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.     

A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule

Due to unreliable production facility and stochastic preventive maintenance, deriving an optimal production inventory decision in practice is very complicated. In this paper, we develop a production model for deteriorating items with stochastic preventive maintenance time and rework using the first in first out (FIFO) rule. From our literature search, no study has been done on the above problem. The problem is solved using a simple search procedure; this makes it more practical for use by industries. Two case examples using uniform and exponential distribution preventive maintenance time are applied. Examples and sensitivity analysis are conducted for each case. The results show that rework and preventive maintenance time have significant affected the total cost and the optimal production time. This provides helpful managerial insights to help management in making smart decisions.     

A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule

Due to unreliable production facility and stochastic preventive maintenance, deriving an optimal production inventory decision in practice is very complicated. In this paper, we develop a production model for deteriorating items with stochastic preventive maintenance time and rework using the first in first out (FIFO) rule. From our literature search, no study has been done on the above problem. The problem is solved using a simple search procedure; this makes it more practical for use by industries. Two case examples using uniform and exponential distribution preventive maintenance time are applied. Examples and sensitivity analysis are conducted for each case. The results show that rework and preventive maintenance time have significant affected the total cost and the optimal production time. This provides helpful managerial insights to help management in making smart decisions.     

Joint production and subcontracting planning of unreliable multi-facility multi-product production systems

This article addresses the problem of joint optimization of production and subcontracting of unreliable production systems. The production system considered presents a common problem in the pharmaceutical industry. It is composed of multiple production facilities with different capacities, each of which is capable of producing two different classes of medications (brand name and generic). The resort to subcontracting is double: first, it involves the quantity of products received on a regular basis in order to compensate for insufficient production capacity in existing facilities, second, when needed, urgent orders are also launched in order to reduce the risk of shortages caused by breakdowns of manufacturing facilities. Failures, repairs and urgent delivery times may be represented by any probability distributions.The objective is to propose a general control policy for the system under consideration, and to obtain, in the case of two facilities, optimal control parameters that minimize the total incurred cost for a specific level of the customer service provided. Given the complexity of the problem considered, an experimental optimization approach is chosen in order to determine the optimal control parameters. This approach includes experimental design, analysis of variance, response surface methodology and simulation modeling. It allows the accurate representation of the dynamic and stochastic behaviors of the production system and the assessment of optimal control parameters. Other control parameters which represent the subcontracting are introduced and three joint production/subcontracting control policies (general, urgent, regular) are compared to one another. The proposed joint production/regular subcontracting control policy involves a cost decrease of up to 20%, as compared to results obtained by Dror et al. [1], who used a simplified control policy in addition to a heuristic solution approach for a real case study. This policy offers not only cost savings, but is also easier to manage, as compared to that proposed by Dror et al. [1]. Numerical examples and a sensitivity analysis are also performed to illustrate the robustness of the proposed control policy and the solution approach.     

An integrated vendor-buyer cooperative inventory model for items with imperfect quality

This article develops a model to determine an optimal integrated vendor-buyer inventory policy for flawed items in a just-in-time (JIT) manufacturing environment. The aim is to minimize the total joint annual costs incurred by the vendor and the buyer. The proposed model extends the integrated vendor-buyer inventory model by accounting for imperfect quality items. The expected annual integrated total cost function is derived and an analytic solution procedure is proposed to determine the optimal policy. Finally, numerical examples are also given to illustrate the solution procedure presented in this article.     

Effects of maintenance policies on the productivity of flexible manufacturing cells

Flexible manufacturing cells (FMCs) often operate with increasing failure rate due to extensive utilization and wear-outs of equipment. While maintenance plans can eliminate wear-out failures, random failures are still unavoidable. This paper discusses a procedure that combines simulation and analytical models to analyze the effects of corrective, preventive, and opportunistic maintenance policies on productivity of a flexible manufacturing cell. The production output rate of an FMC, which is a function of availability, is determined under different maintenance policies and mean time between failures.     

基于投产点库存的随机综合生产计划模型研究

以企业基于投产点法的生产与库存控制策略为研究起点,分析了随机需求条件下生产系统服务水平与库存水平的数量关系,并将产品在计划期间的平均库存量引入综合生产计划模型。模型中计划期产量是与产品需求具有相同分布的随机变量,模型的优化目标是通过确定最佳的投产库存量和生产系统服务水平,求得相应的计划期产量区间。提出了模型的计算机辅助求解算法,并采用案例分析验证了模型的有效性。     

随机供需条件下装配商的订购-定价联合决策问题

针对随机供需条件下装配商的订购与定价联合决策这一难题，运用随机非线性规划方法，以装配商期望利润最大化为目标，建立零部件订购量与最终产品定价的多维优化模型。刻画了给定价格时的最优订购量和给定订购量时的最优价格，最后给出关于最优订购-定价的必要条件。通过数值算例验证了模型结论并进一步探讨随机供需的影响，为装配商的订购-定价决策以及供应商改进提供有益的管理启示。     

A hybrid inventory management system responding to regular demand and surge demand

This paper proposes a hybrid policy for a stochastic inventory system facing regular demand and surge demand. The combination of two different demand patterns can be observed in many areas, such as healthcare inventory and humanitarian supply chain management. The surge demand has a lower arrival rate but higher demand volume per arrival. The solution approach proposed in this paper incorporates the level crossing method and mixed integer programming technique to optimize the hybrid inventory policy with both regular orders and emergency orders. The level crossing method is applied to obtain the equilibrium distributions of inventory levels under a given policy. The model is further transformed into a mixed integer program to identify an optimal hybrid policy. A sensitivity analysis is conducted to investigate the impact of parameters on the optimal inventory policy and minimum cost. Numerical results clearly show the benefit of using the proposed hybrid inventory model. The model and solution approach could help healthcare providers or humanitarian logistics providers in managing their emergency supplies in responding to surge demands.     

考虑缓冲区库存不足情况下的设备维护与缓冲区库存联合优化研究

针对缓冲区库存不足的两设备流水线生产系统(2M1B系统)设备维护问题,提出了生产设备维护与缓冲库存联合优化模型。首先,采用指数分布描述设备故障规律,表达运行周期的总故障次数;其次,通过分析缓冲区库存量在达到额定库存后的变化,提出了利用条件概率改进库存充足和库存不足两种情况下的设备维护和缓冲库存模型,基于更新酬劳定理,以故障次数和额定库存为决策变量,以总费用为目标函数,建立缓冲区库存不足情况下的设备维护与缓冲库存联合优化模型,并且将生产系统的缺货费用集成到了总费用模型;最后,通过算例分析,计算故障次数和最优缓冲区额定库存量,进行了灵敏度分析,验证了模型有效性,丰富了考虑缓冲库存的设备理论。     

Optimal maintenance intervals for a multi-component system

In the manufacturing industry, preventive maintenance (PM) is carried out to minimise the probability of plant unexpected breakdown. Planned PM is preferred as disruption to operation is then minimised. Suggested PM intervals are normally prepared by the original equipment manufacturers (OEMs), however due to the multifaceted relationship between operating context and production requirement for different plants, it is unlikely that these suggested intervals as prescribed by the OEMs are optimal. Reliability, budget and breakdown outages cost are some of the critical factors that will affect the calculation of optimal maintenance intervals. Maintenance managers are required to determine optimal maintenance intervals with the above different requirements set by management. In this paper three models are proposed to calculate optimal maintenance intervals for multi-component system in a factory subjected to minimum required reliability, maximum allowable budget and minimum total cost. Numerical examples are provided to illustrate the application and usefulness of the proposed models.     

考虑故障停机的生产控制与维修计划联合决策模型

通过生产控制与维修计划协同决策,降低生产成本。首先描述生产过程,分析各项费用。其次,建立了考虑生产过程失控、故障率和故障停时间的生产过程控制、生产计划优化和维修管理联合优化决策的模型。通过模型求解,联合制定出生产过程检查策略、生产计划（经济生产批量、生产批次）以及维修计划（PM间隔期）,实现单位时间内总费用最低的目标。再次,案例研究,分析生产过程失控、故障率和故障停机时间对于经济生产批量、生产过程检查策略和生产系统维修计划的影响。该模型从理论上解决了生产过程控制、生产计划优化和维修管理联合优化决策难题,对于指导企业制定生产计划和生产系统的检修计划,进而提高产品质量、降低生产成本、确保准时交货都具有指导意义和实用价值。     

Competing on Time: An Integrated Framework to Optimize Dynamic Time‐to‐Market and Production Decisions

This study develops a comprehensive framework to optimize new product introduction timing and subsequent production decisions faced by a component supplier. Prior to market entry, the supplier performs process design activities, which improve manufacturing yield and the chances of getting qualified for the customer's product. However, a long delay in market entry allows competitors to enter the market and pass the customer's qualification process before the supplier, reducing the supplier's share of the customer's business. After entering the market and if qualified, the supplier also needs to decide how much to produce for a finite planning horizon by considering several factors such as manufacturing yield and stochastic demand, both of which depend on the earlier time‐to‐market decision. To capture this dependency, we develop a sequential, nested, two‐stage decision framework to optimize the time‐to‐market and production decisions in relation to each other. We show that the supplier's optimal market entry and qualification timing decision need to be revised in real time based on the number of qualified competitors at the time of market‐entry decision. We establish the optimality of a threshold policy. Following this policy, at the beginning of each decision epoch, the supplier should optimally stop preparing for qualification and decide whether to enter the market if her order among qualified competitors exceeds a predetermined threshold. We also prove that the supplier's optimal production policy is a state‐dependent, base‐stock policy, which depends on the time‐to‐market and qualification decisions. The proposed framework also enables a firm to quantify how market conditions (such as price and competitor entry behavior) and operating conditions (such as the rate of learning and inventory/production‐related costs) affect time‐to‐market strategy and post‐entry production decisions.     

A simple integrated production policy of an imperfect item for vendor and buyer

This article develops a simple approach for determining an optimal integrated vendor–buyer inventory policy for an item with imperfect quality. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. This model is assumed to produce a certain number of defective items during the production process. Items of poor quality detected in the screening process of a lot are sold at a discounted price. The expected annual integrated total cost function is derived and a solution procedure is proposed to determine the optimal policy. Finally, a numerical example is also given to illustrate the solution procedure presented in this article.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

Managing Electricity Peak Loads in Make‐To‐Stock Manufacturing Lines

In this article, we study the control of stochastic make‐to‐stock manufacturing lines in the presence of electricity costs. Electricity costs are difficult to manage because unit costs increase with the total load, that is, the amount of electricity needed by the manufacturing line at a certain point in time. We demonstrate that standard methods for controlling manufacturing lines cannot be used and that standard analytic results for stochastic manufacturing lines do not hold in the presence of electricity costs. We develop a control policy that balances electricity costs with inventory holding and backorder costs. We derive closed‐form expressions and analytic properties of the expected total cost for manufacturing lines with two workstations and demonstrate the accuracy and robustness of the policy for manufacturing lines with more than two workstations. The results indicate that avoiding electricity peak loads requires additional investment in manufacturing capacity and higher inventory and backorder costs. Our approach also applies to companies which aim at reducing their carbon emissions in addition to their operating costs.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

Multiechelon (R,S) Inventory Model*

Most studies in multiechelon inventory systems have concentrated on understanding the specific aspects of a system's behavior. The problem of optimal policy computation has largely been ignored. In this paper, we investigate a two-echelon inventory system experiencing stochastic demand and a pull system of inventory allocation. Both echelons use an order-up-to-level type control policy. A mathematical model is developed to determine the optimal order level at all echelons and validated through simulation. Two simple algorithms to locate the optimum solution are presented. The use of graphical tools in optimal policy calculation is also discussed.     

Centralization versus decentralization: Risk pooling,risk diversification,and supply chain disruptions

We investigate optimal system design in a multi-location system in which supply is subject to disruptions. We examine the expected costs and cost variances of the system in both a centralized and a decentralized inventory system. We show that, when demand is deterministic and supply may be disrupted, using a decentralized inventory design reduces cost variance through the risk diversification effect, and therefore a decentralized inventory system is optimal. This is in contrast to the classical result that when supply is deterministic and demand is stochastic, centralization is optimal due to the risk-pooling effect. When both supply may be disrupted and demand is stochastic, we demonstrate that a risk-averse firm should typically choose a decentralized inventory system design.     

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.