threshold is achieved: a TT methodology paper.

IntroductionThe World Health Organization recommends TT surveys to be conducted in adults aged 15+ years (TT 15 survey) and certifies elimination of TT as a public health problem when there is less than 1 unknown case per 1,000 people of all ages. There is no standard survey method to accurately confirm this elimination prevalence threshold of 0.1% because rare conditions require large and expensive prevalence survey samples. The aim of this study was to develop an accurate operational research method to measure the total backlog of TT in people of all ages and detect when the elimination threshold is achieved.MethodsBetween July to October 2016, an innovative Community-based, Mapping, Mop-up and Follow-up (CMMF) approach to elimination of TT as a public health problem was developed and tested in Esoit, Siana, Megwara and Naikara sub-locations in Narok County in Kenya. The County had ongoing community-based TT surgical camps and case finders. TT case finders were recruited from existing pool of Community health volunteers (CHV) in the Community Health Strategy Initiative Programme of the Ministry of Health. They were trained, validated and supervised by experienced TT surgeons. A case finder was allocated a population unit with 2 to 3 villages to conduct a de jure pre-survey census, examine all people in the unit and register those with TT (TT all survey). Identified cases were confirmed by TT surgeons prior to surgery. Operated patients were reviewed at 1 day, 2 weeks and 3-6 months. The case finders will also be used to identify and refer new and recurrent cases. People with other eye and medical conditions were treated and referred accordingly. Standardised data collection and computer based data capture tools were used. Case finders kept registers with details of all persons with TT, those operated and those who refused to be operated (refusals). These details informed decision and actions on follow-up and counselling. Progress towards achievement of elimination threshold was assessed by dividing the number of TT cases diagnosed by total population in the population unit multiplied by 1,000.ResultsNarok County Government adopted both the CMMF approach and TT all survey method. All persons in 4,784 households in the four sub-locations were enumerated and examined. The total population projection was 29,548 and pre-survey census 22,912 people. Fifty-three cases of TT were diagnosed. The prevalence was 0.23% and this is equivalent to 2.3 cases per thousand population of all ages. Prior to this study, the project required to operate on at least 30 cases (excess cases) to achieve the elimination threshold of 1 case per 1000 population.ConclusionThe total backlog of TT was confirmed and the project is now justified to lay claim of having eliminated TT as a public health problem in the study area. TT all method may not be appropriate in settings with high burden of TT. Nomadic migrations affect estimation of population size. Non-trachomatous TT could not be ruled-out.

Queue size distribution of Geo/G/1 queue under the Min(N,D)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n+. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n-, n and n+ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.

Combining system dynamics and multi-objective optimization with design space reduction

– The purpose of this paper is to introduce an effective methodology of obtaining Perot-optimal solutions when combining system dynamics (SD) and multi-objective optimization (MOO) for supply chain problems. , – This paper proposes a new approach that combines SD and MOO within a simulation-based optimization framework for generating the efficient frontier for supporting decision making in supply chain management (SCM). It also addresses the issue of the curse of dimensionality, commonly found in practical optimization problems, through design space reduction. , – The integrated MOO and SD approach has been shown to be very useful for revealing how the decision variables in the Beer Game (BG) affect the optimality of the three common SCM objectives, namely, the minimization of inventory, backlog, and the bullwhip effect (BWE). The results from the in-depth BG study clearly show that these three optimization objectives are in conflict with each other, in the sense that a supply chain manager cannot minimize the BWE without increasing the total inventory and total backlog levels. , – Having a methodology that enables effective generation of optimal trade-off solutions, in terms of computational cost, time as well as solution diversity and intensification, assist decision makers in not only making decision in time but also present a diverse and intense solution set to choose from. , – This paper presents a novel supply chain MOO methodology to assist in finding Pareto-optimal solutions in a more effective manner. In order to do so the methodology tackles the so-called curse of dimensionality by reducing the design space and focussing the search of the optimization to regions of inters. Together with design space reduction, it is believed that the integrated SD and MOO approach can provide an innovative and efficient approach for the design and analysis of manufacturing supply chain systems in general.

Setting ART initiation targets in response to changing guidelines: The importance of addressing both steady-state and backlog.

Target setting is useful in planning, assessing and improving antiretroviral treatment (ART) programmes. In the past 4 years, the ART initiation environment has been transformed due to the change in eligibility criteria (starting ART at a CD4+ count <350 cells/μl v. <200 cells/μl) and the roll-out of nurse-initiated management of ART. To describe and illustrate the use of a target-setting model for estimating district-based targets in the era of an expanding ART programme and changing CD4+ count thresholds for ART initiation. Using previously described models and data for annual new HIV infections, we estimated both steady-state need for ART initiation and backlog in a North West Province district, accounting for the shift in eligibility. Comparison of actual v. targeted ART initiations was undertaken. The change in CD4+ count threshold adds a once-off group of newly eligible patients to the pool requiring ART - the backlog. The steady-state remains unchanged as it is determined by the annual rate of new HIV infections in previous years. The steady-state need for the district was 639 initiations/month, and the backlog was ~15,388 patients. After the shift in eligibility in September 2011, the steady-state target was exceeded over several months with some backlog addressed. Of the total backlog for this district, 72% remains to be cleared. South Africa has two pools of patients who need ART: the steady-state of HIV-infected patients entering the programme each year, determined by historical infection rates; and the backlog created by the shift in eligibility. The healthcare system needs to build long- term capacity to meet the steady-state need for ART and additional capacity to address the backlog.

A possibilistic programming approach for capacitated lot-sizing problem in mixed assembly shops

This paper develops a fuzzy multi-objective linear programme (FMOLP) model for solving the bi-objective capacitated lot-sizing problem (CLSP). The proposed model attempts to simultaneously minimise total cost consist of total production variation cost, inventory cost, backlog cost and total setup cost while maximising the resource utilisation. According to the structure of the mixed assembly shops, a multi-product model with multi-item that should be produced during multi-level has been designed. Based on the vagueness and imprecision of the real case, the production, holding and backorder costs and demand of the products were considered as fuzzy number that have their membership function during planning horizon in each period. An interactive fuzzy solution method is developed by combining a number of efficient solution algorithms from the recent literature in order to solve the proposed possibilistic model. In order to demonstrate the significance and applicability of the proposed model as well as the usefulness of the proposed solution approach, numerical experiments are conducted and the results are provided.

2011 Editor Report

Here is the printed version of the report of the editor as presented to the ARIA meeting in August 2011. 1. SUBMISSIONS AND PUBLICATION STATISTICS (JULY 18, 2011) Table 1 provides the historical summary of JRI statistics, including resubmissions as before 2007. This table updates the historical trends in submissions, acceptance rates, and international submission rates (outside of the USA). It also presents the average processing time. The number of submissions increased significantly to 253 in 2010. The acceptance rate has consistently been below 20 percent since 2006. The average processing time decreased significantly to an average of 101 days in 2010. The number of submissions in Table I includes resubmissions. The numbers in Table 2 reflect new submissions only. This presentation style has a significant effect on the numbers and particularly on the acceptance rates. The second table also shows a continuous decrease in the acceptance rate of new submissions. The number of new submissions is quite stable since 2006. The average processing time is also affected by the second method of presenting statistics, shown in Table 2, because the peer-review process is shorter in the second run. The average processing time in Table 2 applies to the first submission, while Table I shows the average over the total number of rounds for which the paper receives a different manuscript number. Many journals publish the type of statistics shown in Table 2, which seem to have the greatest influence over where authors decide to submit their articles for publication. They also paint a more accurate picture of new submissions and acceptance rates. Since January 2007, we have been suggesting a 3-month deadline to the referees. We have also adopted a screening process whereby we return some manuscripts to the authors without a detailed referee report. This screening is usually done by the editor or an associate editor whose expert knowledge on the subject qualifies him or her to decide whether to reject the paper or send it to referees. The two main reasons for returning a paper after the screening process are: (1) a low probability that it will measure up to the standards of the Journal and (2) lack of a link between the content of the paper and the mission of the Journal. The screening process seems to have improved the average processing time in both tables. The last column of both tables provides the international submission rates. A paper is considered international if the affiliation of the corresponding author is outside the United States. Before 2007, a different criterion applied. A paper was considered international if the affiliation of any one of its authors was outside the USA. We have chosen this new criterion because it better highlights the international status of the paper. It is also easier to manage. As the numbers show, the Journal's international reach remains stable over the years with an exception in 2007. More than 50 percent of the papers submitted come from outside the USA. For new manuscripts, the ratio is higher than 60 percent. Tables 3 and 4 show the publication statistics and Table 5 presents the status of manuscripts by year. The measures adopted over the last 2 years have enabled the Journal to significantly reduce the backlog the 3 years preceding the current year. Only 36 articles accepted before 2011 have not been published yet; 10 of the 59 accepted papers in the total backlog will be published in the September issue, and about 12 will be published in the December issue. Following the new contract with Wiley-Blackwell, the Journal will publish 1,100 pages a year instead of 1,000, starting in 2012. Table 6 shows waiting periods for the first decision, measured in months. As you can see, the evaluation process during the first 4 months improved in 2010 (as well as in 2011). The average processing time is 3.93 months in 2010 while it was 5.8 months in 2007. …

Lead-time analysis and a control policy for production lines

We address a control problem for a production line that produces one product to stock and faces random demand. During stockouts, the system quotes a fixed response time for each arriving order, and the customers place their orders only if the response time promised meets their deadlines. Customer orders are filled on a first come, first served basis. A penalty cost is incurred whenever a customer is served later than promised. A two-parameter admission/inventory control policy is implemented that maintains a bounded backlog and a constant inventory position (total inventory minus backlog) in the system. For production lines with exponential processing times and Poisson demand, the mean profit rate of the system is computed analytically using closed queueing network formulae. For systems with general processing or interarrival time distributions, the profit rate is estimated via simulation. Simple properties are established that ensure that the profit maximising control parameters can be determined in finite time using exhaustive search. Numerical results show that the proposed policy performs better than the make-to-order/zero-inventory and the lost-sales/make-to-stock policies.

Analysis of the MAP/G/1 Queue Under the Min(N, D)-Policy

In this paper, we consider the queueing system under the MAP (Markovian Arrival process) arrivals and the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service time of the waiting customers exceeds D, whichever occurs first (Min(N, D)-policy). We analyze the queue length, workload, and waiting time. Then, we present numerical examples in which our analytical results are compared with the simulation estimates for verification purposes. We also compare our system with the M/G/1 queue under the same parameter setting and show that a naive Poisson assumption may severely underestimate the mean performance measures.

The performance of the M/G/1 queue under the dyadic [formula omitted]-policy and its cost optimization

In this paper, we consider the M/G/1 queueing system under the Min ( N , D ) -policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D , whichever occurs first. We first analyze the queue length, the workload and the waiting time. Then, we consider two linear cost models (one based on the mean workload and the other based on the mean queue length) and compare the optimal Min ( N , D ) -policy with the optimal N -policy and the optimal D -policy.

Production control and combined discrete/continuous simulation modeling in failure-prone transfer lines

In this paper, we consider a production system consisting of multiple tandem machines subject to random failures. The objective of the study is to find the production rates of the machines in order to minimize the total inventory and backlog costs. By combining analytical formalism and simulation-based statistical tools such as design of experiments (DOE) and response surface methodology (RSM), an approximation of the optimal control policy is obtained. The combined discrete/continuous simulation modeling is used to obtain an estimate of the cost in a fraction of the time necessary for discrete event simulation by reducing the number of events related to parts production. This is achieved by replacing the discrete dynamics of part production by a set of differential equations that describe this process. This technique makes it possible to tackle optimization problems that would otherwise be too time consuming. We provide some numerical examples of optimization and compare computational times between discrete event and discrete/continuous simulation modeling. The proposed combination of DOE, RSM and combined discrete/continuous simulation modeling allows us to obtain the optimization results in a fairly short time period on widely available computer resources.

Editorial: Thanks to the Many Individuals Who Make Publication of Marketing Science Possible

Announcements and Journal Statistics Marketing Science continues as a bimonthly journal. We are planning a greatest-hits issue and implementing the data report later this year. During the transition from quarterly to bimonthly publication, we were conservative and maintained a larger backlog to ensure timely publication schedules. We currently have approximately 33 manuscripts in copyediting and a total backlog (accepted articles including those still with authors) indicated on our Marketing Science website. We are now returning to a more normal backlog. As noted earlier, bold innovative research in marketing science continues at a record, if not remarkable, pace. Manuscript submissions to Marketing Science, our eminent journal, remain high. As Panel 1 indicates, during the term of the current editor-in-chief, submissions have grown from a stable 124 per year to a projected 348 per year. Panel 2 shows the pattern of submissions. Panel 3 indicates that selectivity remains high. For example, in 2006, the 28 regular published articles represent 8.6% of new submissions that year. Note that new submission excludes Practice Prize and MSI submissions for special sections. A coordinated team effort by diligent area editors, meticulous reviewers, and dedicated, responsive authors has not let the increased volume hurt either the efficiency of the review process or its quality. We continue to decrease total turnaround time while maintaining the same number of quality reviews. Hardworking review teams have been able to maintain the outstanding quality of the journal

A production inventory model with deteriorating items and shortages

A continuous production control inventory model for deteriorating items with shortages is developed. A number of structural properties of the inventory system are studied analytically. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level, backlog level and production cycle time. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

The CLWS heuristic for single machine scheduling problem

A model for real-time control of flexible manufacturing systems is considered. In this model, a machine can process a finite number of part types at specified rates, but only one part type can be processed at any given time. Each switch from one type to another requires setup time. The clear-the-largest-work-after-setup (CLWS) heuristic policy which stabilizes the system in the sense that, in the long run, the required demand is met, has been introduced. That way, a better upper bound on the total work backlog than those available in earlier literature is derived. Computational results for the case of finite horizon show that the error of the heuristic CLWS from the optimal solution is 2.5–3.0% on average. Some computational results that compare the CLWS heuristic to the heuristic available in the earlier literature, for the same problem, are also reported.

Stability of real-time lot-scheduling and machine replacement policies with quality levels

We consider a single machine, multiproduct manufacturing system which can operate at finitely many quality levels. The quality of the machine deteriorates according to a continuous-time Markov process and the only way to improve the quality is by replacing the machine by a new one. In this framework we derive conditions for the stability of the system under a simple class of real-time scheduling/replacement policies. The stability notion that we employ is the recurrence of the total work backlog.

Optimal production planning in pull flow lines with multiple products

The paper is concerned with the problem of optimal production planning in deterministic pull flow lines with multiple products. The objective is to specify the production policy that minimizes the total inventory and backlog costs overtime. Assuming constant product demands and non-decreasing unit holding costs along the flow, an algorithm which obtains the optimal production policy is developed. This algorithm works for the discounted-cost function as well. The HJB equation is used to verify the optimality of the policy, and the computational complexity of the algorithm is discussed. Some illustrative examples are also included.

Replanning the Master Production Schedule for a Capacity‐Constrained Job Shop

This research examines the use of both frozen and replanning intervals for planning the master production schedule (MPS) for a capacity‐constrained job shop. The results show that forecast error, demand lumpiness, setup time, planned lead time, and order size have a greater impact on the mean total backlog, total inventory, and number of setups than the frozen and replanning intervals. The study also shows that a repetitive lot dispatching rule reduces the importance of lot sizing, and a combination of repetitive lot dispatching rule and single‐period order size consistently produces the lowest mean total backlog and total inventory. The results also indicate that rescheduling the open orders every period produces a lower mean total backlog and total inventory when the forecast errors are large relative to the order sizes. This result suggests that the due date of an open order should be updated only when a significant portion of the order is actually needed on the new due date.

Heavy traffic resource pooling in parallel-server systems

We consider a queueing system with r non-identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class. Each arrival requires a single service, which may be provided by any of several different servers in our general formulations the service time distribution depends on both the job class being processed and the server selected. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs onto available servers. A linear program involving only first-moment data (average arrival rates and mean service times) is used to define heavy traffic for a system of this form, and also to articulate a condition of overlapping server capabilities which leads to resource pooling in the heavy traffic limit. Assuming that the latter condition holds, we rescale time and state space in standard fashion, then identify a Brownian control problem that is the formal heavy traffic limit of our rescaled scheduling problem. Because of the assumed overlap in server capabilities, the limiting Brownian control problem is effectively one-dimensional, and it admits a pathwise optimal solution. That is, in the limiting Brownian control problem the multiple servers of our original model merge to form a single pool of service capacity, and there exists a dynamic control policy which minimizes cumulative cost incurred up to any time t with probability one. Interpreted in our original problem context, the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class, and all servers can and should be productively employed except when the total backlog is small. It is conjectured that such ideal system behavior can be approached using a family of relatively simple scheduling policies related to the c\mu rule.

Multiperiod production planning with demand and cost fluctuation

We consider the production planning of a single product over a finite planning horizon. The latter is made up of time periods that may not necessarily be of the same length. In each time period, the product is subject to a constant demand and a finite production capacity. If demand is not satisfied immediately, it is backlogged. The cost rates of carrying inventory or backlogging a unit of the product may also vary from one time period to the next. The objective is to determine an optimal production plan for the product so as to minimize the total inventory and backlog costs incurred over the planning horizon. The problem is formulated as an optimal control problem. First, the optimal solution of the one-time-period problem is determined. Then, based on the one-time-period optimal solution, the optimal solution for the whole planning horizon is obtained by solving a nonlinear programming problem.

Optimal production control of a dynamic two-product manufacturing system with setup costs and setup times

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region, the optimal control policy is determined analytically.

A volterra type integral equation for the characteristic function of the extended compound renewal process with applications

The extended compound renewal process, a generalization of the concept of filtered Poisson process, is introduced. It is shown that its characteristic function is expressible as the solution of a second type Volterua integral equation is solved for some special cases. Moreover, the equation is used to find the first moment and a recursive relationship for the higher order raw moment of the process. Finally, several areas of applications to the GIx/G/∞ queue are investigates including the size of the system, the queue output and the total backlog