Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Two-stage make-to-order remanufacturing with service-level constraints

We consider a firm that meets demand for an order with remanufactured products, new products or a mix of both. There are constraints on the service level. We use a stylized two-stage GI/G/ 1 queuing network model to study the problem. The first stage is unique to each product, whereas remanufactured and new products share the second stage. The objective was to find the optimal, long run production mix that maximizes profit subject to a service-level constraint that restricts the average order lead-time. There is yield in the remanufacturing process, where yield is the per cent of returned used products that result in a good part after remanufacturing. In the analytic model, we make the simplifying assumption that the producer always gets enough return of used products to meet its remanufacturing needs in the production mix. However, we relax this assumption in a simulation. We find that the optimal solution is generally non-trivial, i.e. the firm generally uses a mix of remanufactured and new products to meet demand. When the new product is less profitable than the remanufactured product, then it is optimal to remanufacture 100%, provided that there is enough supply of used products. When the new product is more profitable, however, the proportion of remanufacturing increases as service level increases. We use simulation to test the robustness of the analytic model by including complexities such as stochastic product returns and stochastic production yield.     

Economic determination of specification levels and allocation priorities of semiconductor products

We construct and analyze an economically efficient way of pricing and allocating semiconductor chips of which production technology is characterized by persistent quality variations and of which production capacity is exceeded by potential demand. In our model, specification levels and allocation priorities of competing orders from customers are systematically determined for a single profit maximizing producer. In the proposed scheme, the producer offers a 'product line' of priority classes under an allocation rule that always supplies higher priority classes with higher spec, level chips. This product line design and allocation rule enable us to cast the producer's profit maximization problem as a nonlinear programming formulation. Also, we investigate the optimality of the proposed allocation rule and derive conditions under which the profitability of downgrading is determined.     

Joint production and maintenance planning with machine deterioration and random yield

Production, yield and maintenance are three key components for sustaining the competitiveness of a manufacturing firm. In this paper, we investigate a joint production and maintenance planning problem in a periodic review environment subject to stochastic demand and random yields. The manufacturing system deteriorates from period to period according to a discrete-time Markov chain. The objective is to find an integrated lot sizing and maintenance policy for the system such that the aggregate cost associated with production, holding, backlogging and maintenance is minimised. We formulate this integrated planning problem as a Markov decision process and analyse the structural properties of the optimal policies. We prove that the optimal production and the maintenance policies both exhibit a control limit structure and show that the solution to the finite-horizon problems converges to that of the infinite-horizon problem.     

Joint decision making for production and marketing

The prosperity of a firm depends highly on the functional integration of its various departments, and in particular the cooperation between the production and the marketing departments appears to have a large impact on the well-being of a firm. The aim of this study is to model an aggregate production planning problem that considers the production and marketing functions in a simultaneous manner. The developed multi-period, multi-product model with the objective of profit maximization reflects the characteristics of both departments. Demand for each product in each period is generated through the use of demand functions. The advertising efficiency and price of the products are determined within the model. The cash outflow for advertising expenditures is approximated by a quadratic cost function, and the production cost exhibits economies of scale. Also, stockouts are taken into consideration in the form of backlogging. A solution methodology consisting of two phases is developed, and cases displaying some important characteristics are generated and solved in order to test the performance of the proposed model. This methodology incorporates linear mixed integer programming which is embedded in two different search techniques, along with a dynamic programming-based heuristic procedure.     

Inspection resource assignment in a multistage manufacturing system with an inspection error model

Producing high-quality products at low cost is always one concern for a multi-stage manufacturing system. That is, production costs and inspection efficiency should receive equal importance. Inspection planning to allocate inspection stations should then be performed to manage limited inspection resources during process planning. Product quality and the possible costs can then be concurrently considered when evaluating a manufacturing plan. Except for finite inspection station classes, the limited number of inspection stations of each inspection station class is considered to solve the inspection allocation problem in this research. Rather than utilizing a constant inspection error or a specified inspection error probability distribution determined by previous observations, the inspection allocation problem is solved using relative cost models in which the inspection error model is embedded. The inspection allocation problem can then be solved by practically reflecting the inspection error when tolerances are rapidly changed to satisfy customer requirements. Since determining the optimal inspection allocation plan seems impractical as the problem size becomes quite large, two heuristic methods have been developed by considering the defective rate, manufacturing cost and earliest stage priority in this research. The performance of each method is measured in comparison with the enumeration method that generates the optimal solution. A feasible manufacturing plan can then be determined and confirmed during process planning by concurrently solving the inspection allocation problem.     

Modelling stochastic lead times in a production-inventory system based on the Laplace transform method

Stochastic properties of a multi-period production-inventory system have been studied in several papers by applying the Laplace transform. However, the source of uncertainty has been limited to external demand and the production/replenishment lead time has been assumed to be constant. In this paper, we investigate the situation when the lead time is a random variable. Transform methods are again used to capture the stochastic properties of the system, such as stockout functions. With the objective of maximizing the net present value of the cash flow, we derive conditions for optimal production decisions in this system. The properties of cash outflow due to stockouts will also be discussed.     

Controlling work in process during semiconductor assembly and test operations

This paper introduces a mid-term planning model for scheduling assembly and test operations aimed at minimising the difference between customer demand and product completions each day. A secondary objective is to maximise daily surplus which is a surrogate for throughput. Typically, semiconductor companies have 1000s of products or devices in their catalogue that can be organised into unique groups of up to a 100 devices each. This simplifies the planning process because it is only necessary to consider the groups as a whole rather than the individual devices when constructing schedules. In all, we developed and tested three related models. Each provides daily production rates at each process step for each device group for up to one month at a time. The models are distinguished by how cycle time is treated. The first takes a steady-state approach and uses Little’s Law to formulate a WIP target constraint based on the average cycle time at each processing step. The second and third include integer and fractional cycle times in the variable definitions. To find solutions, raw production data are analysed in a preprocessing step and then converted to input files in a standard format. FlopC++ from the COIN-OR open source software project is used to write and solve the model. Testing was done using three data-sets from the Taiwan AT facility of a global semiconductor firm. By comparing model output with historical data for 6 device groups and 33 process steps, we were able to realise decreases in shortages of up to 40% per month.     

A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand

Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. As the demand and yield own different uncertain natures, they are modelled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon, which is modelled as a scenario tree. Each stage in the demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behaviour. The uncertain yield is modelled as scenarios with stationary probability distributions during the planning horizon. Yield scenarios are then integrated in each node of the demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full recourse for demand scenarios and simple recourse for yield scenarios. We conduct a case study with respect to a realistic scale sawmill. Numerical results indicate that the solution to the multi-stage stochastic model is far superior to the optimal solution to the mean-value deterministic and the two-stage stochastic models.     

Approaches for periodic inventory control under random production yield and fixed setup cost

OR Spectrum - In this paper, we study a multi-period inventory control problem with random demand and stochastically proportional production yield. The model includes nonzero processing lead time...     

Supply management in assembly systems with random yield and random demand

In this paper, we consider an assembly system where a firm faces random demand for a finished product which is assembled using two critical components. The components are procured from the suppliers who, due to production yield losses, deliver a random fraction of the order quantity. We formulate the exact cost function where the decision variables are the target level of finished products to assemble, and the order quantity of the components from the suppliers. Since the exact cost function is analytically complex to solve, we introduce a modified cost function and derive bounds on the difference in the objective function values. Using the modified cost function, we determine the combined component ordering and production (assembly) decisions for the firm. The benefit of coordinating ordering and assembly decisions is numerically demonstrated by comparing the results with two heuristic policies commonly used in practice. In an extension to the model, we consider the case when the firm has the added option of ordering both the components in a set from a joint supplier. First, we consider the case when the joint supplier is reliable in delivery and obtain dominance conditions on the suppliers to be chosen. The maximum price a firm would be willing to pay to ensure reliable supply of components is determined. Later, we consider the uncertainty in the deliveries from the joint supplier and determine conditions under which there is no diversification, that is, either the individual suppliers are used, or the joint supplier is used, but never both.     

Initial allocation compensation algorithm for redundancy allocation: The scanning heuristic

The tiny feature size in current semiconductor integrated circuits naturally requires redundancy strategies to improve manufacturing yield and operating reliability. To find an optimal redundancy architecture that provides maximum yield and reliability is a trade-off problem. In the reliability optimization field, this type of problem is generally called a redundancy allocation problem. In this paper, we propose a new iterative algorithm, the scanning heuristic, to solve the redundancy allocation problem. The solution quality of conventional iterative heuristics is highly dependent on the initial starting point of the algorithm employed. To overcome this weakness, the scanning heuristic systematically divides the original solution space into several small bounded solution spaces. The local optimum in each divided solution space then becomes a candidate for the final solution. The experimental results demonstrate that the proposed heuristic, and subsequently some combinations of heuristics, are superior to existing heuristics in terms of solution quality.     

Production policies under deteriorating process conditions

This paper examines a single-stage production system that manufactures multiple products under deteriorating equipment conditions. The machine condition worsens with production, and improves with maintenance. The condition of the process can be in any one of several discrete states, and transitions from state to state follow a semi-Markov process. In many production environments, the quality or yield of output depends heavily on the condition of the production process. The problem considers the trade-offs between manufacturing products that have a higher profit, a longer processing time, and therefore, a higher deterioration probability versus products that have a smaller profit, shorter processing time with a lower process deterioration probability. The firm needs to determine the optimal production choice in each state in a way that maximizes the long-run expected average reward per unit time.

The paper makes three sets of contributions. First, it introduces the concept of critical ratios for the firm's manufacturing decision at each state regarding whether to switch from one product to another. Second, through the use of critical ratios, the main result shows that the optimal production choice for each state can be determined independently of the actions taken in other states, despite the complex interconnections between the production decisions and state transitions. Third, the paper provides generalizations that illustrate the depth, scope and richness of the proposed solution technique by extending the model in the number of machine states, to settings where maintenance is performed in intermediate states, and to settings where transition probabilities are influenced by both mean and variance of processing times.     

Optimal initial production control period based on a quality growth model

The initial production phase of new products or the initial installation phase of new manufacturing facilities is often unstable because of inexperienced workers and many defective products. An initial production process control, in which the defects in design, production technologies and products are fully fixed and removed, is switched to a normal process control whenever it is ready for actual mass production. This paper discusses a method of deciding the optimal initial production control period, based on a quality growth model. It is determined by the number of products with the minimum expected total quality control cost. Finally a penalty cost due to unattainable loss to the quality goal is introduced in the quality control cost: the realized stabilization level of the initial production process control is lower than the original quality objective. Numerical illustrations of the optimal policy are also presented. Copyright © 1999 John Wiley & Sons, Ltd.     

云环境下大规模定制中资源配置研究

针对传统大规模定制生产模式无法满足日益个性化的产品市场变化,导致产品无法形成生产批量,在生产过程中增加成本和时间的问题,结合云制造的背景环境,提出云环境下大规模定制产品的生产模式,并通过建立包含生产总时间、生产总成本和产品总质量的多目标优化函数模型,使用NSGA-Ⅱ算法对所建模型进行求解,对模式运行中的资源配置问题进行研究。最后通过航模发动机进行算例验证,证明所建模型可以得到解决云环境下大规模定制产品生产过程中资源优化配置问题的最优生产方案。     

Managing production of high-tech products with high production quality variability

We consider production systems in technology industries where output quality of a single production run has a large variance. Firms operating such systems classify products into different quality bins and sell units in one bin at the same tagged quality level and the same price. Consumers have heterogeneous quality preferences and choose that quality that maximises their net utility. We examine firms’ assortment, production and pricing problem. We present a three-stage solution procedure that optimises the production quantity, quality specification and number of bins. In that regard, we show that for a manufacturing technology with known quality distribution and known distribution of customers’ quality preference, the optimal assortment and production quantity are set such that on average, the demand of each bin is exactly fulfilled. We examine the impact of an improved manufacturing technology, variation in consumer preferences and changing price premium on the optimal assortment, lot size, market share, yield loss and the overall profitability. We further show that when the quality distribution of the manufacturing process is unknown, downward substitution leads to product offering of higher quality and higher prices. Finally, we discuss practical considerations for pricing, technology and optimal product offerings, and explain the proliferation of bins witnessed in the last decade in the processor industry.     

Real option-based optimization for financial incentive allocation in infrastructure projects under public–private partnerships

Financial incentives that stimulate energy investments under public–private partnerships are considered scarce public resources, which require deliberate allocation to the most economically justified projects to maximize the social benefits. This study aims to solve the financial incentive allocation problem through a real option-based nonlinear integer programming approach. Real option theory is leveraged to determine the optimal timing and the corresponding option value of providing financial incentives. The ambiguity in the evolution of social benefits, the decision-maker’s attitude toward ambiguity, and the uncertainty in social benefits and incentive costs are all considered. Incentives are offered to the project portfolio that generates the maximum total option value. The project portfolio selection is formulated as a stochastic knapsack problem with random option values in the objective function and random incentive costs in the probabilistic budget constraint. The linear probabilistic budget constraint is subsequently transformed into a nonlinear deterministic one. Finally, the integer non-linear programming problem is solved, and the optimality gap is computed to assess the quality of the optimal solution. A case study is presented to illustrate how the limited financial incentives can be optimally allocated under uncertainty and ambiguity, which demonstrates the efficacy of the proposed method.     

Strongly asymptotically optimal design and control of production and service systems

In this paper we consider production and service systems that can be modeled as single or multiple stage queueing networks. We provide a formal definition of strong asymptotic optimality in the context of design and control of such queueing systems. We describe a simple approach to obtain strongly asymptotically optimal design and control policies for these systems. We illustrate our approach through some examples. In particular we obtain a strongly asymptotically optimal workload allocation for a multiple center service system modeled by the open Jackson network. The objective here is to minimize the expected total holding cost. A simple counter example shows that the much celebrated balanced workload allocation is not even asymptotically optimal for minimizing the expected number of jobs in the system. We show that an index policy is strongly asymptotically optimal for the scheduling control problem in a single stage (G/GI/1) service system. We also obtain a strongly asymptotically optimal allocation of classes of customers to a multiple center service system. This allocation agrees with the traditional wisdom of forming service stations to process similar tasks that reduce fluctuations in processing times. Suggestions for further work on this topic are summarized as well.     

Price and lead time differentiation,capacity strategy and market competition

We study a duopoly market in which customers are heterogeneous, and can be segmented as price or time sensitive. Each firm tailors (differentiates) its products/services for the two customer classes solely based on guaranteed lead time and the corresponding price. Our objective is to understand how competition affects price and lead time differentiation of the firms in the presence of different operations strategy (shared versus dedicated capacity), product substitution and asymmetry between the competing firms. Our results suggest that when firms use dedicated resources to serve the two market segments, pure price competition always tends to decrease individual prices as well as price differentiation, irrespective of the market behaviour. Further, the effect of competition is more pronounced when customers are allowed to self-select, thereby introducing substitutability between the two product options. On the other hand, when firms compete in time, in addition to price, the effect of competition on product differentiation depends crucially on the behaviour of the market. Our results further suggest that the firm with a larger market base should always maintain a larger price and lead time differentiation between the two market segments. Similarly, the firm with a capacity cost advantage should also maintain a larger lead time differentiation.     

Optimal pricing and core acquisition strategy for a hybrid manufacturing/remanufacturing system

Remanufacturing is one of the product recovery options where the quality of used products (cores) is upgraded to ‘as-good-as-new’ conditions. In this article, we consider a monopolist firm selling new and remanufactured products to quality-conscious primary customers and price-sensitive secondary customers, respectively, with one-way substitution, i.e. some primary customers may substitute new products by remanufactured products while secondary customers can never afford to buy new products. We develop economic models under two scenarios – when the supply of cores is unconstrained and when manufacturers have to procure cores at an acquisition price. The major observations of the article are as follows. A firm is better off when there is no constraint on the supply of cores. Even when cores have to be acquired at an acquisition price, the profitability is higher than that when the firm does not engage in remanufacturing activities. When a larger number of primary customers replace new products with remanufactured products, there is partial cannibalization of new product sales; however, the combined market share and profitability of the firm increase. When core supply is constrained and customers are less sensitive to core prices, the limited supply of cores may render remanufacturing an infeasible option for the firm. Therefore, firms should not only generate awareness among primary customers to buy remanufactured products, but also step up efforts to ensure a steady supply of cores. We conclude the article with managerial implications and directions for future research.