A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

Fuzzy inference to assess manufacturing process capability with imprecise data

Process capability indices provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The loss-based process capability index C_pm, sometimes called the Taguchi index, was proposed to measure process capability, wherein the output process measurements are precise. In the present study, we develop a realistic approach that allows the consideration of imprecise output data resulting from the measurements of the products quality. A general method combining the vector of fuzzy numbers to produce the membership function of fuzzy estimator of Taguchi index is introduced for further testing process capability. With the sampling distribution for the precise estimation of C_pm, two useful fuzzy inference criteria, the critical value and the fuzzy P-value, are proposed to assess the manufacturing process capability based on C_pm. The presented methodology takes into the consideration of a certain degree of imprecision on the sample data and leads to the three-decision rule with the four quadrants decision-making plot. The fuzzy inference procedure presented to assess process capability is a natural generalization of the traditional test, when the data are precise the proposed test is reduced to a classical test with a binary decision.     

Optimal average sample number of the SPRT chart for monitoring fraction nonconforming

The Sequential Probability Ratio Test (SPRT) control chart is a powerful tool for monitoring manufacturing processes. It is highly suitable for the applications where testing is destructive or very expensive, such as the automobile airbags test. This article studies the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart’s performance. A design algorithm is proposed to develop the optimal SPRT chart for monitoring the fraction nonconforming p of Bernoulli processes. By optimizing the ASN and other charting parameters, the average detection speed of the SPRT chart is almost doubled. It is also found that the optimal SPRT chart significantly outperforms the optimal np and binomial CUSUM charts, in terms of Average Number of Defectives (AND), under different combinations of the design specifications. It is observed that the SPRT chart using a relatively smaller ASN and a shorter sampling interval (h) has a higher overall detection effectiveness.     

Managing production with flexible capacity deployment for serial multi-stage manufacturing systems

This paper presents a model for serial multi-stage manufacturing systems facing variability from two sources. One source is demand uncertainty; the other is manufacturing uncertainty associated with all manufacturing stages. A production control policy based on the planned lead time and the manufacturing capacity requirement is developed. It is shown that this production control policy has the effect of reducing the variance of production output for all manufacturing stages. Some specific analyses are provided to illustrate the production control policy developed. The model developed provides a vehicle for examining the interrelationships among the production output, the planned lead time and the actual manufacturing flow time. The risk-pooling value over both demand randomness and manufacturing uncertainty, which is achieved through consolidating some manufacturing capacity and deploying flexible capacity among the manufacturing stages, is analyzed. This risk-pooling value can be realized in the form of either reduced manufacturing flow time or increased effective capacity to meet more demand. It is shown that the risk-pooling value increases as the planned lead time decreases.     

Simple heuristics for push and pull remanufacturing policies

Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s, Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters.     

On transmission time through k minimal paths of a capacitated-flow network

The quickest path problem is to minimize the transmission time for sending a specified amount of data through a single minimal path. Two deterministic attributes are involved herein; the capacity and the lead time. However, in many real-life networks such as computer systems, urban traffic systems, etc., the arc capacity should be multistate due to failure, maintenance, etc. Such a network is named a capacitated-flow network. The minimum transmission time is thus not a fixed number. This paper is mainly to evaluate system reliability that d units of data can be transmitted through k minimal paths under time constraint T. A simple algorithm is proposed to generate all minimal capacity vectors meeting the demand and time constraints. The system reliability is subsequently computed in terms of such vectors. The optimal k minimal paths with highest system reliability can further be derived.     

Sensitivity analysis of machine repair problems in manufacturing systems with service interruptions

This paper models a manufacturing system consisting of M operating machines and S spare machines under the supervision of a group of technicians in a repair facility. Machines fail according to a Poisson process, and the repair (service) process of a failed machine may require more than one phase. In each phase, service times are assumed to be exponentially distributed but may be interrupted when the repair facility encounters unpredictable breakdowns. Two models of manufacturing systems are considered. In the first model, technicians repair failed machines at different rates in each phase. In the second model, a two-phase service system with differing numbers of technicians is considered. Profit functions are developed for both models and optimized by a suitable allocation of the number of machines, spares, and technicians in the system. Finally, a sensitivity analysis (see Cao [X.R. Cao, Realization Probabilities: The Dynamics of Queuing Systems, Springer-Verlag: London, 1994; X.R. Cao, The relations among potentials, perturbation analysis, and Markov decision processes, Discrete Event Dynam. Syst.: Theory Applicat. 8 (1998) 71–87]) is performed to provide an approach that quantifies the impact of changes in the parameters on the profit models.     

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L^?-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.     

Evaluating focused factory benefits with queuing theory

In this paper, we study the benefits of a focused factory using lead-time as a performance measure. Specifically, we model a production process, using multi-class (multiple product types), general interarrival and processing time distributions with multiple machines (GI/G/c) queuing models for deriving each product’s mean lead-time. We also perform simulations for estimating the standard deviation of lead times. There are two product types: a standard and a customized product. The customized product has a more variable demand pattern than the standard product, and also requires additional processing time (setup and run time) in its production process. We assume that management is willing to sacrifice the lead-time performance of the customized product in favor of improved performance for the standard product. The paper shows that focusing the factory is more attractive for plants operating at higher utilization, and manufacturing products that have higher processing time and demand variability differentials between product types.     

Considering manufacturing cost and scheduling performance on a CNC turning machine

A well known industry application that allows controllable processing times is the manufacturing operations on CNC machines. For each turning operation as an example, there is a nonlinear relationship between the manufacturing cost and its required processing time on a CNC turning machine. If we consider total manufacturing cost (F₁) and total weighted completion time (F₂) objectives simultaneously on a single CNC machine, making appropriate processing time decisions is as critical as making job sequencing decisions. We first give an effective model for the problem of minimizing F₁ subject to a given F₂ level. We deduce some optimality properties for this problem. Based on these properties, we propose a heuristic algorithm to generate an approximate set of efficient solutions. Our computational results indicate that the proposed algorithm performs better than the GAMS/MINOS commercial solver both in terms of solution quality and computational requirements such that the average CPU time is only 8% of the time required by the GAMS/MINOS.     

Lead time and response time in a pull production control system

In the late 80s, most manufacturers have shifted their manufacturing strategies from cost and quality to speed. This paper focuses on two performance measures of speed: manufacturing lead time and response time. Manufacturing lead time is the sum of the processing time to convert raw material to finished goods and the waiting time at the buffers. Response time is the time between the customer places an order and the customer receives the order. In this paper we develop a queueing model of a pull-based production control system for a single-stage facility. The intent of the model is two-fold. First, we highlight the trade-off between manufacturing lead time and response time. Second, we develop an optimization model to determine an optimal control system that guarantees certain delivery performance (in terms of response time).     

On p-norm linear discrimination

We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p is rational. Since such reformulations typically lead to SOCP problems with large numbers of second order cones, an “economical” representation that minimizes the number of second order cones is proposed. A case study illustrating the developed model on several popular data sets is conducted.     

Manufacturing technology policy and deployment of processing innovations

This is a report of a study on the evolution of manufacturing technology policy during the deployment of domestic advanced manufacturing systems in thirty-four plants and two panels of data collection separated by one year. Changing firm environment was significantly correlated with pioneering product introduction business strategy (p<0.05). More importantly, it was found that manufacturing technology policy is significantly (p<0.05) associated with pioneering business strategy. Further, findings indicate that fine-tuning or modest adjustment in this policy (versus doing nothing or drastic change) was significantly (p<0.05) associated with the maximum levels of reported utilization of these new systems in a subsample of second panel, complete data cases (n=21). This curvilinear relationship between the absolute value of changes in technology policy and performance measure did not hold for the percentage of target cycle time achieved nor uptime, although results concerning performance are considered preliminary at the time of this writing. Advertising this processing technology tends to be inversely related to the radicalness of the technology incorporated into the system (p=0.076) during the deployment period tracked thus far. That is, firms installing more radical systems tend to become very cautious about sharing information about the project once installation begins.     

Decision-making in testing process performance with fuzzy data

Over the years, numerous process capability indices (PCIs) have been proposed to the manufacturing industry to provide numerical measures of process performance. Most research efforts have focused on developing and investigating PCIs that assess process capability by precise measurements of output quality. However, real observations of continuous quantities are not precise numbers; in practice, they are more or less imprecise. Since observations of continuous random variables are imprecise the values of related test statistics become imprecise. Therefore, decision rules for statistical tests have to be adapted to this situation. This article presents a set of confidence intervals that produces triangular fuzzy numbers for the estimation of C_pk index using Buckley’s approach with some modification. Additionally, a three-decision testing rule and step-by-step procedure are developed to assess process performance based on fuzzy critical values and fuzzy p-values. This concept is also illustrated with an example for testing process performance.     

Local ratio with negative weights

We present local ratio interpretations of known algorithms for minimums-tcut and the assignment problem. Our interpretations are the first application of local ratio with negative weights. These interpretations lead to primal-dual analyses that are based on new IP formulations.     

A new approach to assess product lifetime performance for small data sets

Because of cost and time limit factors, the number of samples is usually small in the early stages of manufacturing systems, and the scarcity of actual data will cause problems in decision-making. In order to solve this problem, this paper constructs a counter-intuitive hypothesis testing method by choosing the maximal p-value based on a two-parameter Weibull distribution to enhance the estimate of a nonlinear and asymmetrical shape of product lifetime distribution. Further, we systematically generate virtual data to extend the small data set to improve learning robustness of product lifetime performance. This study provides simulated data sets and two practical examples to demonstrate that the proposed method is a more appropriate technique to increase estimation accuracy of product lifetime for normal or non-normal data with small sample sizes.     

Inventory strategies for systems with fast remanufacturing

We describe hybrid manufacturing/remanufacturing systems with a long lead time for manufacturing and a short lead time for remanufacturing. We review the classes of inventory strategies for hybrid systems in the literature. These are all based on equal lead times. For systems with slow manufacturing and fast remanufacturing, we propose a new class. An extensive numerical experiment shows that the optimal strategy in the new class almost always performs better and often much better than the optimal strategies in all other classes.     

Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customer due dates

We consider a two-stage make-to-order manufacturing system with random demands, processing times, and distributed customer due dates. The work to each stage is released based on a planned lead time. A general approach to minimize total inventory holding and customer order tardiness cost is presented to find the optimal manufacturing capacities and planned lead times for each manufacturing stage. Expressions are derived for work-in process inventories, finished-goods-inventory and expected backorders under the assumption of a series of M/M/1 queuing systems and exponentially distributed customer required lead times. We prove that the distribution of customer required lead time has no influence on the optimal planned lead times whenever capacity is predefined but it influences the optimal capacity to invest into. For the simultaneous optimization of capacity and planned lead times we present a numerical study that shows that only marginal cost decreases can be gained by setting a planned lead time for the upstream stage and that a considerable cost penalty is incurred if capacity and planned lead time optimization are performed sequentially.     

On the behavior of some two-variable p-adic L-functions

We give some p-adic integral representations for the two-variable p-adic L-functions introduced recently by G. Fox. For powers of the Teichmüller character, we use the integral representation to extend the L-function to a larger domain, in which it is a meromorphic function in the first variable and an analytic element in the second. These integral representations imply systems of congruences for the generalized Bernoulli polynomials, improving previous results of Fox, Gunaratne, and the author; they also lead to generalizations of some formulas of Diamond and of Ferrero and Greenberg for p-adic L-functions in terms of the p-adic gamma and log gamma functions.     

Quantile regression metamodeling: Toward improved responsiveness in the high-tech electronics manufacturing industry

Both technology and market demands within the high-tech electronics manufacturing industry change rapidly. Accurate and efficient estimation of cycle-time (CT) distribution remains a critical driver of on-time delivery and associated customer satisfaction metrics in these complex manufacturing systems. Simulation models are often used to emulate these systems in order to estimate parameters of the CT distribution. However, execution time of such simulation models can be excessively long limiting the number of simulation runs that can be executed for quantifying the impact of potential future operational changes. One solution is the use of simulation metamodeling which is to build a closed-form mathematical expression to approximate the input–output relationship implied by the simulation model based on simulation experiments run at selected design points in advance. Metamodels can be easily evaluated in a spreadsheet environment “on demand” to answer what-if questions without needing to run lengthy simulations. The majority of previous simulation metamodeling approaches have focused on estimating mean CT as a function of a single input variable (i.e., throughput). In this paper, we demonstrate the feasibility of a quantile regression based metamodeling approach. This method allows estimation of CT quantiles as a function of multiple input variables (e.g., throughput, product mix, and various distributional parameters of time-between-failures, repair time, setup time, loading and unloading times). Empirical results are provided to demonstrate the efficacy of the approach in a realistic simulation model representative of a semiconductor manufacturing system.