Total Backlog Research Articles

Flashforward: The Current and Future Applications of Vibrational Spectroscopy for Forensic Purposes

ABSTRACTVibrational spectroscopy combined with machine learning has a great potential for forensic applications. For example, handheld Raman spectroscopic instruments are already used by law enforcement agencies for precise, confirmatory identification of drugs. Beyond drug identification, several emerging technologies based on vibrational spectroscopy are currently under development for forensic investigative purposes, including the analysis of questioned documents, gunshot residue, fabrics, soil, hair, nails, and nail polish. This article provides a comprehensive overview of the application of vibrational spectroscopy in various areas of forensic analysis, particularly focusing on forensic serology and the analysis of trace evidences. In the case of forensic serology, the methodology allows for determining complex aspects of serological casework, including the time since deposition of a stain, as well as the phenotypic profile of the stain donor—namely, sex, race, and age. Furthermore, gunshot residues can be accurately identified by grain, caliber, and manufacturer when Raman spectroscopy is paired with machine learning. This integration of advanced spectroscopic techniques with machine learning holds great promise for furthering both the accuracy and efficiency of investigations, helping to reduce the total backlog of evidence investigation currently plaguing modern forensic laboratories.

A deterministic fluid model for production and energy mode control of a single machine

Improving machines’ energy efficiency through dynamic energy mode control to meet demand requirements with minimal energy consumption is a promising approach. This study considers a machine operating in working, idle, off, and warmup energy modes with different energy consumption in each mode. A deterministic fluid model is developed to analyze an energy mode control policy that determines when to keep the machine working, off or idle, and switch to other modes based on the inventory/backlog level to minimize the total energy, inventory, and backlog costs. This approach facilitates the derivation of closed-form expressions for the optimal thresholds and the associated costs. This modeling approach allows us to prove that a policy that operates the machine between the working and off modes or the working and idle modes is always better than a hybrid policy that operates the machine in working, off, and idle modes simultaneously. We use the solution of the deterministic fluid model to propose an approximate policy for machines with stochastic production, warmup, and demand processes. We compare the results of the proposed approximation method with the optimal solution of a stochastic system where the production and warmup times are exponential and the demand inter-arrival times have Erlang distribution. The optimal solution for the stochastic system is determined by solving a Markovian Decision Process (MDP). Our numerical experiments show that the proposed approximation method predicts the optimal policy type for the stochastic case with a 89.3% accuracy, and the average error between the optimal cost and the cost obtained with the approximation method is 1.37% for 729 different cases tested. Furthermore, the computational efficiency of the proposed approximation is around 250 times better than the effort to determine the optimal policy using an MDP approach. We propose this approximation method where the control parameters are given in closed form as an easy-to-implement and effective policy to control energy modes to minimize the total energy, inventory, and backlog costs. Furthermore, we present the deterministic fluid modeling approach as a versatile approach to analyze energy mode control problems.

The effects and benefits of a latent print AFIS deferral policy

Forensic laboratories in the United States had an estimated backlog of 570,100 requests for all forensic services at the end of 2014. Latent print requests represented approximately 12% of that total backlog [1, NIJ 2019]. With ever-increasing demands and backlogs, a review of laboratory or section practices becomes vital to operations. Work process and business practice changes can increase efficiencies and result in the reduction of casework backlogs and turnaround times. The automated fingerprint identification system (AFIS) deferral policy implemented by the Latent Print Comparative Section (LPCS) of the Phoenix Police Department Laboratory Services Bureau (PPD LSB) was employed to address the latent print backlog. Five years of multiple AFIS request types were analyzed to demonstrate the positive effects and benefits of such policies, including a 26.32% decrease in turnaround time over the data collection and analysis period and a 90.96% reduction in backlogged requests for one year.

Nowcasting waiting lists for elective procedures and surgery in England: a modelling study

BackgroundThe COVID-19 pandemic resulted in extensive disruption to the delivery of elective health services. Official figures of NHS waiting lists in England do not account for patients on the hidden waiting list (ie, patients who have symptoms or disease requiring elective procedures who have not been placed on the waiting list due to pandemic-related disruption). The aim of this study was to model the elective procedure backlog in England, including the hidden waiting list. MethodsWe used publicly available activity data from NHS Digital to estimate procedure-level backlogs in England for the pandemic period (from Jan 1, 2020, to Dec 31, 2022) compared with expected population need for elective procedures based on pre-pandemic trends, adjusting for population growth and ageing, as well as patient deaths while on the waiting list. The primary outcome was the elective procedure backlog. Elective procedures were defined as including surgery, endoscopy, interventional radiology, and interventional cardiology. The secondary outcome was the procedural hidden waiting list. The elective procedure backlog was reported by specialty and procedure. FindingsThe total elective procedure backlog in England on Dec 31, 2022, was modelled to be 4 519 467 procedures. The hidden waiting list was 3 621 423, comprising 80·3% of the total backlog. Half the total backlog (2 228 348, 49·3%) was in people aged 16–59 years. The largest backlogs were in general surgery (1 463 423, 32·4%), orthopaedics (1 001 850, 22·2%), and urology (510 649, 11·3%). Overall, 84·7% (3 827 687 procedures) of the backlog were for day-case procedures. The procedures with the greatest total backlog were sigmoidoscopy and colonoscopy (546 930, 12·1%), gastroscopy (376 089, 8·3%), cataract surgery (238 912, 5·3%), and lower limb joint replacement (209 976, 4·6%). InterpretationNHS waiting lists are an unreliable guide to the true population need for elective procedures. Initiatives are needed to identify and prioritise patients requiring urgent treatment. Most need is for low-complexity high-volume day-case surgery. Sustained, ring-fenced funding is required to invest in scaling up the operative workforce and facilities, and to increase the resilience of surgical services to avoid existing backlogs being compounded by future external pressures. This modelling study is based on an assumption that over the course of the pandemic the incidence of surgical disease did not change. FundingNone.

P005 Using novel remote electronic monitoring to measure and manage the Rheumatology Clinic backlog generated by COVID-19

Abstract Background/Aims During the COVID-19 pandemic we were unable to provide regular outpatient services for patients with chronic rheumatic diseases. A “backlog” of 6812 patients without an allocated follow-up appointment accrued by September 2021. We quantified this cohort and analysed attempts to deliver care remotely (using video, telephone, and electronic remote management forms (RMFs)). Methods We selected a 12-month “window” (May 2020-May 2021) and analysed the number of patients awaiting follow-up during this period. This was initially 3259 patients out of the total backlog 6812. We revisited the number of patients remaining in that cohort on four occasions between September 2021 and September 2022: at baseline, then at 1-, 2-, 6- and 12-month intervals. Each audit cycle was conducted using the same methodology. Alongside usual follow up pathways, (face to face, video or telephone), we implemented remote management forms (RMFs) for different disease groups which were designed by the department; they contained a triage questionnaire, including calculation of disease severity scores, and questions about medications. These were sent out by clinicians to some patients in lieu of a telephone, video or face to face appointments. Data from RMFs was stored in a secure database for clinician review. Data analysis performed in Microsoft Excel and R (version 4.2.1). Results The number of patients without allocated follow-up appointments reduced from 3259 to 326 between Sep-21 and Sep-22. This is a 90% reduction in the backlog over a 12-month period, with a 71% reduction achieved by 6 months. There was a significant, progressive reduction in the number of patients over time (p < 0.001 - Chi-square test for trend). Of the 1956 RMFs completed between Sep-21 - Mar-22, only 261 patients recorded a previous appointment date. 154/261 (59%) were completed by patients waiting in the “window” of May-20 - May-21. This indicates a preferential use of RMFs targeting backlog patients. Between 2-8% of the total backlog patients were managed using RMFs based on available data. Conclusion We have significantly reduced the size of our backlog of outpatient follow-up due to COVID-19 over a 12-month period. In-addition these results likely underestimate the effect of RMFs due to this dataset being incomplete. Remote management made a sizeable contribution to this reduction, meaning some of this reduction was achieved without face-to-face encounters. The use of 1956 forms over a 6-month period shows robust integration of our RMFs into outpatient services disrupted by COVID-19 and provides evidence for remote management as a useful tool in outpatient management, with relevance to areas such as Patient Initiated Follow Up pathways. Further work is needed to clarify where remote management is best deployed and which patient groups benefit most from this. Disclosure D. Kurzeja: None. A. Soni: None. J. Jackman: None. J. David: None. R. Luqmani: None.

A Dynamic Analysis for Mitigating Disaster Effects in Closed Loop Supply Chains

The increased level of complexity in the case of Closed Loop Supply Chains (CLSCs) turns them into vulnerable systems under a disaster event. The latter calls for a methodological approach that allows a dynamic study under alternative policies in mitigating the disaster effects with a focus on creating sustainable CLSCs. For this reason, we provide a System Dynamics (SD)-based analysis for disaster events on the operation of CLSCs. By “disaster event”, we mean three different categories taking shape on the basis of duration. Furthermore, three different demand patterns emerging due to the disaster event are examined. We assume that the disaster event affects the manufacturer, and we examine the system response under different mitigation policies. For each demand pattern two different mitigation policies at the manufacturer level are examined by considering the total CLSC profit and demand backlog as measures of policy performance. For each combination, extensive simulation experimentation reveals sustainable policy recommendations under alternative settings regarding the reduction in the manufacturer’s production.

A Fuzzy Production Inventory Model for Deteriorating Items with Shortages

In this paper we have developed a supply chain production inventory model for deteriorating items with shortage under Fuzzy environment. 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. In reality it is seen that we cannot define all parameters precisely due to imprecision or uncertainty in the environment. So, we have defined the inventory parameter deterioration rate as triangular fuzzy numbers. The signed distance method and graded mean integration method have been used for defuzzification. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level and backlog level. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

Elastic job scheduling with unknown utility functions

We consider a bipartite network consisting of job schedulers and parallel servers. Jobs arrive at the schedulers following stochastic processes with unknown arrival rates, and get routed to the servers, which execute the jobs with unknown service rates. The jobs are elastic, as their “size”, i.e., the amount of service needed for their completion, is determined by the schedulers. After a job finishes execution, some utility is obtained where the utility value depends on the job’s size through some underlying concave utility function. We consider the setting where the utility functions are unknown apriori, while a noisy observation of the utility value of each job is obtained upon its completion. Our goal is to design a policy that makes job-size and routing decisions to maximize the total utility obtained by the end of the time horizon T. We measure the performance of a policy by regret, i.e., the gap between the expected utility obtained under the policy and that under the optimal policy. We first establish an upper bound on the regret of a generic policy, that consists of the cumulative difference in utility between the job-size decisions of the policy and the solution to a static optimization problem, and the total backlog of unfinished jobs at the end of the time horizon. We then propose a policy that simultaneously controls the cumulative utility difference and backlog of unfinished jobs, and achieves an order optimal regret of Õ(T). Our policy solves the elastic job scheduling problem by extending the Stochastic Convex Bandit Algorithm to handle unknown and stochastic constraints, and making routing decisions based on the Join-the-Shortest-Queue rule. It also presents a principled approach to extending algorithms for zeroth-order convex optimization to the settings with unknown and stochastic constraints.

Pembangunan Sistem Informasi Manajemen Laboratorium Terpadu Universitas ABC

The need for information technology at this time has become an obligation for every company or organization. One that applies the development of information technology is ABC University. ABC University is a university that was founded in 2012 and along with the development of educational infrastructure every year, in 2020 ABC University has just completed the construction of an integrated laboratory building that functions as a place for research, learning, and academic and non-academic activities. This Integrated Laboratory will be used by 17 study programs at ABC University, more than 3000 students as well as lecturers and the academic community. With the limited number of rooms and laboratory assets for a large number of laboratory users, a system that functions to facilitate the use of laboratories is needed, starting from scheduling laboratory use, borrowing laboratory space, and borrowing laboratory equipment, Therefore, an information system needs to be developed in order to meet the needs of the ABC University Integrated Laboratory, namely the ABC University Integrated Laboratory Management Information System (MIS). The method used in developing this Integrated Laboratory SIM is the Scrum method which includes sprint planning, daily scrum, sprint review, and sprint retrospective. Based on 5 iterations during the development process of the Integrated Laboratory MIS, the total backlog items obtained were 65 backlog items. The ABC University Integrated Laboratory MIS has also been hosted on ABC University's servers and can be accessed via the https://labterpadu.itk.ac.id link.

Association between government policy and delays in emergent and elective surgical care during the COVID-19 pandemic in Brazil: a modeling study

BackgroundThe impact of public health policy to reduce the spread of COVID-19 on access to surgical care is poorly defined. We aim to quantify the surgical backlog during the COVID-19 pandemic in the Brazilian public health system and determine the relationship between state-level policy response and the degree of state-level delays in public surgical care. MethodsMonthly estimates of surgical procedures performed per state from January 2016 to December 2020 were obtained from Brazil's Unified Health System Informatics Department. Forecasting models using historical surgical volume data before March 2020 (first reported COVID-19 case) were constructed to predict expected monthly operations from March through December 2020. Total, emergency, and elective surgical monthly backlogs were calculated by comparing reported volume to forecasted volume. Linear mixed effects models were used to model the relationship between public surgical delivery and two measures of health policy response: the COVID-19 Stringency Index (SI) and the Containment & Health Index (CHI) by state. FindingsBetween March and December 2020, the total surgical backlog included 1,119,433 (95% Confidence Interval 762,663–1,523,995) total operations, 161,321 (95%CI 37,468–395,478) emergent operations, and 928,758 (95%CI 675,202–1,208,769) elective operations. Increased SI and CHI scores were associated with reductions in emergent surgical delays but increases in elective surgical backlogs. The maximum government stringency (score = 100) reduced emergency delays to nearly zero but tripled the elective surgical backlog. InterpretationStrong health policy efforts to contain COVID-19 ensure minimal reductions in delivery of emergent surgery, but dramatically increase elective backlogs. Additional coordinated government efforts will be necessary to specifically address the increased elective backlogs that accompany stringent responses.

Reimagining forensic science – The mission of the forensic laboratory

The year 2020 brought the COVID-19 pandemic, and increased focus on American racial injustice and victims’ rights, spurring a reimagining of law enforcement and justice services. As forensic laboratories serve investigation and justice with objective data to drive investigations, prosecutions, and exonerations, it is worthwhile to also reimagine forensic science service. With comparators of cost and quality relatively fixed to the consumers of forensic service, service in the form of timeliness of turn-around-time is the main competitive measure of effectiveness. A total backlog can be defined as all cases submitted to the forensic laboratory where a report has not yet been issued. Within a total backlog are the in-analysis backlog and the awaiting start of analysis backlog. By eliminating the awaiting analysis backlog, analysis could begin immediately upon submission. This would provide analysis in as short a time as technology permitted, optimizing the value of forensic laboratory service.

COVID-19 and cataract surgery backlog in Medicare beneficiaries.

To forecast the volume of cataract surgery in Medicare beneficiaries in the United States in 2020 and to estimate the surgical backlog that may be created due to COVID-19. Medicare Beneficiaries, United States. Epidemiologic modeling. Baseline trends in cataract surgery among Medicare beneficiaries were assessed by querying the Medicare Part B Provider Utilization National Summary data. It was assumed that once the surgical deferment is over, there will be a ramp-up period; this was modeled using a stochastic Monte Carlo simulation. Total surgical backlog 2 years postsuspension was estimated. Sensitivity analyses were used to test model assumptions. Assuming cataract surgeries were to resume in May 2020, it would take 4 months under an optimistic scenario to revert to 90% of the expected pre-COVID forecasted volume. At 2-year postsuspension, the resulting backlog would be between 1.1 and 1.6 million cases. Sensitivity analyses revealed that a substantial surgical backlog would remain despite potentially lower surgical demand in the future. Suspension of elective cataract surgical care during the COVID-19 surge might have a lasting impact on ophthalmology and will likely result in a cataract surgical patient backlog. These data may aid physicians, payers, and policymakers in planning for postpandemic recovery.

Combining Contract Theory and Lyapunov Optimization for Content Sharing With Edge Caching and Device-to-Device Communications

The paper proposes a novel framework based on the contract theory and Lyapunov optimization for content sharing in a wireless content delivery network (CDN) with edge caching and device-to-device (D2D) communications. The network is partitioned into a set of clusters. In a cluster, users can share contents via D2D links in coordination with the cluster head. Upon receiving the content request from any user in its cluster, the cluster head either delivers the content itself or forwards the request to another node, i.e., a base station (BS) or another user in the cluster. The content access at the BS and in each cluster is modeled as a queuing system, where arrivals represent the content requests directed to respective nodes. The objective is to assign content delivery nodes to stabilize all queues while minimizing the time-averaged network cost given incomplete information about content sharing costs of the users and unknown distribution of the network state defined by users’ locations and their cached/requested content. The proposed framework allows the users to truthfully reveal their content sharing expenditures, minimize the time-averaged network cost and stabilize the queuing system representing the CDN. Based on this framework, a distributed content access and delivery algorithm where the node assignments are made by every cluster head independently is developed. It is shown that the algorithm converges to the optimal policy with the trade-off in total queue backlog and achieves a superior performance compared with some other D2D content sharing policies.

Game Theory and Lyapunov Optimization for Cloud-Based Content Delivery Networks With Device-to-Device and UAV-Enabled Caching

The paper considers a cloud-based Content Delivery Network (CDN) with Device-to-Device (D2D) and Unmanned Aerial Vehicle (UAV) enabled caching. The network is managed by the operator that offers content transfer services to the set of Content Providers (CPs). A subscriber of any CP can receive its content either by first, cellular content transfer via a terrestrial Base Station (BS) or a UAV, or by second, D2D content transfer from another subscriber of this CP. Each CP aims to maximize its expected payoff defined as a reciprocal of the weighted sum of the expected content transfer cost and delay for its subscribers. The operator's objective is to maximize its long-term average revenue and stabilize the queuing system which represents the content transfer services. To model the interactions between the operator and the CPs, a novel framework is proposed that combines: first, cooperative game that enables the CPs to form coalitions in which all subscribers can exchange content via D2D links, thereby reducing content transfer costs and delays; second, Lyapunov optimization based dynamic channel and UAVs' activity allocation policy of the operator. Through analytical and numerical evaluations, it is proven that if the operator and each CP are rational, the network reaches a state where all the CPs are in the stable coalitional structure, whereas, the dynamic policy of the operator is optimal with the trade-off in the total queue backlog.

Production and replacement planning of a deteriorating remanufacturing system in a closed-loop configuration

This paper deals with the control of a hybrid manufacturing/remanufacturing system subject to random breakdowns and repairs. Given the heterogeneity of returned products, the remanufacturing machine deteriorates with time as a result of imperfect repairs, and needs to be replaced. The manufacturing machine receives homogeneous raw materials, and is not affected by this type of deterioration. The main objective of this paper is to find the production rates of both machines and the replacement rate of the remanufacturing machine that minimize the total cost, including production, inventory holding, backlog, repair and replacement costs, over an infinite planning horizon. A novel mathematical model is proposed for the underlying class of problems related to the history of breakdowns and repairs. This model is characterized by the extension of the state space, leading to a Markov decision model, allowing a derivation of the optimality conditions. Otherwise, such conditions are impossible to obtain. Optimality conditions in the form of Hamilton-Jacobi-Bellman (HJB) equations are thus developed. We show that despite the increased state space dimension, the problem remains tractable, and the solutions of HJB equations are obtained numerically. Finally, an illustrative example and a sensitivity analysis are provided to verify the robustness of the control policies obtained.

Analysis of Millimeter-Wave Multi-Hop Networks With Full-Duplex Buffered Relays

The abundance of spectrum in the millimeter-wave (mm-wave) bands makes it an attractive alternative for future wireless communication systems. Such systems are expected to provide data transmission rates in the order of multi-gigabits per second in order to satisfy the ever-increasing demand for high rate data communication. Unfortunately, mm-wave radio is subject to severe path loss, which limits its usability for long-range outdoor communication. In this paper, we propose a multi-hop mm-wave wireless network for outdoor communication, where multiple full-duplex buffered relays are used to extend the communication range, while providing end-to-end performance guarantees to the traffic traversing the network. We provide a cumulative service process characterization for the mm-wave propagation channel with self-interference in terms of the moment generating function of its channel capacity. Then, we then use this characterization to compute probabilistic upper bounds on the overall network performance, i.e., total backlog and end-to-end delay. Furthermore, we study the effect of self-interference on the network performance and propose an optimal power allocation scheme to mitigate its impact in order to enhance network performance. Finally, we investigate the relation between relay density and network performance under a sum power constraint. We show that increasing relay density may have adverse effects on network performance, unless the self-interference can be kept sufficiently small.

Trachoma Elimination: Approaches, Experiences and Performance of Interventions in Amhara Regional State, Ethiopia

Background: Trachoma is caused by conjunctival infection with a Bacteria, Chlamydia trachomatis. According to WHO grading system trachomatous trichiasis (TT), leads to irreversible blindness. Amhara national state of Ethiopia has the highest burden of TT. Despite huge efforts the region has big backlog and far from the target. Methodology/Principal findings: We carried out a review and trend analysis on previous years of Trachoma intervention in the region. We also designed a logical frame work, which bring all actors together. Then the new approach of TT surgery intervention frame work ''The MUST was implemented. The regional total TT backlog as of June 2017 was found to be 245,504. From all the surgeries carried out between 2012 and mid-2017, 32% (11687) was done only in 2016. All the ten zones of the region showed dramatic performance than ever after the new approach implemented in the region. East Gojjam [31.9% (73742)] followed by South Gondar [12.3% (28491)] zones took the highest share of TT surgery performances of the national regional state (NRS) during in the era of new approach reporting periods (2015-mid 2017). From the total of 23 districts (woredas) of the region which clear their TT backlog, eight of them are found to be in East Gojjam zone. South Gondar perform 36.4% (14,978) in 2016 from all the reporting periods of TT surgeries conducted during 2012-mid 2017. Facial cleanliness coverage among school children was found to be 90.4% and 90.8% in 2016 and mid 2017 respectively. Household latrine ownership coverage was 68.2% (6,805) and 68.5% (6772) during the same reporting periods respectively. Conclusions: Amhara national state has still huge TT backlog. The new approach showed an assurance of clearing TT backlog before 2020. The sustainable intervention (hygiene and environmental) are not yet strong like treatment-based interventions.

The impact of service level constraints in deterministic lot sizing with backlogging

This paper studies the impact of service level constraints in the context of the capacitated and uncapacitated lot sizing problems with deterministic demand and backlogging over a discrete and finite time horizon. Because the standard formulation of these problems cannot distinguish between a backlog and a backorder, we use a reformulation to explicitly make this distinction. We then formulate several service level constraints adapted from the stochastic inventory control literature and introduce new ones. We analyze the impact of these constraints on the structure of the optimal solutions in terms of the number of backorders and total backlog, and on the performance of these solutions in terms of various service level indicators (proportion of periods with no backlog, proportion of backorders over total demand, maximum delay, average unit waiting time for an item). We also consider the introduction of various types of backordering costs (both fixed and duration dependent) and study their impact. We find that they tend to stabilize the structure of solutions, regardless of the service level constraints imposed. Finally, we analyze the impact of a first-in first-out order management policy and show that it helps improving most solutions.

Channel and queue aware joint relay selection and resource allocation for MISO-OFDMA based user-relay assisted cellular networks

User-relay assisted orthogonal frequency division multiple access (OFDMA) networks are cost-effective solutions to meet the growing capacity and coverage demands of the next generation cellular networks. These networks can be used with multiple antennas technology in order to obtain a diversity gain to combat signal fading and to obtain more capacity gain without increasing the bandwidth or transmit power. Efficient relay selection and resource allocation are crucial in such a multi-user, multi-relay and multi-antenna environment to fully exploit the benefits of the combination of user-relaying and multiple antennas technology. Thus, we propose a channel and queue aware joint relay selection and resource allocation algorithm for multiple-input single-output (MISO)-OFDMA based user-relay assisted downlink cellular networks. Since, the proposed algorithm is not only channel but also queue-aware, the system resources are allocated efficiently among the users. The proposed algorithm for the MISO-OFDMA based user-relay assisted scheme is compared to existing MISO-OFDMA based non-relaying and fixed relay assisted schemes and it is also compared with the existing single-input single-output (SISO)-OFDMA based user-relay assisted scheme. Simulation results revealed that the proposed scheme outperforms the existing schemes in terms of cell-edge users’ total data rate, average backlog and average delay.

A Stochastic Production-Inventory Model in a Two-State Production System With Inventory Deterioration, Rework Process, and Backordering

The existing economic production quantity (EPQ) models in imperfect production systems normally assume either deteriorating production processes or deteriorating inventory. In this paper, the two aspects are combined together in a single approach to solve single machine, single product EPQ problem. There are assumed to be two states: 1) in-control and 2) out-of-control state. At the beginning of each production cycle, the production process is in control with a low defective rate. After a certain time period, the production process switches from an in-control to an out-of-control state. As a result, the defect rate increases to another level and more defective items are produced. Defective products are reworked after the normal production process all together but before that they are stored in an inventory, so a corresponding inventory holding cost is generated. Backordering is also considered in this model and products are first used to satisfy the backlog demand in each production run. Three different cases are considered and discussed in which the switch of state occurs in the backlog period, the inventory surplus period, and after the normal production period, respectively. By finding the optimal total production and backlog quantity, the expected total cost per unit product is minimized.