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.     

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.     

Planning for demand failure: A dynamic lot size model for clinical trial supply chains

This paper examines the optimal production lot size decisions for clinical trial supply chains. One unique aspect of clinical trial supply chains is the risk of failure, meaning that the investigational drug is proven unsafe or ineffective during human testing and the trial is halted. Upon failure, any unused inventory is essentially wasted and needs to be destroyed. To avoid waste, manufacturers could produce small lot sizes. However, high production setup costs lead manufacturers to opt for large lot sizes and few setups. To optimally balance this tradeoff of waste and destruction versus production inefficiency, this paper generalizes the Wagner-Whitin model (W-W model) to incorporate the risk of failure. We show that this stochastic model, referred to as the failure-risk model, is equivalent to the deterministic W-W model if one adjusts the cost parameters properly to reflect failure and destruction costs. We find that increasing failure rates lead to reduced lot sizes and that properly incorporating the risk of failure into clinical trial drug production can lead to substantial cost savings as compared to the W-W model without the properly adjusted parameters.     

The Common Cycle Economic Lot Scheduling Problem with Backorders: Benefits of Controllable Production Rates

In this paper, we deal with the production scheduling ofseveral products that are produced periodically, in a fixed sequence, ona single machine. In the literature, this problem is usually referred to asthe Common Cycle Economic Lot Scheduling Problem. We extend thelatter to allow the production rates to be controllable at the beginningof as well as during each production run of a product. Also, we assumethat unsatisfied demand is completely backordered. The objective is todetermine the optimal schedule that satisfies the demand for all theproducts and that realizes the minimum average setup, inventoryholding and backlog cost per unit time. Comparison with previousresults (when production rates are fixed) reveals that averagecosts can be reduced up to 66% by allowing controllable productionrates.     

The economic order quantity repair and waste disposal model with entropy cost

As markets have become more and more competitive, disorder has become a prevailing characteristic of modern production systems that are operating in complex, dynamic and uncertain environments. Minimizing disorder in these production systems requires stringent control measures by management, with costs that are usually hidden or difficult to estimate. Not accounting for these costs leads to less efficient production systems. This paper postulates that the behaviour of production systems very much resembles that of physical systems. Such a parallel suggests that improvements to production systems may be achievable by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). The applicability of these laws is demonstrated in a simple reverse supply chain context, where products are collected and later repaired at some rate while other products might be disposed outside according to some waste disposal rate. Numerical examples are provided.     

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。     

Reducing lost-sales rate in (T, R, L) inventory model with controllable lead time

In order to establish a good image and to enhance customer’s loyalty, many efforts such as upgrading the servicing facilities, maintaining a high quality of products and increasing expenditure on advertisement could be made by a selling shop. Naturally, an extra-added cost must be spent for these efforts and it is expected to have a result to reduce the shortage cost of lost-sales and the total expected annual cost. This paper explores a probabilistic inventory model with optimal lost-sales caused by investment due to two different types of cost functions. We consider that the lead time can be shortened at an extra crashing cost, which depends on the length of the lead time. Moreover, we assume that the lost-sales rate can also be reduced by capital investment. The purpose of this paper is to establish a (T, R, L) inventory model with controllable lead time and to analyze the effects of increasing two different types of investments to reduce the lost-sales rate, in which the review period, lead time and lost-sales rate are treated as decision variables. We first formulate the basic periodic review model mathematically with the capital investment to reduce lost-sales rate. Then two models are discussed, one with normally distributed protection interval demand and another with distribution-free case. For each model, two investment cost functional forms, logarithmic and power, are employed for lost-sales rate reduction. Two computational algorithms with the help of the software Matlab are furnished to determine the optimal solution. In addition, six numerical examples and sensitivity analysis are presented to illustrate the theoretical results and obtain some managerial insights. Finally, the effect of lost-sales rate reduction is investigated. By framing this new model, we observe that a significant amount of savings can be easily achieved to increase the competitive edge in business. The results in the numerical examples indicate that the savings of expected annual total cost are realized through lost-sales reduction.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.     

回收率依赖回收产品质量的再制造EOQ模型

研究回收率依赖回收产品质量情况下制造/再制造混合系统的EOQ模型.该模型假设顾客的需求可通过新产品的制造和回收产品的再制造两种方式满足,且这两种产品无质量差异;需求率是确定的、连续的;总成本包括制造和再制造的固定启动成本,可销售产品和回收品的库存成本,以及缺货成本.当假设缺货成本无限大时给出不允许缺货情况下的模型.给出算例验证模型的有效性.     

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.     

Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint

In this paper, a multiproduct single-machine production system under economic production quantity (EPQ) model is studied in which the existence of only one machine causes a limited production capacity for the common cycle length of all products, the production defective rates are random variables, shortages are allowed and take a combination of backorder and lost sale, and there is a service rate constraint for the company. The aim of this research is to determine the optimal production quantity, the allowable shortage level, and the period length of each product such that the expected total cost, including holding, shortage, production, setup and defective items costs, is minimized. The mathematical model of the problem is derived for which the objective function is proved to be convex. Then, a derivative approach is utilized to obtain the optimal solution. Finally, two numerical examples in each of which a sensitivity analysis is performed on the model parameters, are provided to illustrate the practical usage of the proposed methodology.     

回收率依赖价格的再制造EPQ模型研究

研究了考虑回收率依赖于回收品价格,并带有废弃处理的制造和再制造混合系统的(1,R)和(M,1)EPQ模型.在模型中,采用新产品的制造和回收产品的再制造两种方式来满足客户的需要,回收产品部分用于再制造,其余作为废弃处理;总平均成本包括与回收产品、可销售产品有关的库存持有成本,与制造和再制造有关的生产成本和固定成本,与回收品及制造所需原材料的采购成本以及废弃处理成本.模型给出最优生产策略及总平均成本的表达式.算例验证了所建模型的计算方法,并分析了新引人决策变量p(回收产品单价占制造新产品所需原料价格的比例对总平均成本的变化率的影响.     

A multi-objective mathematical model for the industrial hazardous waste location-routing problem

Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multi-objective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers; minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues; and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database.     

A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money

In this paper, a production-repairing inventory model in fuzzy rough environment is proposed incorporating inflationary effects where a part of the produced defective units are repaired and sold as fresh units. Here, production and repairing rates are assumed as dynamic control variables. Due to complexity of environment, different costs and coefficients are considered as fuzzy rough type and these are reduced to crisp ones using fuzzy rough expectation. Here production cost is production rate dependent, repairing cost is repairing rate dependent and demand of the item is stock-dependent. Goal of the research work is to find decisions for the decision maker (DM) who likes to maximize the total profit from the above system for a finite time horizon. The model is formulated as an optimal control problem and solved using a gradient based non-linear optimization method. Some particular cases of the general model are derived. The results of the models are illustrated with some numerical examples.     

Production planning problem with sequence dependent setups as a bilevel programming problem

Each of n products is to be processed on two machines in order to satisfy known demands in each of T periods. Only one product can be processed on each machine at any given time. Each switch from one item to another requires sequence dependent setup time. The objective is to minimize the total setup time and the sum of the costs of production, storage and setup. We consider the problem as a bilevel mixed 0–1 integer programming problem. The objective of the leader is to assign the products to the machines in order to minimize the total sequence dependent setup time, while the objective of the follower is to minimize the production, storage and setup cost of the machine. We develop a heuristics based on tabu search for solving the problem. At the end, some computational results are presented.     

The effect of product variety on supply-chain performance

We present a stylized model for analyzing the effect of product variety on supply-chain performance for a supply chain with a single manufacturer and multiple retailers. The manufacturer produces multiple products on a shared resource with limited capacity and the effect of changeovers on supply-chain cost is due primarily to setup time rather than setup cost. We show that the expected replenishment lead time and the retailers' costs are concave increasing in product variety and that the increase is asymptotically linear. Thus, if setup times are significant, the effect of product variety on cost is substantially greater than that suggested by the risk-pooling literature for perfectly flexible manufacturing processes, where the cost increases proportionally to the square root of product variety. We demonstrate that disregarding the effect of product variety on lead time can lead to poor decisions and can lead companies to offer product variety that is greater than optimal. The results of our analysis enable decision-makers to quantify the effect of product variety on supply-chain performance and thus to determine the optimal product variety to offer. The results can also be used to evaluate how changes in the manufacturing process, the supply-chain structure, and the customer demand rate can improve the performance of supply chains with high product variety.     

An economic production lot size model in an imperfect production system

The paper investigates an EPL (Economic Production Lotsize) model in an imperfect production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘in-control’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective (imperfect), in ‘out-of-control’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.     

维修中心参与回收时闭环供应链的定价决策及回收模式选择

维修中心参与回收是闭环供应链研究面临的新情境。本文将维修中心可以免费获得零部件的情形考虑进来, 分别给出了回收商单回收渠道模式、回收商与第三方维修中心双回收渠道模式, 在此基础上深入研究了两种模式下闭环供应链的定价决策及回收模式选择问题。结果表明:两种模式下, 官方维修中心免费获得零部件数量的增加都会对制造商利润产生积极影响, 但不会对其回购价产生影响; 双回收渠道模式下, 第三方维修中心免费获得零部件数量的增加会使制造商的回购价降低, 使其利润增加。从有偿回收产品总数量最大化的角度来看, 当第三方维修中心免费获得零部件的数量较低且两种渠道之间的竞争程度较高时, 应该选择双回收渠道模式。从制造商利润最大化的角度来看, 模式选取决策与两种模式下官方维修中心免费获得零部件数量的相对大小有关。     

维修中心参与回收时闭环供应链的定价决策及回收模式选择

维修中心参与回收是闭环供应链研究面临的新情境。本文将维修中心可以免费获得零部件的情形考虑进来,分别给出了回收商单回收渠道模式、回收商与第三方维修中心双回收渠道模式,在此基础上深入研究了两种模式下闭环供应链的定价决策及回收模式选择问题。结果表明：两种模式下,官方维修中心免费获得零部件数量的增加都会对制造商利润产生积极影响,但不会对其回购价产生影响;双回收渠道模式下,第三方维修中心免费获得零部件数量的增加会使制造商的回购价降低,使其利润增加。从有偿回收产品总数量最大化的角度来看,当第三方维修中心免费获得零部件的数量较低且两种渠道之间的竞争程度较高时,应该选择双回收渠道模式。从制造商利润最大化的角度来看,模式选取决策与两种模式下官方维修中心免费获得零部件数量的相对大小有关。     

On a facility location problem with applications to tele-diagnostic

Consider an undirected graph G modelling a network. Each vertex in the graph contains some physical devices, which can be monitored and possibly repaired from a remote site in case they become faulty. We assume that there can be two kinds of faults in the system: soft faults, which can be repaired remotely from another site (i.e., a monitor), and severe faults which cannot be repaired remotely and require further (possibly human) interventions. We assume that soft faults happen with some fixed probability λ, 0 < λ ≤ 1. We investigate the problem of locating monitors in the network so as to minimize the total expected communication cost per fault. We formalize such a problem as a location problem with a cost function depending on λ and study some properties of the optimal solutions. The latter are exploited for investigating the complexity of the problem and providing efficient approximation algorithms.