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 analysis of setup cost reduction in a two stage system

This paper investigates the impact of investing in setup cost reduction in a two stage manufacturing process. Closed form relationships are developed for the cases of investment in primary stage setup cost reduction, investment in finishing stage setup cost reduction, and simultaneous investment in setup cost reduction in both stages. Numerical results are presented which compare each of the models to the basic model. These results indicate that when investment in both stages is feasible, it is most effective to simultaneously invest in setup cost reduction. Failing this, the next best alternative is to invest in setup cost reduction in the finishing stage.     

Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials

This paper deals with inventory models that unify the decisions for raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of nonconforming items is produced. The objective is to minimize the total variable cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis for the basic model is extended to cases where the proportion of defective items is not constant or the defective rate is a function of production setup cost.     

Manufacturer-buyer coordination for newsvendor-type-products with two ordering opportunities and partial backorders

In a recent paper [Weng, Z.K., 2004. Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model. European Journal of Operational Research 156, 148–161], a newsvendor-type coordination model was developed for a single-manufacturer single-buyer channel with two ordering opportunities. This paper further extends the model to the case where the excess demand after the first order is partially backlogged and both parties share the manufacturing setup cost of the second order (if happened). We show that the decentralized system would perform best if the manufacturer covers utterly the second production setup cost, which is opposite to that obtained in Weng (2004). Another extension in the present paper is that in the centralized system, the second order decision is made by the buyer based on the channel’s benefit rather than based on the buyer’s benefit as in Weng (2004). It is proved that the expected profit of the system in our paper is always larger than that in Weng (2004). In order to maximize the expected profit of the channel, two coordinated policies are proposed to achieve perfect coordination: a two-part-tariff policy for the special case that the buyer pays all the manufacturing setup cost, and a revised revenue-sharing contract for the case that two parties share the manufacturing setup cost.     

Optimization of Single-Item Multi-Stage Stochastic Production — Inventory Systems

This paper presents a mathematical model developed for optimization of single-item multi-stage production-inventory systems. The demands are assumed to occur randomly at the same rate whereas processing and setup times are different, each following exponential distributions with different means. The model assumes a "one-for-one ordering" inventory policy and that on total system cost expression comprising setup, holding and penalty costs is obtained for optimization. As a special case, single stage, cost expressions become the same as those obtained by Baker. Computational results for two stages are given. Implications of aggregating the two stages into an equivalent simple stage are discussed.     

An approach for integrated scheduling and lot-sizing

In this paper a non time discrete approach is developed for an integrated planning procedure, applied to a multi-item capacitated production system with dynamic demand. The objective is to minimize the total costs, which consist of holding and setup costs for one period. The model does not allow backlog. Furthermore, a production rate of zero or full capacity is the only possibility. The result is a schedule, lot-sizes and the sequences for all lots. The approach is based on a specific property of the setup cost function, which allows for replacement of the integer formulation for the number of setup activities in the model. In a situation where the requirements for the multi-item continuous rate economic order quantity, the so-called economic production lot (EPL) formula, are fulfilled, both the EPL as well as the presented model results are identical for the instances dealt with. Moreover, with the new model problems with an arbitrary demand can be solved.     

The effect of different arrival rates on the N-policy of M/G/1 with server setup

It is very important in many real-life systems to decide when the server should start his service because frequent setups inevitably make the operating cost too high. Furthermore, today's systems are too intelligent for the input to be assumed as a simple homogenous Poisson process. In this paper, an M/G/1 queue with general server setup time under a control policy is studied. We consider the case when the arrival rate varies according to the server's status: idle, setup and busy states. We derive the distribution function of the steady-state queue length, as well as the Laplace–Stieltjes transform of waiting time. For this model, the optimal N-value from which the server starts his setup is found by minimizing the total operation cost of the system. We finally investigate the behavior of system operation cost and the optimal N for various arrival rates by a numerical study.     

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.     

成品油调和配方优化研究

成品油调和是石油炼制过程中的重要环节,直接影响炼油企业的经济效益。本文以石化行业为背景,针对成品油调和配方优化问题进行了研究,在满足成品油质量指标约束的条件下,以最小化企业生产成本为目标,建立了混合整数规划模型,提出了基于遗传算法的有效求解策略,并根据某炼油厂的实际生产数据进行了仿真实验,计算结果反映了库存成本与启动成本之间的平衡关系,即:当单位库存成本不变,单位启动成本逐渐变大时,库存总成本随之增大,启动次数随之减少。反之,当单位启动成本不变,单位库存成本逐渐变大时,启动次数随之增大,库存总成本随之减少。     

Optimal investment in setup reduction in manufacturing systems with WIP inventories

A number of models have been proposed to predict optimal setup times, or optimal investment in setup reduction, in manufacturing cells. These have been based on the economic order quantity (EOQ) or economic production quantity (EPQ) model formulation, and have a common limitation in that they neglect work-in-process (WIP) inventories, which can be substantial in manufacturing systems. In this paper a new model is developed that predicts optimal production batch sizes and investments in setup reduction. This model is based on queuing theory, which permits it to estimate WIP levels as a function of the decisions variables, batch size and setup time. Optimal values for batch size and setup time are found analytically, even though the total cost model was shown to be strictly non-convex.     

Setup cost reduction in (<Emphasis Type="Italic">Q,r</Emphasis>) policy with lot size,setup time and lead-time interactions

It is often assumed in most deterministic and stochastic inventory models that lead-time is a given parameter and the optimal operating policy is determined on the basis of this unrealistic assumption. However, the manufacturing lead-time is made up of several components (moving time, waiting time, setup time, lot size, and rework time) most of which should be treated as controllable variables. In this paper the effect of setup cost reduction is addressed in a stochastic continuous review inventory system with lead-time depending on lot size and setup time. An efficient iterative procedure is developed to determine the near optimal lot size, reorder point and setup time. Furthermore, a sensitivity analysis is carried out to assess the cost savings that can be realised by investing in setup.     

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.     

Application of a Fuzzy Programming Through Stochastic Particle Swarm Optimization to Assessment of Filter Management Strategies in Fluid Power System Under Uncertainty

A fuzzy programming through stochastic particle swarm optimization is developed for the assessment of filter allocation and replacement strategies in fluid power system (FPS) under uncertainty. It can not only handle uncertainties expressed as L-R fuzzy numbers but also enhance the system robustness by transforming the fuzzy inequalities into inclusive constraints. As the simulation results indicate, the developed model can successfully decrease the total cost and enhanced the safety of system. Generally, it is believed that the model can help identify excellent filter allocation and replacement strategy with minimized operation cost and system failure risk while protecting the system.     

Coordinated maintenance in a multi-component system with compound Poisson deterioration

This paper proposes a coordinated maintenance model in a multi-component system with compound Poisson deterioration. The main contribution is a policy-iteration approach for Semi-Markov processes that optimizes the threshold at which the component is eligible for preventive maintenance if another component requires corrective maintenance. The methodology is novel as we develop explicit expressions for the policy evaluation and prove these expressions to satisfy the set of linear equations which characterize traditional policy evaluation. By doing so, long-run average cost savings are achieved, since setup costs can be shared.     

An analysis of setup cost reduction in a two stage system with power investment function

Recently, a framework for analyzing investment decisions as they relate to setup cost reduction in two stage production processes has appeared in the literature. Closed form results were developed for the case of logarithmic investment function. This paper extends the results to the case of power investment function. We present an algorithm for calculating the optimal values of the decision variables. A numerical example is utilized to reveal some interesting aspects of this system.     

A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity

A fuzzy EOQ model is developed with limited storage capacity where demand is related to the unit price and the setup cost varies with the quantity produced/purchased. Here fuzziness is introduced in both objective function and storage area. It is solved by both fuzzy nonlinear and geometric programming techniques for linear membership functions. The model is illustrated with a numerical example and a sensivity analysis is made. Generalisation to a multi-item problem is also presented and its numerical results are compared with those of the crisp model.     

Lot sizing for a single product recovery system with variable setup numbers

Inventory systems for joint remanufacturing and manufacturing have recently received considerable attention. In such systems, used products are collected from customers and are kept at the recoverable inventory warehouse for future remanufacturing. In this paper a production–remanufacturing inventory system is considered, where the demand can be satisfied by production and remanufacturing. The cost structure consists of the EOQ-type setup costs, holding costs and shortage costs. The model with no shortage case in serviceable inventory is first studied. The serviceable inventory shortage case is discussed next. Both models are considered for the case of variable setup numbers of equal sized batches for production and remanufacturing processes. For these two models sufficient conditions for the optimal type of policy, referring to the parameters of the models, are proposed.     

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.     

Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule

This paper considers an infinite-capacity M/M/c queueing system with modified Bernoulli vacation under a single vacation policy. At each service completion of a server, the server may go for a vacation or may continue to serve the next customer, if any in the queue. The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. The explicit closed-form of the rate matrix is derived and the useful formula for computing stationary probabilities is developed by using matrix analytic approach. System performance measures are explicitly developed in terms of computable forms. A cost model is derived to determine the optimal values of the number of servers, service rate and vacation rate simultaneously at the minimum total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures.     

A note on fuzzy inventory model with storage space and budget constraints

In 1997, Roy and Maiti developed a fuzzy EOQ model with fuzzy budget and storage capacity constraints where demand is influenced by the unit price and the setup cost varies with the quantity purchased [T.K. Roy, M. Maiti, A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity, Eur. J. Oper. Res. 99 (1997) 425–432]. However, their procedure has some questionable points and their numerical examples contain rather peculiar results. The purpose of this paper is threefold. First, for the same inventory model with fuzzy constraints, based on the max–min operator, we proposed an improved solution procedure. Second, we review the solution procedure by Roy and Maiti that is based on Kuhn–Tucker approach to point out their questionable results. Third, we compare Roy and Maiti’s approach with ours to explain why our approach can solve the problem and theirs cannot. Numerical examples provided by them also support our findings.