Backlog Level Research Articles

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.

An Energy-Efficient Controller for Wirelessly-Powered Communication Networks

In a wirelessly-powered communication network (WPCN), an energy access point (E-AP) supplies the energy needs of the network nodes through radio frequency wave transmission, and the nodes store their received energy in their batteries for possible data transmission. In this paper, we propose an online control policy for energy transfer from the E-AP to the wireless nodes and for data transfer among the nodes. With our proposed control policy, all data queues of the nodes are stable, while the average energy consumption of the network is shown to be within a bounded gap of the minimum energy required for stabilizing the network. Our proposed policy is designed using a quadratic Lyapunov function to capture the limitations on the energy consumption of the nodes imposed by their battery levels. We show that under the proposed control policy, the backlog level in the data queues and the stored energy level in the batteries fluctuate in small intervals around some constant levels. Consequently, by imposing a negligible average data drop rate, the data buffer size and the battery capacity of the nodes can be significantly reduced.

Production planning incorporating issues of reliability and backlogging with service level constraint

To stay competitive in present-day turbulent business environment, managers of manufacturing firms must achieve crucial operational goals, such as maintaining product quality, reducing operating costs, and attaining customer satisfaction. In real manufacturing systems, allowing backordering sometimes can be an effective strategy to help smooth manufacturing schedules and lower operating costs. However, the consequence of excessive shortages is the undesirable service level which reduces customer satisfaction and goodwill. To cope with this unwanted result, a maximal permitted backlogging level is set as an operating constraint to achieve the minimum required service level. Also, production of scrap items and stochastic breakdown are both inevitable in the manufacturing processes. Motivated by addressing aforementioned issues and providing insight information to managers for supporting their operational decision makings, this paper investigates the optimal runtime for a fabrication system with backordering, service level constraint, stochastic breakdown, and scrap. Mathematical model was developed and optimization methods are used to decide the optimal runtime that minimizes total system costs. Various key insights relating to joint impacts of backlogging, service level, stochastic breakdown, and scrap on the optimal runtime decision are revealed through a numerical illustration along with sensitivity analyses.

Inventory Control Systems Model for Strategic Capacity Acquisition

Variation of installed industrial capacity has been found to follow a cyclic pattern. This paper discusses the application of control theory to the problem of the timely acquisition of extra production capacity. The control system based model presented here is compared with a System Dynamics model proposed by Sterman. Key differences are the method of implementing rational decisions about deployment of extra capacity and the use of a nonlinear APVIOBPCS inventory model. Benefits of this new model are a more measurable process and the ability to select parameter values to optimise capacity deployment. Simulation of the model indicates that the results found by Sterman underestimate the production backlog and time taken to reach equilibrium. The use of a Proportional, Integral, and Derivative (PID) controller in the capacity control loop model illustrates that it is possible not only to alter the backlog levels but at the same time to reduce the sales force and improve the revenue. The model also shows clearly that the impact of not increasing capacity promptly results in catastrophic failure of sales as a structural, rather than a business, problem. This model is simple enough to be implemented as a spreadsheet for use as a guide by managers.

A Petri net based simulation to study the impact of customer response to stock-out on supply chain performance

AbstractBased on a Petri-net based simulation model, we investigate the effect of different customer response to stock-out on both the stock-out supply chain and the competing supply chain. Five types of customer stock-out responses are incorporated in the model to quantitatively assess the correlation between customer response and supply chain performance including bullwhip effect (BWE), on-hand inventory, and backlog level. After presenting the results of a series of Petri-net based simulation experiments, we discuss opportunities for both manufacturers and retailers to work better together to mitigate supply chain disruption. We also discuss the value of information sharing on mitigating BWE.

Carbon-capped Distribution Planning: A JIT Perspective

Products distribution and transportation is one of the largest sources of CO2 emission in supply chains. To date, a number of researchers have argued that intensive transportation activities through popular distribution strategies such as Just-In-Time (JIT) could significantly increase carbon emissions within logistics chains. However, a systematic understanding of how JIT distribution affects carbon emissions is still lacking in current literature. In this study, we develop a bi-objective optimization model for a carbon-capped JIT distribution of multiple products in a multi-period and multi-echelon distribution network. The aims are to jointly minimize total logistics cost and to minimize the maximum carbon quota allowed per period (carbon cap). The considered problem is investigated under three different carbon emission constraints namely periodic, cumulative and global. Since the studied problem is NP-Hard, a non-dominated sorting genetic algorithm-II (NSGA-II) is developed and its parameters are tuned by Taguchi method. For further quality improvement of the developed solution approach, a novel local search approach called modified firefly algorithm incorporates NSGA-II. Different sizes of the problem are considered to compare the performances of the proposed hybrid NSGA-II and the classical one. Finally, the results are presented along with some policy and managerial insights. For policy makers, the findings show the impact of varying the carbon emission cap on total cost and total emissions under JIT distribution concept. From managerial perspectives, we analyze the relationships between average inventory holding and backlog level per period which can assist mangers to identify critical decisions for JIT distribution of products in carbon-capped environment.

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.

Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in ) O(T2) time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O(T) when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O(T3logT) time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.

CRITICAL INFRASTRUCTURE RISK IN NHS ENGLAND: PREDICTING THE IMPACT OF BUILDING PORTFOLIO AGE

NHS Trusts in England must adopt appropriate levels of continued investment in routine and backlog maintenance if they are to ensure critical backlog does not accumulate. This paper presents the current state of critical backlog maintenance within the National Health Service (NHS) in England through the statistical analyses of 115 Acute NHS Trusts. It aims to find empirical support for a causal relationship between building portfolio age and year-on-year increases in critical backlog. It makes recommendations for the use of building portfolio age in strategic asset management. The current trend across this sample of NHS Trusts may be typical of the whole NHS built asset portfolio and suggests that most Trusts need to invest between 0.5 and 1.5 per cent of income (depending upon current critical backlog levels and Trust age profile) to simply maintain critical backlog levels. More robust analytics for building age, condition and risk-adjusted backlog maintenance are required.

System dynamics model for optimizing the recycling and collection of waste material in a closed-loop supply chain

To meet the immediate environmental challenges and sustainable development, Closed-loop Supply Chain (CLSC) management has become increasingly important and urgent. This is in lieu with some severe problems such as global ecological damage, resource wastages and shortages and pollution of the environment, and discretionary exploitation of natural resources. On the other hand, re-manufacturing of used merchandise and bringing them back to the market provides environmental and customer benefits to Original Equipment Manufacturers (OEMs), in addition to cutting back their production cost. This paper aims at evaluating the system behavior of an electrical manufacturing company as a case of study, by using System Dynamics (SD) simulating of Closed-loop Supply Chain (CLSC). VENSIM PLE software developed the simulation model. Based on the initial result, customer satisfaction and Green Image Factor (GIF) are lacking in the system. Therefore, to tackle this issue, an improvement model with a collection center was proposed. Results derived from the improved model presented a data of which the demand backlog level fell by 21.19%. Furthermore, the customer satisfaction in the system rose by 21.6%. In addition, as a result of an increase in GIF level from 14.80% to 48.1%, the return products rate rose from 184 items to 614. The method in this research can be used to investigate a variety of CLSC systems and their effects before implementing them in real life.

A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory

This paper addresses a real-life production planning problem arising in a manufacturer of luxury goods. This problem can be modeled as a single item dynamic lot-sizing model with backlogging, outsourcing and inventory capacity. Setup cost is included in the production cost function, and the production level at each period is unbounded. The holding, backlogging and outsourcing cost functions are assumed to be linear. The backlogging level at each period is also limited. The goal is to satisfy all demands in the planning horizon at minimal total cost. We show that this problem can be solved in O(T4logT) time where T is the number of periods in the planning horizon.

A three-dimensional searched-based algorithm for an imperfect production System

This paper deals with the production and inventory problems under partial backlogging, trade credit and reworking of imperfect quality items. The objective is to determine the optimal production lot size and maximum backlogging level simultaneously while still minimizing the total cost. The problem is modeled as a four-branch function with dual variables. A three-dimensional searched-based algorithm was developed to solve the problem described. Numerical examples are given to illustrate the solution procedure and discuss the impact of various system parameters. The study concludes with a computational analysis that leads to variety of managerial insights. Key word: Optimization, imperfect production system, reworking, trade credit, partial backlogging.

Study on the Bounded Inventory Model with Returning Items and Disposals

This paper addresses a dynamic lot sizing problem with mixed returning items and disposals and bounded inventory. The returning items mean that returns are in good enough condition to re-enter the inventory supply stream. The producing, the holding, backlogging and disposals cost functions are concave cost functions. Furthermore, backlogging level and inventory level at each period is limited. The goal is to minimize the total cost of production, inventory holding/backlogging and disposal. A dynamic programming algorithm with complexity O(T3) is developed to solve this model, where T is the length of the planning horizon.

Development of genetic fuzzy logic controllers for complex production systems

Complex production systems can produce more than one part type. For these systems, production rate and priority of production for each part type is determined by production controllers. In this paper, genetic fuzzy logic control (GFLC) methodology is used to develop two production control architectures namely “genetic distributed fuzzy” (GDF), and “genetic supervisory fuzzy” (GSF) controllers. Previously these controllers have been applied to single-part-type production systems. In the new approach the GDF and GSF controllers are developed to control complex production systems. The methodology is illustrated and evaluated using two test cases; two-part-type production line and re-entrant production systems. Genetic algorithm is used to tune the membership functions of input variables of GSF or GDF controllers. The objective function of the GSF controller minimizes the production cost based on work-in-process (WIP) and backlog costs, while surplus minimization is considered by GDF controller. The results show that GDF and GSF controllers can improve the performance of production systems. GSF controllers decrease the WIP level and its variations. GDF controllers show their abilities in reducing the backlog level but generally, production cost for GDF controller is greater than GSF controller.

Revenue management in single-stage CONWIP production systems

We study a joint admission/inventory control problem for a manufacturing system producing one product to meet random demand. The system employs a constant work- in-process policy (CONWIP) whereby the total inventory of raw material and finished items is kept constant, and accepts orders only as long as the backlog is below a certain level. The objective is to determine the CONWIP and backlog levels that maximize the mean profit rate of the system. The system is modelled as a single server with a finite queue. It turns out that the mean profit rate is either concave or decreasing in one control parameter and also decreasing for large values of the other control parameter. A simple algorithm is developed which tracks down the globally optimum design in finite time. Numerical results show that the joint admission/inventory control policy achieves higher profit than other production control policies that have been examined in the literature.

Energy-efficient scheduling with delay constraints in time-varying uplink channels

In this paper, we investigate the problem of minimizing the average transmission power of users while guaranteeing the average delay constraints in time-varying uplink channels. We design a scheduler that selects a user for transmission and determines the transmission rate of the selected user based on the channel and backlog information of users. Since it requires prohibitively high computation complexity to determine an optimal scheduler for multi-user systems, we propose a low-complexity scheduling scheme that can achieve near-optimal performance. In this scheme, we reduce the complexity by decomposing the multiuser problem into multiple individual user problems. We arrange the probability of selecting each user such that it can be determined only by the information of the corresponding user and then optimize the transmission rate of each user independently. We solve the user problem by using a dynamic programming approach and analyze the upper and lower bounds of average transmission power and average delay, respectively. In addition, we investigate the effects of the user selection algorithm on the performance for different channel models. We show that a channel-adaptive user selection algorithm can improve the energy efficiency under uncorrelated channels but the gain is obtainable only for loose delay requirements in the case of correlated channels. Based on this, we propose a user selection algorithm that adapts itself to both the channel condition and the backlog level, which turns out to be energy-efficient over wide range of delay requirement regardless of the channel model.

PERFORMANCE EVALUATION OF GENETIC DISTRIBUTED FUZZY CONTROLLERS FOR MULTI-PART-TYPE PRODUCTION LINE

Genetic distributed fuzzy (GDF) controllers are proposed for multi-part-type production line. These production systems can produce more than one part type. For these systems, "production rate" and "priority of production" for each part type is determined by production controllers. The GDF controllers have already been applied to single-part-type production systems. The methodology is illustrated and evaluated using a two-part-type production line. For these controllers, genetic algorithm (GA) is used to tune the membership functions (MFs) of GDF. The objective function of the GDF controllers minimizes the surplus level in production line. The results show that GDF controllers can improve the performance of production systems. GDF controllers show their abilities in reducing the backlog level. In production systems in which the backlog has a high penalty or is not allowed, the implementation of GDF controllers is advisable.

Assessing capacity scalability policies in RMS using system dynamics

This paper presents a model for assessing different capacity scalability policies in Reconfigurable Manufacturing System (RMS) for different changing demand scenarios. The novelty of this approach is two fold: (1) it is the first attempt to explore different capacity scalability policies in RMS based on multiple performance measures, mainly scaling rate, Work In Process level, inventory level and backlog level; and (2) the dynamic scalability process in RMS is modeled for the first time using System Dynamics. Different policies for capacity scalability for various demand scenarios were assessed. Numerical simulation results obtained using the developed capacity scalability model showed that the best capacity scalability policy to be adopted for RMS is dependent on the anticipated demand pattern as well as the various manufacturing objectives. The presented assessment results will help the capacity scalability planners better decide the different tradeoffs between the competing strategic and operational objectives of the manufacturing enterprise, before setting the suitable capacity scalability plan parameters.

Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging

AbstractThis paper derives the optimal replenishment policy for imperfect quality economic manufacturing quantity (EMQ) model with rework and backlogging. The classic EMQ model assumes that all items produced are of perfect quality. However, in real‐life manufacturing settings, generation of imperfect quality items is almost inevitable. In this study, a random defective rate is assumed. All items produced are inspected and the defective items are classified as scrap and repairable. A rework process is involved in each production run when regular manufacturing process ends, and a rate of failure in repair is also assumed. Unit disposal cost and unit repairing and holding costs are included in our mathematical modelling and analysis. The renewal reward theorem is employed in this study to cope with the variable cycle length. The optimal replenishment policy in terms of lot‐size and backlogging level that minimizes expected overall costs for the proposed imperfect quality EMQ model is derived. Special cases of the model are identified and discussed. Numerical example is provided to demonstrate its practical usage. Copyright © 2006 John Wiley & Sons, Ltd.

Coordinating quality, production and sales in manufacturing systems

We explore the benefits of jointly designing quality tolerances, customer admission and production control policies in manufacturing systems producing a single product to meet demand. These problems have been addressed separately in the past. We consider a simple admission/production control policy whereby the system produces until stock reaches a certain level and accepts orders until the backlog reaches another critical level. We model the system using queueing theory and propose an easily implementable procedure for selecting the optimal quality tolerances and the critical stock and backlog levels. From theoretical and numerical results, it appears that the proposed policy achieves a higher profit than other manufacturing practices, in which there is little or no coordination between the production, sales and quality control departments.