Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times.We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.     

Optimal production control of a dynamic two-product manufacturing system with setup costs and setup times

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region, the optimal control policy is determined analytically.     

Transient and steady-state analysis of a manufacturing system with setup changes

This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.     

多阶段生产系统最优生产批量和原材料订购决策模型

Sarker和Parija(1996)建立了生产系统最优生产批量和原材料订购决策模型。然而他们的模型仅局限于单阶段生产系统,本文将他们的模型扩展到多阶段生产系统,我们首先建立了使整个多阶段生产系统总成本最小的各阶段最优生产批量、原材料订购批量及阶段之间的运输批量模型,然后分析了原材料订购费、半成品运费及设备安装费的敏感性。最后,我们结合实例综合分析了原材料订购费、半成品运输费和设备安装费的变化及最小值点取整后对原材料订购决策、最优生产批量和总成本的影响。     

An economic production quantity model with a positive resetup point under random demand

In this paper, an extended economic production quantity (EPQ) model is investigated, where demand follows a random process. This study is motivated by an industrial case for precision machine assembly in the machinery industry. Both a positive resetup point s and a fixed lot size Q are implemented in this production control policy. To cope with random demand, a resetup point, i.e., the lowest inventory level to start the production, is adapted to minimize stock shortage during the replenishment cycle. The considered cost includes setup cost, inventory carrying cost, and shortage cost, where shortage may occur at the production stage and/or at the end of one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex with respect to decision parameters s and Q. Further computational study has demonstrated that the proposed model outperforms the classical EPQ when demand is random. In particular, a positive resetup point contributes to a significant portion of this cost savings when compared with that in the classical lot sizing policy.     

Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.     

Dynamic setup reduction in production lot sizing with nonconstant deterministic demand

We examine three production policies under nonconstant, deterministic demand and dynamic setup cost reduction, where a decision to invest in setup reduction is made at the beginning of each period of a planning horizon. The three production policies are the reorder point, order quantity (s, Q) policy; the fixed production cycle, variable order quantity (t, Q_i) policy; and the variable production cycle, variable order quantity (t_i, Q_i). We study the behavior of the total relevant cost and develop a lot sizing and an investment solution procedure. Numerical examples are provided and dynamic setup cost reduction is compared with static setup cost reduction, where the decision to invest in setup reduction is made only at the initial setup.     

A production–inventory model in an imperfect production process

The paper develops a model to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process. The basic assumption of the classical Economic Manufacturing Quantity (EMQ) model is that all manufacturing items are of perfect quality. The assumption is not true in practice. Most of the production system produces perfect and imperfect quality items. In some cases the imperfect quality (non conforming) items are reworked at a cost to restore its quality to the original one. Rework cost may be reduced by improvements in product reliability (i.e., decreasing in product reliability parameter). Lower value of product reliability parameter results in increase development cost of production and also smaller quantity of nonconforming products. The unit production cost is a function of product reliability parameter and production rate. As a result, higher development cost increases unit production cost. The problem of optimal planning work and rework processes belongs to the broad field of production–inventory model which deals with all kinds of reuse processes in supply chains. These processes aim to recover defective product items in such a way that they meet the quality level of ‘good item’. The benefits from imperfect quality items are: regaining the material and value added on defective items and improving the environment protection. In this point of view, a model is introduced here to guide a firm/industry in addressing variable product reliability factor, variable unit production cost and dynamic production rate for time-varying demand. The paper provides an optimal control formulation of the problem and develops necessary and sufficient conditions for optimality of the dynamic variables. In this purpose, the Euler–Lagrange method is used to obtain optimal solutions for product reliability parameter and dynamic production rate. Finally, numerical examples are given to illustrate the proposed model.     

能源回购补偿机制下基于无限阶段折扣准则的最优生产与库存策略

世界经济的快速发展和工业化进程的推进促使各国电力需求激增,电力供需矛盾为能源回购项目的发展提供了条件。为能够实现错峰用电和缓解能源需求的紧张,能源回购项目在每个阶段出现能源短缺时,将根据短缺的不同程度为限产(或停产)企业提供了金额不同的资金补偿。因此,在该能源回购补偿机制下,企业需要确定每个阶段是否参加能源回购项目及其相应的生产库存策略,来实现其期望折扣成本的最小化。本文研究了能源回购补偿机制下企业以最小化期望折扣成本为目标的无限阶段最优生产/库存策略。引入启动成本和多个能源需求状态的资金补偿水平后,在合理的假设条件下,证明了每个阶段生产商的最优生产/库存策略在高峰状态为(sⁱ,S)策略,在非高峰状态为(s⁰,S,A)策略。     

Coordinated production and inspection in a tandem system

We study the coordination of production and quality control in a tandem-queue system. There are two stages, with a single server at stage one that can engage in processing an item, or inspecting the produced item, or staying idle; whereas the second stage represents the aggregate of the rest of the production facility. We focus on the optimal control of the first stage, where both the production and inspection times follow general distributions. We formulate a semi-Markov decision program with a long-run average objective, and derive the stationary optimal policy to control and coordinate the production, inspection, and idling processes. We show that there exists a threshold valuei ^–, such that under the optimal policy, once the threshold is reached, production should be suspended at the first stage; and this leads naturally toi ^–+1 being the required buffer capacity between the two stages.Supported in part by NSF Grant MDI-9523029.Supported in part by HKUST Grant DAG95/96.BM52.     

Controlling adverse effect on work in process inventory while reducing machine setup time

Earlier research has found that the presence of setup time variance can cause an adverse effect on waiting time and inventory as one reduces setup time for a product on a single machine that processes a number of products in a cyclic production system [Sarkar, D., Zangwill, W.I., 1991. Variance effects in cyclic production systems. Management Science 37 (4) 444–453; Zangwill, W.I., 1987. From EOQ towards ZI. Management Science 33 (10) 1209–1223]. This finding validates what other researchers had believed from a rather anecdotal perspective: “variability reduction” is extremely important for improving overall effectiveness of a pull or JIT system [Schonberger, Richard J., 1982. Japanese Manufacturing Techniques: Nine Hidden Lessons in Simplicity. The Free Press, New York]. In this paper, we offer explicit mathematical equations that characterize the variance levels in order to offer exact conditions under which WIP improves or worsens when one reduces setup time.     

An EPQ model with setup cost and process quality as functions of capital expenditure

This paper considers an economic production quantity (EPQ) model with imperfect production processes, in which the setup cost and process quality are functions of capital expenditure. The mathematical model is derived to investigate the effects of an imperfect production process on the optimal production cycle time when capital investment strategies in setup reduction and process quality improvement are adopted. An efficient procedure is developed to find the optimal production run length, setup cost and process quality. Finally, a numerical example is provided to illustrate the theoretical results. Some managerial implications are also included.     

An elaborative unit cost structure-based fuzzy economic production quantity model

The purpose of this paper is to investigate and propose a fuzzy extended economic production quantity model based on an elaboratively modeled unit cost structure. This unit cost structure consists of the various lot-size correlative components such as on-line setups, off-line setups, initial production defectives, direct material, labor, and depreciation in addition to lot-size non-correlative items. Thus, the unit cost is correlatively modeled to the production quantity. Therefore, the modeling or the annual total cost function developed consists of not only annual inventory and setup costs but also production cost. Moreover, via the concept of fuzzy blurred optimal argument and the vertex method of the α-cut fuzzy arithmetic (or fuzzy interval analysis), two solution approaches are proposed: (1) a fuzzy EPQ and (2) a compromised crisp EPQ in the fuzzy sense. An optimization procedure, which can simultaneously determine the α-cut-vertex combination of fuzzy parameters and the optimizing decision variable value, is also proposed. The sensitivity model for the fuzzy total cost and thus EPQ to the various cost factors is provided. Finally, a numerical example with the original data collected from a firm demonstrates the usefulness of the new model.     

An analytical model for reverse automotive production planning and pricing

Automotive shredders need a reverse production planning strategy that includes determining at what price to purchase vehicle hulks from different sources. In this paper, we formulate the automotive reverse production planning and pricing problem in a nonlinear programming model, develop an approximate supply function for hulks when adjacent shredders price independently, and compare two hulk pricing strategies in three trends for ferrous metal and hulk prices: constant, increasing and decreasing. The case study results indicate that adjusting purchase price based on hulk composition in coordination with planning for purchasing, storing and processing can increase net revenue by 7–15%.     

Optimization of setup times in the furniture industry

The aim of this paper is to develop a scheduling policy oriented towards minimizing setup times in the made-to-order furniture industry. The task is treated as a dynamic job shop scheduling problem, with the exception that customers?? orders collected over a?specified period of time are combined into a?production plan and released together. A?simulation of a production flow based on technological routes of real subassemblies was performed. The proposed method of calculating a setup time eliminates the need to determine machine setup time matrices. Among the tested priority rules the best performance was observed in the case of the hierarchical rule that combines similar setup, the earliest due date and the shortest processing time. This rule allowed the setup time per operation to be reduced by 58?% compared to a combination of the earliest due date with the shortest setup and processing time rule and by over 70?% compared to the single shortest processing time rule.     

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing – both dynamic and static – is beneficial and assess the value of the dynamic policy.     

Single Supplier Scheduling for Multiple Deliveries

The problem of scheduling the production and delivery of a supplier to feed the production of F manufacturers is studied. The orders fulfilled by the supplier are delivered to the manufacturers in batches of the same size. The supplier's production line has to be set up whenever it switches from processing an order of one manufacturer to an order of another manufacturer. The objective is to minimize the total setup cost, subject to maintaining continuous production for all manufacturers. The problem is proved to be NP-hard. It is reduced to a single machine scheduling problem with deadlines and jobs belonging to F part types. An O(NlogF) algorithm, where N is the number of delivery batches, is presented to find a feasible schedule. A dynamic programming algorithm with O(N ^F /F ^F–2) running time is presented to find an optimal schedule. If F=2 and setup costs are unit, an O(N) time algorithm is derived.     

Minimum Hellinger distance estimation for supercritical Galton–Watson processes

This paper studies the asymptotic behavior of the minimum Hellinger distance estimator of the underlying parameter in a supercritical branching process whose offspring distribution is known to belong to a parametric family. This estimator is shown to be asymptotically normal, efficient at the true model and robust against gross errors. These extend the results of Beran (Ann. Statist. 5, 445–463 (1977)) from an i.i.d., continuous setup to a dependent, discrete setup.     

A two-bottleneck system with binomial yields and rigid demand

This study considers multistage production systems where production is in lots and only two stages have non-zero setup costs. Yields are binomial and demand, needing to be satisfied in its entirety, is “rigid”. We refer to a stage with non-zero setup cost as a “bottleneck” (BN) and thus to the system as “a two-bottleneck system” (2-BNS). A close examination of the simplest 2-BNS reveals that costs corresponding to a particular level of work in process (WIP) depend upon costs for higher levels of WIP, making it impossible to formulate a recursive solution.For each possible configuration of intermediate inventories a production policy must specify at which stage to produce next and the number of units to be processed. We prove that any arbitrarily “fixed” production policy gives rise to a finite set of linear equations, and develop algorithms to solve the two-stage problem. We also show how the general 2-BNS can be reduced to a three-stage problem, where the middle stage is a non-BN, and that the algorithms developed can be modified to solve this problem.     

A dynamic lot sizing model with exponential machine breakdowns

This paper addresses the dynamic lot sizing model with the assumption that the equipment is subject to stochastic breakdowns. We consider two different situations. First we assume that after a machine breakdown the setup is totally lost and new setup cost is incurred. Second we consider the situation in which the cost of resuming the production run after a failure might be substantially lower than the production setup cost. We show that under the first assumption the cost penalty for ignoring machine failures will be noticeably higher than in the classical lot sizing case with static demand. For the second case, two lot sizes per period are required, an ordinary lot size and a specific second (or resumption) lot size. If during the production of a future period demand the production quantity exceeds the second lot size, the production run will be resumed after a breakdown and terminated if the amount produced is less than this lot size. Considering the results of the static lot sizing case, one would expect a different policy. To find an optimum lot sizing decision for both cases a stochastic dynamic programming model is suggested.