Stohastic optimal production control problem with corrective maintenance

We consider a production control problem in a manufacturing system with failure-prone machines and a constant demand rate. The objective is to minimise a discounted inventory holding and backlog cost over an infinite planning horizon. The availability of the machines is improved through a corrective maintenance strategy. The decision variables are the production and the machine repair rates, which influence the inventory levels and the system capacity, respectively. It is shown that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. Such a policy is modified herein and parameterised by factors representing the thresholds of involved products and switching inventory levels for corrective maintenance. With the obtained policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal production and corrective maintenance policies, respectively. The usefulness of the proposed approach is illustrated through a numerical example.     

Production control of a manufacturing system with multiple machinestates

The production control of a single-product manufacturing system with arbitrary number of machine states (failure modes) is discussed. The objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost. The optimal production policy has a special structure and is called a hedging-point policy. If the hedging points are known, the optimal production rate is readily specified. Assuming a set of tentative hedging points, the simple structure of the optimal policy is utilized to find the steady-state probability distribution of the surplus (inventory or backlog). Once this function is determined, the average surplus cost is easily calculated in terms of the values of the hedging points. The average cost is then minimized to find the optimum hedging points     

A simulation optimization approach in production planning of failure prone manufacturing systems

In this paper, the implementation of a new method to control the production rate of manufacturing systems, based on the combination of stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology is outlined. The system under study consists of several parallel machines, multiple-product manufacturing system. Machines are subject to failures and repairs and their capacity process is assumed to be a finite state Markov chain throughout the analytical control model. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. The structure of the hedging point policy is then parameterized by factors representing the thresholds of involved products. With such a policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal control policy. We obtain that the hedging point policy is also applicable to a wide variety of complex problems including non-exponential failure and repair times distributions and random demand rates. Analytical solutions may not be easily obtained for such complex situations.     

Production control of a pull system with production and demanduncertainty

We consider a continuous material-flow manufacturing system with an unreliable production system and a variable demand source which switches randomly between zero and a maximum level. The failure and repair times of the production system and the switching times of the demand source are assumed to be exponentially distributed random variables. The optimal production flow control policy that minimizes the expected average inventory carrying and backlog costs is characterized as a double-hedging policy. The optimal hedging levels are determined analytically by minimizing the closed-form expression of the cost function. We investigate two approximate single hedging policies. It is empirically shown that an approximate policy that uses a single hedging level which is the sum of a production uncertainty term and a demand uncertainty term gives accurate results for the expected average cost     

A simulation optimization based control policy for failure prone one-machine,two-product manufacturing systems

This paper presents the optimal flow control for a one-machine, two-product manufacturing system subject to random failures and repairs. The machine capacity process is assumed to be a finite state Markov chain. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that for constant demand rates and exponential failure and repair time distributions of the machine, the hedging point policy is optimal. Next, the hedging point policy is extended to non-exponential failure and repair time distributions models. The structure of the hedging point policy is parameterized by two factors representing the thresholds of involved products. With such a policy, simulation experiments are coupled with experimental design and response surface methodology to estimate the optimal control policy. Our results reveal that the hedging point policy is also applicable to a wide variety of complex problems (i.e. non-exponential failure and repair time distributions) where analytical solutions may not be easily obtained.     

Production rate control for failure-prone production systems withno backlog permitted

In this paper, we consider systems in which backlog is not allowed. We show that the hedging point policy is still optimal. For systems with backlog, it is usually quite straightforward to show that their optimal cost-to-go functions are convex-a key property that is needed for the hedging point policy to be optimal. With no backlog permitted, it becomes much more difficult to establish the convexity property, and the explicit formulas for the optimal hedging point and the optimal cost-to-go functions have to be obtained, based on which the convexity property can then be verified. The method we use in this paper to derive these explicit formulas is mainly based on an interesting relationship between the inventory process of the system under the hedging point policy and some stochastic processes which are well studied in queueing theory     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

Modelling and analysis of inventory replenishment for perishable agricultural products with buyer–seller collaboration

In this article, we study the inventory replenishment model for perishable agricultural products in a simple two-level supply chain. Collaborative forecasting is introduced into the inventory replenishment decisions to avoid overstocking and understocking of agricultural products, and to maximise profits. We analyse the model with ordering cost, holding cost, shortage cost, deterioration cost and opportunity lost cost of perishable agricultural products. Extensive numerical analysis is carried out to study the performance of the inventory policy. The optimal replenishment policy that minimises the total cost can be obtained from the model. It has demonstrated that the supply chain cost decreases with supplier and retailer's collaborative forecasting.     

Optimal production control in a discrete manufacturing system withunreliable machines and random demands

We consider a production control problem in a manufacturing system with a failure-prone machine and a stochastic demand. The objective is to minimize a discounted inventory holding and backlog cost over an infinite planning horizon. The optimal production control of continuous, stochastic manufacturing systems with a failure-prone machine and a constant demand has been considered in Akella and Kumar (1986). However, the problem of optimal production control for discrete stochastic manufacturing systems with uncertain demands remains open. In this paper, we investigate a case where the exogenous demand forms a homogeneous Poisson flow. Primarily, we show that the optimal production control for such a system is of the threshold control type. In addition, the explicit form of production control policy and the objective functions are provided. Numerical examples are included to demonstrate the results obtained in the paper and to compare with the one in Akella and Kumar     

Control of manufacturing systems with a two-value, production-dependent failure rate

In this paper we consider a failure prone, single machine, single part-type, limited inventory, manufacturing system subject to a non-homogeneous Markov failure/repair process with the failure rate depending on the production rate through a two-value function. The problem is to minimize a cost function which includes a penalty for waiting customers. We derive and prove the optimality of a policy which depends on a threshold but is not the so-called hedging point policy, optimal for the Markov homogeneous case.     

Maintenance scheduling and production control of multiple-machine manufacturing systems

This paper deals with the production and preventive maintenance control problem for a multiple-machine manufacturing system. The objective of such a problem is to find the production and preventive maintenance rates for the machines so as to minimize the total cost of inventory/backlog, repair and preventive maintenance. A two-level hierarchical control model is presented, and the structure of the control policy for both identical and non-identical manufacturing systems is described using parameters, referred to here as input factors. By combining analytical formalism with simulation-based statistical tools such as experimental design and response surface methodology, an approximation of the optimal control policies and values of input factors are determined. The results obtained extend those available in existing literature to cover non-identical machine manufacturing systems. A numerical example and a sensitivity analysis are presented in order to illustrate the robustness of the proposed approach. The extension of the proposed production and preventive maintenance policies to cover large systems (multiple machines, multiple products) is discussed.     

A general model for EOQ inventory systems with partial backlogging and linear shortage costs

We present a mathematical model which generalises several known deterministic Economic Order Quantity (EOQ) inventory systems with partial backlogging. This inventory model considers purchasing cost, holding cost, shortage costs and replenishment cost. Shortage costs (backorder cost and lost sales cost) are both made up of a fixed cost and a variable cost which depends on the length of the waiting time for the next replenishment. The optimal policy is characterised through a sequential optimisation procedure. To illustrate the model, numerical examples and sensitivity results are given.     

An integrated replenishment model with quantity discounts, reentry and downward substitution for control wafers

This paper considers control wafers replenishment problem in wafer fabrication factories. A dynamic lot-sizing replenishment problem with reentry and downward substitution is examined in a pulling control production environment. The objective is to set the inventory level so as to minimize the total cost of control wafers, where the costs include order cost, purchase cost, setup cost, production cost and holding cost, while maintaining the same level of production throughput. In addition, purchase quantity discounts and precise inventory level are considered in the replenishment model. The control wafers replenishment problem is first constructed as a network, and is then transformed into a mixed integer programming model. Lastly, an efficient heuristic algorithm is proposed for solving large-scale problems. A numerical example is given to illustrate the practicality for empirical investigation. The results demonstrate that the proposed mixed integer programming model and the heuristic algorithm are effective tools for determining the inventory level of control wafers for multi-grades in multi-periods.     

On continuous review stochastic (s, S) inventory systems with ordering delays

In this paper a continuous review (s, S) inventory system with ordering delays is considered. Demands for the item arrive according to a Poisson process. When the inventory level drops to s, the order is triggered. However, due to an unavoidable delay, the order is actually placed after a random amount of time. Once the order is placed, it is instantaneously delivered bringing the inventory level back to S. Under a cost structure which includes a setup cost, a holding cost and a penalty cost, an expression for the expected cost per unit time for given control values is obtained. Then some properties of the cost functions are developed to characterize the optimal policy. Based on these properties, an efficient search procedure to find the optimal (s, S) policy is presented.     

The production size and inventory policy for a manufacturer in a two-echelon inventory model

This paper proposes a two-echelon inventory model for a periodical commodity, in which the market and manufacturing channels are combined. This model can be used to solve the production policy, the order policies of the raw materials for the manufacturer, and order size for the retailer. By assuming that the retailers’ demand obeys normal distribution and that the retailer makes orders according to the Newsboy Rule, we derive the necessary and sufficient conditions for the optimal solution of production size, wholesale price, and replenishment cycle of raw materials for the manufacturer. Also, the necessary condition is explored in order to gain managerial insights and economic implications based on numerical examples and sensitivity analysis.     

允许缺货待补的季节性商品二阶联合库存最优订购策略

针对季节性商品提出了二阶单周期缺货待补联合库存模型,其中假设零售商的库存策略采用报童模型且零售商的需求量服从正态分布。对制造商总利润函数的最优解,提出了充分与必要条件,以期可以简便迅速地获得制造商的最优生产批量以及最优订购周期。最后,通过数值算例及在管理上的含义对必要条件进行了充分的讨论。     

价格波动下的生产-库存控制研究

研究原材料价格波动下多级生产-库存系统的控制问题.所有的原材料价格、半成品加工成本、成品的生产成本、库存费用率和产品的需求率都随时间变动,为此,分析了最优采购、加工、生产决策的必要和充分条件,得到了在某些假设条件下的最优生产-库存策略为JIT(Just-in-time)采购、加工、生产策略,或者为在最开始阶段以最大能力进行采购、加工、生产活动的Bang-Bang策略.     

A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: An NSGA-II with tuned parameters

In this research, a bi-objective vendor managed inventory model in a supply chain with one vendor (producer) and several retailers is developed, in which determination of the optimal numbers of different machines that work in series to produce a single item is considered. While the demand rates of the retailers are deterministic and known, the constraints are the total budget, required storage space, vendor's total replenishment frequencies, and average inventory. In addition to production and holding costs of the vendor along with the ordering and holding costs of the retailers, the transportation cost of delivering the item to the retailers is also considered in the total chain cost. The aim is to find the order size, the replenishment frequency of the retailers, the optimal traveling tour from the vendor to retailers, and the number of machines so as the total chain cost is minimized while the system reliability of producing the item is maximized. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimization algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. The parameters of both algorithms are first calibrated using the Taguchi approach. Then, the performances of the two algorithms are compared in terms of some multi-objective performance measures. Moreover, a local searcher, named simulated annealing (SA), is used to improve NSGA-II. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.     

Optimality of hedging point policies in the production control offailure prone manufacturing systems

We study the necessary and sufficient conditions for the optimality of the hedging point policy for production systems in which the failure rate of machines depends on the rate of production. We focus on a one machine one part-type and infinite horizon discounted cost problem. It is shown that when the failure rate is independent of the rate of production and a constant, the hedging point policy is provably optimal. The main result of this paper is to show that the linearity of the failure rate function is both necessary and sufficient for the optimality of the hedging point policy     

The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains

Market demand of agri-products is influenced by uncertain factors, such as weather, temperature, and customer preferences. In integrated agricultural supply chains, traditional inventory models are useless because of the stochastic demand and deteriorative characteristic of agri-products. This paper provides a method to determine the optimal replenishment policy of integrated agricultural supply chains with stochastic demand. In these EOQ/EPQ models, shortages are allowed and are backlogged if market demand is stochastic. The objective function is to minimize the total cost of the supply chain in the planning horizon. The total cost includes the ordering cost, the holding cost, the shortage cost and the purchasing cost. Thinking of the nonlinear relationship and dynamic forces in models, a system dynamic (SD) simulation model is constructed to find the optimal lot size and replenishment interval. Finally, an example is given to make a sensitivity analysis of the simulation model. Compared to traditional methods (such as equalize stochastic demand), the total cost decreases by 16.27% if the supply chains adopt the new replenishment policy. The results illustrated that the new replenishment policy (with intelligent method) is beneficial to help supply chain make decision scientifically. Moreover, the intelligent method can simulate stochastic demand perfectly, and it is effectively for solving the complicated and mathematically intractable replenishment problem.