Production lot sizing with process deterioration and machine breakdown under inspection schedule

The paper develops integrated production, inventory and maintenance models for a deteriorating production system in which the production facility may not only shift from an ‘in-control’ state to an ‘out-of-control’ state but also may break down at any random point in time during a production run. In case of machine breakdown, production of the interrupted lot is aborted and a new production lot is started when the on-hand inventory is depleted after corrective repair. The process is inspected during each production run to examine the state of the production process. If it is found in the ‘in-control’ state then either (a) no action is taken except at the time of last inspection where preventive maintenance is done (inspection policy-I) or (b) preventive maintenance is performed (inspection policy-II). If, however, the process is found to be in the ‘out-of-control’ state at any inspection then restoration is done. The proposed models are formulated under general shift, breakdown and repair time distributions. As it is, in general, difficult to find the optimal production policy under inspection policy-I, a suboptimal production policy is derived. Numerical examples are taken to determine numerically the optimal/suboptimal production policies of the proposed models, to examine the sensitivity of important model parameters and to compare the performance of inspection and no inspection policies.     

具有多元马氏需求的多产品多阶段库存优化模型

本文研究一类新的多产品库存控制策略,即具有多元马氏需求特征的多产品多阶段的订货点订货量(Q, R, SS)策略,该策略考虑市场需求在不同产品之间具有多元马氏转移特征,并考虑缺货因素设置安全库存。论文首先建立了多产品多阶段的多元马氏需求预测模型,并通过该模型确定了各种产品需求之间的关系。同时,在该模型的理论基础上,提出了多产品多阶段的总期望成本模型及其最优(Q, R, SS)策略,进而结合算例给出模型的最优策略的数值解。     

Assessing Service Level Targets in Production and Inventory Planning*

In production and stock planning, the relationship between customer service, defined as the ability to meet demand for finished goods from in-stock inventory, and expected profits or expected costs can be represented by a simple reliability curve. The shape of this curve depends upon the parameters of the demand process, specifically the expected level of demand, standard deviation and correlation structure, as well as upon the capacities and initial state of the production and inventory system. A model is presented which explicitly determines this trade-off curve for a firm. The model is intended both as an operational model to aid managers in setting revenue and service targets which are compatible with the capacities and resources of the firm, and as a tool for exploring relationships between the parameters of the demand process and the constraints of the physical production and inventory system. The results illustrate that the level of risk depends strongly on the variability of the demand process, the cost structure, the capacities and initial state of the system and, to a lesser extent, the correlation in demand between succeeding periods. Results suggest that establishing service level targets consistent with the firm's strategic orientation must be done in consideration of both the characteristics of the demand process and the capacities of the production and inventory system. The model provides a tool for estimating the premium above unit cost which must be paid to provide a designated service level.     

考虑产品变质的VMI混合补货发货策略及优化仿真

本文研究了“产品可变质”情况下的VMI库存补货与装运调度问题,并建立了Poisson需求过程下的VMI混合补货发货模型,根据此模型通过简单的规划求解即可得到使长期平均成本最小的最佳混合策略组合。由于模型推演过程中涉及到对补货周期内期望发货次数的近似估计,因而模型解是拟最优的。算例和模型仿真显示,模型结果与仿真结果十分相近,从而模型有效性得以确认。     

Modelling and controlling product manufacturing systems using bond-graphs and state equations: Continuous systems and discrete systems which can be represented by continuous models

This paper presents an approach to the modelling and control phases involved in a cooperative process of design and management of the manufacturing systems. Modelling the evolution of the production flow, in the different sections of the system, is based upon the use of the bondgraph methodology in order to reach the state formalism which constitutes one of the modern representations of automation. The class of the systems studied ranges from continuous systems to discrete systems, which can be represented by a continuous approach according to the level of approximation required. The first part of this paper is dedicated to the development of generic models associated with the various basic entities of the manufacturing systems. Then, the bondgraph model of any system is obtained by assembling generic models in relation to the implementation of the means of the studied system, thus guaranteeing a representation which is quite close to the engineering sketches. Finally, switching to the state equation is performed systematically with the easiness provided by this formalism while taking into account the causality principle. An application, involving most of the elementary models developed, concludes the paper.     

OPTIMAL AND NEAR OPTIMAL CONTROL OF A TWO-PART-TYPE STOCHASTIC MANUFACTURING SYSTEM WITH DYNAMIC SETUPS

This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other, a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero for both products. The problem is formulated as an optimal stochastic control problem. The optimal policy is obtained numerically by discretizing the continuous time continuous state opti-mality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.     

Application of load-oriented manufacturing control in industry

This paper deals with multi-stage lotsizing models for imperfect production processes. The effect of imperfect quality on lotsizing decisions and effect ofinspection errorsare taken into consideration in the proposed models. Numerical examples are presented for illustration purposes. The developed models are very helpful for justifying quality assurance and quality improvement efforts.     

Optimal Production and Admission Policies in Make‐to‐Stock/Make‐to‐Order Manufacturing Systems

In this article, we study optimal production and admission control policies in manufacturing systems that produce two types of products: one type consists of identical items that are produced to stock, while the other has varying features and is produced to order. The model is motivated by applications from various industries, in particular, the automobile industry, where a part supplier receives orders from both an original equipment manufacturer and the aftermarket. The product for the original equipment manufacturer is produced to stock, it has higher priority, and its demands are fully accepted. The aftermarket product is produced to order, and its demands can be either accepted or rejected. We characterize the optimal production and admission policies with a partial‐linear structure, and using computational analysis, we provide insights into the benefits of the new policies. We also investigate the impact of production capacity, cost structure, and demand structure on system performance.     

Determination of economic production quantity in a multi-stage production system

In this paper two models have been suggested for determining economic production quantity in a multi-stage production system. The demand for the product is assumed constant and it is supplied by manufacturing the product in equal production runs. The production lot is transported in a number of sub-batches of equal sizes. Each sub-batch is processed on the production stages without wait during process. As a result of processing the sub-batches without wait during process, the processing on the production stages is interrupted. Expressions have been derived for the manufacturing cycle time, the total process inventory and the finished product inventory and then total variable cost models have been suggested and manipulated for obtaining the economic production quantity.     

Foundations and Implications of a Proposed Unified Services Theory

Diverse businesses, such as garbage collection, retail banking, and management consulting are often tied together under the heading of “services”, based on little more than a perception that they are intangible and do not manufacture anything. Such definitions inadequately identify managerial and operational implications common among, and unique to, services. We present a “Unified Services Theory” (UST) to clearly delineate service processes from non‐service processes and to identify key commonalities across seemingly disparate service businesses. The UST defines a service production process as one that relies on customer inputs; customers act as suppliers for all service processes. Non‐services (such as make‐to‐stock manufacturing) rely on customer selection of outputs, payment for outputs, and occasional feedback, but production is not dependent upon inputs from individual customers. The UST reveals principles that are common to the wide range of services and provides a unifying foundation for various theories and models of service operations, such as the traditional “characteristics of services” and Customer Contact Theory. The UST has significant operational corollaries pertaining to capacity and demand management, service quality, services strategy, and so forth. The UST provides a common reference point to which services management researchers can anchor future theory‐building and theory‐testing research.     

Integration of process planning and production planning and control in cellular manufacturing

Organisations willing to succeed in global competition have to integrate their internal and external processes. This especially includes planning and production control (PPC) processes. Optimised allocation of the production resources and quick response to demand changes result in lower cost and improvement of production performance. Practitioners and researchers have been trying to achieve these goals using production planning techniques. Although the results are significant, it seems necessary to integrate production operations in order to improve the production performance. The goals, information and decisions taken in production planning and control and process planning are often very different and difficult to integrate in Cellular Manufacturing (CM) environments. Designing an efficient PPC system and integrating it with process planning in a cellular environment is of the same importance. The following paper proposes first a comprehensive framework of integrated process planning and production planning and control in CM. Then, with respect to this framework and utilising the domain knowledge in the area of CM systems, an integrated model based on Integrated Definition Modeling Language is developed. The application of the models has been considered as a case study for a production system in electronics and telecommunication sector in a plant in Iran. The validity and completeness of the proposed model is tested by a panel of experts in the areas of production planning and control in CM environments.     

Production control for just-in-time tool-and-die manufacturing

The strategy to implement production control varies in different types of manufacturing systems. We address the issue of production control in unit-based manufacturing systems where the production batch size of the final product is one or two, the product is custom designed and is made up of numerous individual components with similar process routeings lor special machine tools, turbines, boilers, tool-and-die, injection moulding equipment, custom fabrication, etc. We have developed algorithms to generate master production schedules in this particular domain of manufacturing systems using the concept of workgroups. We show how a Kanban-based JIT shopfloor control and purchasing system can be implemented in such systems in tandem with an inventory management system by utilizing the concept of demand lists. We also propose a model for practical implementation of production control in this domain. The methodology is illustrated at a tool-and-die plant where a CIM software is used to apply the JIT-based production control. Preliminary results show a significant reduction in lead times. We try to show the relationship between research and industrial applications of productions of production control and how to bridge the gap between them.     

Optimal Ordering Policies for Stochastic Inventory Problems with Observed Information Delays

Information delays exist in an inventory system when it takes time to collect, process, validate, and transmit inventory/demand data. A general framework is developed in this paper to describe information flows in an inventory system with information delays. We characterize the sufficient statistics for making optimal decisions. When the ordering cost is linear, the optimality of a state‐dependent base‐stock policy is established even when information flows are allowed to cross over time. Additional insights into the problem are obtained via a comparison between our models and the models with stochastic order lead times. We also show that inventory can substitute for information and vice versa.     

CAPACITY AND PRODUCTION DECISIONS IN STOCHASTIC MANUFACTURING SYSTEMS: AN ASYMPTOTIC OPTIMAL HIERARCHICAL APPROACH

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions. The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the purchase. The objective is to minimize the discounted costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting problem in which the random capacity is replaced by its mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.     

Parallel-machine scheduling of deteriorating jobs with potential machine disruptions

We consider parallel-machine scheduling of deteriorating jobs in a disruptive environment in which some of the machines will become unavailable due to potential disruptions. This means that a disruption to some of the machines may occur at a particular time, which will last for a period of time with a certain probability. If a job is disrupted during processing by a disrupted machine and it does not need (needs) to re-start after the machine becomes available again, it is called the resumable (non-resumable) case. By deteriorating jobs, we mean that the actual processing time of a job grows when it is scheduled for processing later because the machine efficiency deteriorates over time due to machine usage and aging. However, a repaired machine will return to its original state of efficiency. We consider two cases, namely performing maintenance immediately on the disrupted machine when a disruption occurs and not performing machine maintenance. In each case, the objective is to determine the optimal schedule to minimize the expected total completion time of the jobs in both non-resumable and resumable cases. We determine the computational complexity status of various cases of the problem, and provide pseudo-polynomial-time solution algorithms and fully polynomial-time approximation schemes for them, if viable.     

Reliability Analysis Based on the Losses from Failures

The conventional reliability analysis is based on the premise that increasing the reliability of a system will decrease the losses from failures. On the basis of counterexamples, it is demonstrated that this is valid only if all failures are associated with the same losses. In case of failures associated with different losses, a system with larger reliability is not necessarily characterized by smaller losses from failures. Consequently, a theoretical framework and models are proposed for a reliability analysis, linking reliability and the losses from failures. Equations related to the distributions of the potential losses from failure have been derived. It is argued that the classical risk equation only estimates the average value of the potential losses from failure and does not provide insight into the variability associated with the potential losses. Equations have also been derived for determining the potential and the expected losses from failures for nonrepairable and repairable systems with components arranged in series, with arbitrary life distributions. The equations are also valid for systems/components with multiple mutually exclusive failure modes. The expected losses given failure is a linear combination of the expected losses from failure associated with the separate failure modes scaled by the conditional probabilities with which the failure modes initiate failure. On this basis, an efficient method for simplifying complex reliability block diagrams has been developed. Branches of components arranged in series whose failures are mutually exclusive can be reduced to single components with equivalent hazard rate, downtime, and expected costs associated with intervention and repair. A model for estimating the expected losses from early-life failures has also been developed. For a specified time interval, the expected losses from early-life failures are a sum of the products of the expected number of failures in the specified time intervals covering the early-life failures region and the expected losses given failure characterizing the corresponding time intervals. For complex systems whose components are not logically arranged in series, discrete simulation algorithms and software have been created for determining the losses from failures in terms of expected lost production time, cost of intervention, and cost of replacement. Different system topologies are assessed to determine the effect of modifications of the system topology on the expected losses from failures. It is argued that the reliability allocation in a production system should be done to maximize the profit/value associated with the system. Consequently, a method for setting reliability requirements and reliability allocation maximizing the profit by minimizing the total cost has been developed. Reliability allocation that maximizes the profit in case of a system consisting of blocks arranged in series is achieved by determining for each block individually the reliabilities of the components in the block that minimize the sum of the capital, operation costs, and the expected losses from failures. A Monte Carlo simulation based net present value (NPV) cash-flow model has also been proposed, which has significant advantages to cash-flow models based on the expected value of the losses from failures per time interval. Unlike these models, the proposed model has the capability to reveal the variation of the NPV due to different number of failures occurring during a specified time interval (e.g., during one year). The model also permits tracking the impact of the distribution pattern of failure occurrences and the time dependence of the losses from failures.     

NERJIT: Using Net Requirement Data in Kanban‐Controlled Jumbled‐Flow Shops

The bold lines that have separated the application of specific production planning and control techniques to specific production systems are being blurred by continuous advances in production technologies and innovative operational procedures. Oral communication among dispatchers and production units has given way to electronic communication between production planners and these units by continuous progress in information technologies. Current production literature alludes to the idea that, collectively, these advances have paved the way for application of Just‐In‐Time (JIT) production concepts, which were originally developed for mass production systems, in intermittent production systems. But this literature does not actually consider the possibility. This article presents a modification to JIT procedures to make them more suitable for jumbled‐flow shops. This article suggests providing real‐time information about net‐requirements for each product to each work center operator for setting production priorities at each work center. Simulation experiments conducted for this study show that using Net‐Requirements in JIT (NERJIT) reduces customer wait time by 45–60% while reducing inventory slightly. The analysis of work centers’ input and output stock‐point inventories shows that using the information about net‐requirements results in production of items that are in current demand. NERJIT results in smaller input stock‐point inventory and availability of products with higher priority in the output stock‐points of work centers.     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

Supply Performance in Multi‐Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi‐echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end‐product demand and spare parts (subassemblies) demand. The multi‐echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi‐echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation‐based inventory optimization approach is developed to search for the best base‐stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample‐path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on‐hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.     

Randomization Approaches for Network Revenue Management with Customer Choice Behavior

In this study, we present new approximation methods for the network revenue management problem with customer choice behavior. Our methods are sampling‐based and so can handle fairly general customer choice models. The starting point for our methods is a dynamic program that allows randomization. An attractive feature of this dynamic program is that the size of its action space is linear in the number of itineraries, as opposed to exponential. It turns out that this dynamic program has a structure that is similar to the dynamic program for the network revenue management problem under the so called independent demand setting. Our approximation methods exploit this similarity and build on ideas developed for the independent demand setting. We present two approximation methods. The first one is based on relaxing the flight leg capacity constraints using Lagrange multipliers, whereas the second method involves solving a perfect hindsight relaxation problem. We show that both methods yield upper bounds on the optimal expected total revenue. Computational experiments demonstrate the tractability of our methods and indicate that they can generate tighter upper bounds and higher expected revenues when compared with the standard deterministic linear program that appears in the literature.