Fatima Zahra Mhada

Production control of unreliable manufacturing systems producing defective items

Purpose – This paper seeks to address the production control problem of a failure‐prone manufacturing system producing a random fraction of defective items.Design/methodology/approach – A fluid model with perfectly mixed good and defective parts has been proposed. This approach combines the descriptive capacities of continuous/discrete event simulation models with analytical models, experimental design, and regression analysis. The main objective of the paper is to extend the Bielecki and Kumar theory, appearing under the title “Optimality of zero‐inventory policies for unreliable manufacturing systems”, under which the machine considered produced only good quality items, to the case where the items produced are systematically a mixture of good as well as defective items.Findings – The paper first shows that for constant demand rates and exponential failure and repair time distributions of the machine, the Bielecki‐Kumar theory, adequately revisited, provides new and coherent results. For the more complex...

Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts

An unreliable single part type transfer line with fixed inter machine buffer sizes is considered. In general, imperfect machines operating on imperfect raw material, or partially processed raw material, will result in the production of a mix of conforming and non conforming parts. The problem of optimal joint assignment of buffer sizes and inspection station positions is considered. The performance measure to be optimized is a combination of work in process storage, finished parts shortage, and parts inspection costs. A simplified quality aware machine Markovian model is proposed, and an approximate decomposition scheme for the analysis of the resulting transfer line model is developed, and then validated against detailed Monte Carlo simulations. The decomposition scheme lends to a dynamic programming based buffer size optimization scheme. The latter is implemented; joint buffer and inspections station positioning optimization results are reported.

Approximate performance analysis of CONWIP disciplines in unreliable non homogeneous transfer lines

For a given choice of the maximum allowable total storage parameter, the performance of constant work-in-process (CONWIP) disciplines in unreliable transfer lines subjected to a constant rate of demand for parts, is characterized via a tractable approximate mathematical model. For a (n−1) machines CONWIP loop, the model consists of n multi-state machine single buffer building blocks, separately solvable once a total of (n−1)2 unknown constants shared by the building blocks are initialized. The multi-state machine is common to all building blocks, and its n discrete states approximate the joint operating state of the machines within the CONWIP loop; each of the first (n−1) blocks maps into a single internal buffer dynamics, while the nth building block characterizes total work-in-process (wip) dynamics. The blocks correspond to linear n component state equations with boundary conditions. The unknown (shared) constants in the block dynamics are initialized and calculated by means of successive iterations. The performance estimates of interest—mean total wip, and probability of parts availability at the end buffer in the loop—are obtained from the model and validated against the results of Monte Carlo simulations.

A stochastic hybrid state model for optimizing hedging policies in manufacturing systems with randomly occurring defects

The paper addresses the optimal production control problems for an unreliable manufacturing system that produces items that can be regarded as conforming or nonconforming. A new stochastic hybrid state Markovian model with three discrete states, also called modes is introduced. The first two, operational sound and operational defective are not directly observable, while the third mode, failure, is observable. Production of defective parts is respectively initiated and stopped at the random entrance times to and departure times from the defective operational mode. The intricate, piecewise-deterministic dynamics of the model are studied, and the associated Kolmogorov equations are developed under the suboptimal class of hedging policies. The behavior of the model is numerically investigated, optimized under hedging policies, and subsequently compared to that of a tractable extension of the two-mode Bielecki-Kumar single machine model, where both conforming and defective parts are simultaneously produced in the operational mode, while the ratio of produced non conforming to conforming parts remains fixed.

Multilevel hybrid method for optimal buffer sizing and inspection stations positioning

Designing competitive manufacturing systems with high levels of productivity and quality at a reasonable cost is a complex task. Decision makers must face numerous decision variables which involve multiple and iterative analysis of the estimated cost, quality and productivity of each design alternative. This paper adresses this issue by providing a fast algorithm for solving the buffer sizing and inspection positioning problem of large production lines by combining heuristic and exact algorithms. We develop a multilevel hybrid search method combining a genetic algorithm and tabu search to identify promising locations for the inspection stations and an exact method that optimizes rapidly (in polynomial time) the buffers’ sizes for each location. Our method gives valuable insights into the problem, and its solution time is a small fraction of that required by the exact method on production lines with 10–30 machines.

A Hybrid Method for Solving Buffer Sizing and Inspection Stations Allocation

The buffer sizing problem in unreliable production lines is an important, indeed, complex combinatorial optimization problem with many industrial applications. These applications include quality, logistics and manufacturing production systems. In the formulation of the problem, the system consists of n machines, n fixed-size buffers and m inspection station in series. The objective is to minimize a combined storage and shortage costs, and also specifying the optimal location of inspection stations in the system. The present paper aims at optimizing a generalization of the model previously proposed in (Mhada et al., 2014) using a novel approach. In this approach, we combine Tabu Search (TS) and Genetic Algorithm (GA) to identify search regions with promising locations of inspection stations and an exact method to optimize the assignment of buffer sizes for each location. This approach provides a balance between diversification and intensification. Numerical results on test problems from previous research are reported. Using this approach, we can reduce the solution time by more than 97% in some cases.

Buffer dimensioning and control stations positioning with a space partitioning-tabu search approach

Abstract We propose an efficient heuristic method based on Space Partitioning (SP) and Tabu Search (TS) to solve the buffer sizing problem in unreliable production lines with several inspection stations. In such problem, we have an unreliable production line consisting of a certain number of machines and fixed-size buffers. These machines produce a single part with two different quality levels: conforming and non-conforming parts. The production line may contain inspection stations whose job is to reject the non-conforming parts from the line. The production line must meet a constant rate of demand for the conforming finished parts. The objective is to minimize the average long term combined storage and shortage costs, while also specifying the optimal location of inspection stations. This design problem is a difficult mixed integer nonlinear program. Solving even a small instance of 10 machines and one inspection station using a direct dynamic programming method takes hours. If we especially increase the number of machines or the inspection stations, the dynamic programming approach becomes drastically inefficient. The method we propose divides the search space into a set of disjoint subspaces using a space partitioning technique. Tabu search is used to intensify the search in the selected subspaces. This combined method finds optimal solutions for small instances in a fraction of dynamic programming time. For the largest instances (up to 20 machines) the dynamic programming approach was unable to solve, our method finds high-quality solutions in reasonable times.

Kolmogorov equations based approximate analysis and sizing of constant work in process unreliable manufacturing system loops

CONWIP or constant work in process is an important manufacturing systems production discipline whereby within a CONWIP loop, there is a cap on the maximum amount of work in process that is permitted at any time. This allows for some mobile storage within the loop, albeit a bounded amount. Enforcement of the discipline is carried out at the entrance of the loop. The presence of a loop wide constraint creates indirectly a significant degree of solidarity among the machines within the loop. This property is exploited to develop a model of storage dynamics involving a number of (virtual) macro machines having some common states and interacting through some unknown parameters which are then estimated. Numerical results are presented and an application in minimal CONWIP loop storage sizing for a given demand rate and service level requirement is reported.