Gad Rabinowitz

A two-item newsboy problem with substitutability

Previous research on the newsboy problem is based on the assumption that in case of a shortage, unsatisfied demand is lost. Such an assumption is inappropriate for items that have a close substitute. In this paper, we formulate a two-item newsboy problem with substitutability (TINPS). Upper and lower bounds on the optimal order quantities of the two items are derived. Since analytical solutions to the problem are difficult to obtain, a Monte Carlo simulation is used to identify the optimal solution to the TINPS. Order quantities identified by the simulation provide higher expected profit than would have been obtainable without considering substitutability.

Inspection allocation for multistage deteriorating production systems

The paper deals with the layout and operation of an inspection system used for detecting malfunctioning processors in a multistage production system. This problem involves three inter-related decisions: (i) the overall inspection capacity; (ii) the assignment of inspection tasks to inspectors; and (iii) the scheduling of the inspectors tasks. These decisions require a trade-off between the cost of inspectors and the loss associated with non-conforming products. A hierarchical heuristic solution procedure is proposed to support these three related decisions. Numerical experiments demonstrate the performance of the heuristic, showing that solution criteria are very close to their lower bounds. Although we use production terminology, the results might be applicable to any organization, which inspects and maintains a variety of characteristics of its branches or activities.

Cycle-Time Key Factor Identification and Prediction in Semiconductor Manufacturing Using Machine Learning and Data Mining

Within the complex and competitive semiconductor manufacturing industry, lot cycle time (CT) remains one of the key performance indicators. Its reduction is of strategic importance as it contributes to cost decreasing, time-to-market shortening, faster fault detection, achieving throughput targets, and improving production-resource scheduling. To reduce CT, we suggest and investigate a data-driven approach that identifies key factors and predicts their impact on CT. In our novel approach, we first identify the most influential factors using conditional mutual information maximization, and then apply the selective naive Bayesian classifier (SNBC) for further selection of a minimal, most discriminative key-factor set for CT prediction. Applied to a data set representing a simulated fab, our SNBC-based approach improves the accuracy of CT prediction in nearly 40% while narrowing the list of factors from 182 to 20. It shows comparable accuracy to those of other machine learning and statistical models, such as a decision tree, a neural network, and multinomial logistic regression. Compared to them, our approach also demonstrates simplicity and interpretability, as well as speedy and efficient model training. This approach could be implemented relatively easily in the fab promoting new insights to the process of wafer fabrication.

Optimal and heuristic inspection schedules for multistage production systems

Consider a single inspection facility that can be quickly switched among multiple inspection tasks. It can be used (for example) for detecting malfunction (or down state) production stages in a multistage production system. We assume that a properly working (or up state) production stage moves to a down state in any period with fixed probability. The stage then stays down until it is inspected and immediately restored back to an up state. Our purpose is to schedule inspections among the different production stages so as to maximize the fraction of good items produced. An optimal inspection schedule for a two stage production system is provided. For the general case of more than two stages, four heuristics are compared. We conclude that the proposed dynamic schedule is easy to derive, always feasible, and outperforms the static schedules.

Optimal robot operation and selection using quality and output trade-off

This paper presents a two-stage model for industrial robot operation and selection in a multi-product manufacturing system. The quality of the production process is related to robot repeatability and the output rate is related to robot speed. Robot repeatability deteriorates with increased speed. In the second stage, a one-period robot operational model maximises the expected profit of a risk-neutral decision maker, leading to optimal robot speed and production quantity decisions. Using the optimal speeds and quantities of the operational model and taking into account demand uncertainties, the first stage robot selection model is solved.

In-line Inspection Impact on Cycle Time and Yield

The semiconductor industry constantly drives for high yield and low cycle time (CT), while most current manufacturing practices consider them separately. This research investigates and exhibits the relationship between CT and yield as affected by in-line metrology inspections of production lots. Among the various factors that impact the tradeoff between CT and yield, we focus on single operation monitors and investigate their measure rate and scheduling. The research assumes a simplified production cell consisting of three operation steps that represent a typical segment in a production line. We compose and apply dynamic policies for metrology inspections via simulation and analytical methods. The aim is to concurrently reduce the CT accumulated and increase the yield achieved due to inspections. Ten inspection policies are compared under nine different operation scenarios. The results of most of the policies present a concave curve of yield versus CT. The curve illustrates that growing inspection rate increases both yield and CT until the yield reaches a maximum and then starts to decline. The cause for the yield decline is longer delay in corrective feedback to an out-of-control production tool due to longer waiting time for inspection. A cost-benefit CT-yield objective function is defined and demonstrates that the newly composed dynamic inspection policies are superior to the commonly used fixed measure rate policy. Future research could relax part of the simplified production cell assumptions in order to consider more realistic model structure and scenarios.

Resource sharing and scheduling for cyclic production in a computer-integrated manufacturing cell

Abstract This paper deals with the decision making for resource sharing and scheduling for a class of computer-integrated manufacturing cells. Each such cell is characterized by a set of resources and it can be used for the cyclic production of several products. The production (processing) of each product requires a set of operations with sequence constraints among them. Each operation can be performed using alternative modes. Each mode defines the subset of resources needed for the operation and the timing of their use. Resource setup times are sequence-dependent. The problem is to choose the best mode for each operation and, accordingly, to allocate and schedule resources in order to minimize make-span time. A general (feasible) mixed 0–1 LP model is proposed. A customized Branch and Bound type solution algorithm is presented, which fathoms only feasible solutions and finds all optimum solutions.

A scheduling model for multirobot assembly cells

We propose a mixed 0–1 linear programming model for repetitive scheduling of multirobot assembly and machining cells. The approach adopted is monolithic as opposed to hierarchical to avoid system suboptimization. The model permits any number of alternative ways (or modes) to perform each operation. A mode of an operation is determined by the required resources (facilities) and the duration of their use. The model incorporates facility changeover times. Robot collisions are avoided. Several objective functions are formulated to support different purposes. The scheduling problem of a multirobot assembly cell is formulated and solved by using commercially available mathematical programming software. Solutions under four different objective functions are reported.Acknowledging the complexity and considerable size of the formulation required, we prescribe and illustrate specific methods to achieve size reduction. Finally, for successful use of our model, an information processing schema is offered as a general guidance to help data management needed by the model.

An experimental analysis of solution performance in a resource sharing and scheduling problem

In this paper we study the performance of a branch and bound enumeration procedure in solving a comprehensive mixed-integer linear programming formulation of a resource-sharing and scheduling problem (RSSP). The formulation is monolithic and deterministic. Various independent factors of an RSSP generally influence the size of the problem. An experimental analysis is performed to examine how such factors influence performance. We found that the number of resources, the total number of modes allowed in the problem, and the average number of renewable resources used in the problem have significant influence on the computational time as well as other performance measures. In addition, some intermediate response variables are identified and additional insights regarding the influences of the independent factors on these variables are provided.

The relationship between yield and flow time in a production system under inspection

This work studies the relationship between Yield and Flow Time (FT) in a production system monitored by in-line inspection. It originates in the known semiconductors Yield vs. FT trade-off premise, but can be adapted to other industries. We challenge the common premise, and suggest an alternate analytical model to demonstrate this relationship. The model relies on a simplified production system that represents a repetitive segment in a production line. It illustrates that rising inspection rate increases both Yield and FT while exhibiting a trade-off. However with further growing inspection rate the Yield reaches a maximum and then starts to decline, while FT continues to increase. The Yield decline is explained by longer delay of inspection results which trigger the repair of an out-of-control machine. Clearly, lower Yield performance and higher FT are undesired. Our work defines this relationship with the analytical model and validates it with simulation. The model can be embedded in a decision support tool to pre-determine the inspection policy, while simultaneously considering Yield and FT.