可变抽样区间几何EWMA控制图的经济设计

为了降低生产过程周期成本,本文对单位缺陷数服从几何分布时,可变抽样区间的指数加权移动平均(EWMA)控制图进行经济设计。首先建立可变抽样区间几何EWMA控制图的经济模型,使单位时间期望费用最小来确定参数的最优值;其次用遗传算法来寻找经济模型的最优解;最后对可变抽样区间几何EWMA控制图的经济模型进行灵敏度分析和最优性分析。研究结果表明单位时间期望费用分别随着异常原因发生的频率、过程失控时单位时间的质量费用、发现异常原因的时间期望值和纠正过程的时间期望值的增大而增大。     

On the Effect of Product Variety in Production–Inventory Systems

In this paper, we examine the effect of product variety on inventory costs in a production–inventory system with finite capacity where products are made to stock and share the same manufacturing facility. The facility incurs a setup time whenever it switches from producing one product type to another. The production facility has a finite production rate and stochastic production times. In order to mitigate the effect of setups, products are produced in batches. In contrast to inventory systems with exogenous lead times, we show that inventory costs increase almost linearly in the number of products. More importantly, we show that the rate of increase is sensitive to system parameters including demand and process variability, demand and capacity levels, and setup times. The effect of these parameters can be counterintuitive. For example, we show that the relative increase in cost due to higher product variety is decreasing in demand and process variability. We also show that it is decreasing in expected production time. On the other hand, we find that the relative cost is increasing in expected setup time, setup time variability and aggregate demand rate. Furthermore, we show that the effect of product variety on optimal base stock levels is not monotonic. We use the model to draw several managerial insights regarding the value of variety-reducing strategies such as product consolidation and delayed differentiation.     

Analysis of expected queueing delays for decision making in production planning

Concepts such as Time Based Competition and criticism of traditional cost accounting's role as a basis for decision making in production planning have emphasized the need for operational measures as indicators of manufacturing performance. One such measure is the expected queueing delay at a production facility. In this paper a typical bottleneck work center is considered where semi-manufactured products are processed in batches. The expected queueing delay depends on the batch sizes used at the work center. Emphasis is placed on the derivation of analytical expressions of (bounds on) the minimal expected queueing delay that can be achieved by an optimal batching decision. The analytical expressions can be applied easily to support managerial decisions on reduction of setup time and on expansion of capacity.     

生产线随机崩坍情形下的变质品EPQ策略

变质品生产过程,可能率先出现"次品"的不稳定生产情形,随后机器崩坍;生产状态稳定性迁移时机、机器崩坍时间、维修时间皆乃随机变量;同时,企业无法观测当期需求,只能根据前期需求而随机地安排启动生产时刻.理论模型及数值算例皆表明,此种情况下,企业可以非等周期生产,存在组织生产次数(N)与生产率(P)的优解.敏感度分析看出,当需求拖后率增加、变质率+次品率降低时,企业成本显著降低,但首期生产启动时刻、生产率几乎没有变化.     

Optimal control of a divergent multi-echelon inventory system

Consider a divergent multi-echelon inventory system, such as a distribution system or a production system. At every facility in the system orders are placed (or production is initiated) periodically. The order arrives after a fixed lead time. At the end of each period linear costs are incurred penalty costs are incurred at the most downstream facilities for back-orders. The objective is to minimize the expected holding and penalty costs per period. We prove that under the balance assumption it is cost optimal to control every facility by an order-up-to-policy. The optimal replenishment policy, i.e. the order-up-to-level and the allocation functions at each facility, can be determined by system decomposition. This decomposition reduces complex multi-dimensional control problems to simple one-dimensional problems.     

Theory of exchange

In the context of production activity, several parameters play an important role in the total cost estimation and its optimization. These parameters include facility setup cost, inventory carrying cost, and manufacturing cost for the basic model. Shortages can be incorporated in certain environment and costs associated with shortages need to be included in the analysis. It is expected that the industries will run their manufacturing facility at an optimum level. In the multi-product manufacture, optimum common cycle time approach is usually adopted and all the items are produced in each cycle. A situation may occur in the real world, in which a particular parameter concerning an item is exchanged with that of another item. It is of interest to examine the aftereffects. Otherwise also, for the purpose of internal benchmarking, a deliberate exchange of parameters can take place. This can be implemented in case of cost improvement. A generalized approach is presented and discussion is made with reference to various parameters.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.     

The stochastic economic lot sizing problem for non-stop multi-grade production with sequence-restricted setup changeovers

We study a variant of the stochastic economic lot scheduling problem (SELSP) encountered in process industries, in which a single production facility must produce several different grades of a family of products to meet random stationary demand for each grade from a common finished-goods (FG) inventory buffer that has limited storage capacity. When the facility is set up to produce a particular grade, the only allowable changeovers are from that grade to the next lower or higher grade. Raw material is always available, and the production facility produces continuously at a constant rate even during changeover transitions. All changeover times are constant and equal to each other, and demand that cannot be satisfied directly from inventory is lost. There is a changeover cost per changeover occasion, a spill-over cost per unit of product in excess whenever there is not enough space in the FG buffer to store the produced grade, and a lost-sales cost per unit short whenever there is not enough FG inventory to satisfy the demand. We model the SELSP as a discrete-time Markov decision process (MDP), where in each time period the decision is whether to initiate a changeover to a neighboring grade or keep the set up of the production facility unchanged, based on the current state of the system, which is defined by the current set up of the facility and the FG inventory levels of all the grades. The goal is to minimize the (long-run) expected average cost per period. For problems with more than three grades, we develop a heuristic solution procedure which is based on decomposing the original multi-grade problem into several 3-grade MDP sub-problems, numerically solving each sub-problem using value iteration, and constructing the final policy for the original problem by combining parts of the optimal policies of the sub-problems. We present numerical results for problem examples with 2–5 grades. For the 2- and 3-grade examples, we numerically solve the exact MDP problem using value iteration to obtain insights into the structure of the optimal changeover policy. For the 4- and 5-grade examples, we compare the performance of the decomposition-based heuristic (DBH) solution procedure against that obtained by numerically solving the exact problem. We also compare the performance of the DBH method against the performance of three simpler parameterized heuristics. Finally, we compare the performance of the DBH and the exact solution procedures for the case where the FG inventory storage consists of a number of separate general-purpose silos capable of storing any grade as long as it is not mixed with any other grade.     

Optimal design of unreliable production–inventory systems with variable production rate

In this article, we study an economic manufacturing quantity (EMQ) problem for an unreliable production facility where the production rate is treated as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate of the machine is assumed to be dependent on the production rate. The unit production cost is also taken as a function of the production rate, as the machine can be operated at different production rates resulting in different unit production costs. The basic EMQ model is formulated under general failure and general repair time distributions and the optimal production policy is derived for specific failure and repair time distributions viz., exponential failure and exponential repair time distributions. Considering randomness of the time to machine failure and corrective repair time, the model is extended to the case where certain safety stocks in inventory may be useful to improve service level to customers. Optimal production policies of the proposed models are derived numerically and the sensitivity of the optimal results with respect to those parameters which directly influence the machine failure and repair rates is also examined.     

Economic Production Lot Size Model with Variable Production Rate and Imperfect Quality

The classical economic production lot size (EPL) model assumes a constant production rate that is predetermined and inflexible, and perfect quality. Recent models have removed the assumption of perfect quality while maintaining the inflexible production rate assumption. Production rates in many cases, such as orders filled by a machine, can be changed. Moreover, unit production cost and process quality depend on the production rate. In this paper, we extend the EPL model to cases where the production rate is a decision variable. Unit production cost becomes a function of the production rate. Also, the quality of the production process deteriorates with increased production rate. We solve the proposed model for special cost and quality functions and illustrate the results with a numerical example. The results show that, for cases where increases in the production rate lead to a significant deterioration in quality, the optimal production rate may be smaller than the rate that minimizes unit production cost. For cases where quality is largely independent of the production rate, the optimal production rate may be larger than the rate that minimizes unit production cost.     

Optimal core acquisition and remanufacturing policies under uncertain core quality fractions

Cores acquired by a remanufacturer are typically highly variable in quality. Even if the expected fractions of the various quality levels are known, then the exact fractions when acquiring cores are still uncertain. Our model incorporates this uncertainty in determining optimal acquisition decisions by considering multiple quality classes and a multinomial quality distribution for an acquired lot. We derive optimal acquisition and remanufacturing policies for both deterministic and uncertain demand. For deterministic demand, we derive a simple closed-form expression for the total expected cost. In a numerical experiment, we highlight the effect of uncertainty in quality fractions on the optimal number of acquired cores and show that the cost error of ignoring uncertainty can be significant. For uncertain demand, we derive optimal newsboy-type solutions for the optimal remanufacture-up-to levels and an approximate expression for the total expected cost given the number of acquired cores. In a further numerical experiment, we explore the effects of demand uncertainty on the optimal acquisition and remanufacturing decisions, and on the total expected cost.     

Explicit formula of optimal replacement under additive shock processes

The optimal machine replacement problem is discussed for the case, where damage processes are general jump processes. Considering an expected average cost and an expected discounted cost, an explicit formula of optimal replacement time is shown under appropriate conditions for damage processes.     

Public and private optimization at a service facility with approximate information on congestion

An M/GI/1 queueing model is considered, where the arrival rate to the facility is a continuous variable which depends, in the steady state, upon the average congestion at the facility. The population of customers arriving to the facility is partitioned into several classes dependent on the ratio of the value of time to the reward due to service but are served according to first-in-first-out rule. It is shown that under the privately optimal behavior of the individuals the facility will be dominated by the class with the highest net reward per value of time. The publicly optimal policy which maximizes the net reward due to service, after costs of waiting are deducted, is shown either to admit only a single class of customers to the facility, thus discriminating against the other classes or to be indifferent to the mix of classes. The class chosen for admission may not be the class which would have privately dominated the facility. When the expected delay experienced at the facility is fixed, a policy of tolls and rebates for the customers is obtained that will assure equal access to the facility for all customers irrespective of their classes. It is shown that the publicly optimal policy, under the condition of fixed aggregate arrival rate to the facility, is shown to be deversified.The optimal arrival rates desired by a single class are derived for two cases. When the proportions of arrivals from the classes are fixed, the aggregate arrival rate desired by a class is shown to be not greater than the equilibrium rate for the individuals from that class. Alternatively, when the aggregate arrival rate is fixed, conditions are obtained under which a class will prefer usage of the facility by several classes to its own domination.     

自由作业的供应链排序研究

研究一类集成工件加工和发送的供应链排序模型,即研究如何安排工件在自由作业机器上加工,把加工完毕的工件分批发送给下游客户,使得含生产排序费用和发送费用的目标函数最优.这里,分别取工件最大送到时间和平均送到时间为生产排序费用;而发送费用是由固定费用和与运输路径有关的变化费用组成.利用排序理论和动态规划方法,构造了自由作业供应链排序问题的多项式时间近似算法,并分析算法的性能比.     

Economic production lot-sizing for an unreliable machine under imperfect age-based maintenance policy

This paper is concerned with the joint determination of both economic production quantity and preventive maintenance (PM) schedules under the realistic assumption that the production facility is subject to random failure and the maintenance is imperfect. The manufacturing system is assumed to deteriorate while in operation, with an increasing failure rate. The system undergoes PM either upon failure or after having reached a predetermined age, whichever of them occurs first. As is often the case in real manufacturing applications, maintenance activities are imperfect and unable to restore the system to its original healthy state. In this work, we propose a model that could be used to determine the optimal number of production runs and the sequence of PM schedules that minimizes the long-term average cost. Some useful properties of the cost function are developed to characterize the optimal policy. An algorithm is also proposed to find the optimal solutions to the problem at hand. Numerical results are provided to illustrate both the use of the algorithm in the study of the optimal cost function and the latter’s sensitivity to different changes in cost factors.     

Economic lot scheduling problem with imperfect production processes

In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.     

Nonstationary denumerable state Markov decision processes – with average variance criterion

In this paper, we consider the nonstationary Markov decision processes (MDP, for short) with average variance criterion on a countable state space, finite action spaces and bounded one-step rewards. From the optimality equations which are provided in this paper, we translate the average variance criterion into a new average expected cost criterion. Then we prove that there exists a Markov policy, which is optimal in an original average expected reward criterion, that minimizies the average variance in the class of optimal policies for the original average expected reward criterion.     

Minimizing the Total Cost in an Integrated Vendor—Managed Inventory System

In this paper we consider a complex production-distribution system, where a facility produces (or orders from an external supplier) several items which are distributed to a set of retailers by a fleet of vehicles. We consider Vendor-Managed Inventory (VMI) policies, in which the facility knows the inventory levels of the retailers and takes care of their replenishment policies. The production (or ordering) policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The cost includes the fixed and variable production costs at the facility, the inventory costs at the facility and at the retailers and the transportation costs, that is the fixed costs of the vehicles and the traveling costs. We study two different types of VMI policies: The order-up-to level policy, in which the order-up-to level quantity is shipped to each retailer whenever served (i.e. the quantity delivered to each retailer is such that the maximum level of the inventory at the retailer is reached) and the fill-fill-dump policy, in which the order-up-to level quantity is shipped to all but the last retailer on each delivery route, while the quantity delivered to the last retailer is the minimum between the order-up-to level quantity and the residual transportation capacity of the vehicle. We propose two different decompositions of the problem and optimal or heuristic procedures for the solution of the subproblems. We show that, for reasonable initial values of the variables, the order in which the subproblems are solved does not influence the final solution. We will first solve the distribution subproblem and then the production subproblem. The computational results show that the fill-fill-dump policy reduces the average cost with respect to the order-up-to level policy and that one of the decompositions is more effective. Moreover, we compare the VMI policies with the more traditional Retailer-Managed Inventory (RMI) policy and show that the VMI policies significantly reduce the average cost with respect to the RMI policy.     

Economic lot scheduling with uncontrolled co-production

The aim of this paper is to analyze the effects of uncontrolled co-production on the production planning and lot scheduling of multiple products. Co-production occurs when a proportion of a certain production comes out as another product. This is typical in the process industry where quality and process specifications can lead to diversified products. We assume that there is no demand substitution and each product has its own market. Furthermore, we assume that co-production cannot be controlled due to technical and/or cost considerations. We introduce two models that extend the common cycle economic lot scheduling (ELSP) setting to include uncontrolled co-production. In the first model we do not allow for shortages and derive the optimal cycle time expression. In the second model, we allow for planned backorders and characterize the optimal solution in closed form. We provide a numerical study to gain insight about co-production. It seems that the cycle time increases with co-production rate and utilization of the system. The effect of co-production on long-term average cost does not exhibit a certain characteristic.