Javad Sadr

Decomposition/aggregation-based dynamic programming optimization of partially homogeneous unreliable transfer lines

The general problem of buffers sizing for mean work in process/inventory minimization in a particular class of single part unreliable manufacturing flow lines, subjected to a constant rate of demand for finished parts, is analyzed. Two variants of the problem are considered: buffers sizing for average work in process minimization when there is a fixed requirement on parts availability in the buffer next to last; minimization of an aggregate measure of average work in process and demand backlog when the complete flow line is considered. A fluid model of part production is employed. The production control policies of interest are suboptimal, strictly decentralized, and are unambiguously parameterized by the size of buffer levels. Optimization of policy parameters is based on the analysis of the structural properties of an associated dynamic program. The latter is built around an approximate, flow line decomposition based, buffer levels dependent theoretical expression of the policy performance measure. The nature of the related flow line approximations is discussed and numerical results of the dynamic programming procedure are reported. Scalability of the computations is demonstrated. The numerical results suggest that when parameters are optimal, both a form of flow line balancing and a just in time internal production principle, are in place.

Unreliable Transfer Lines: Decomposition/Aggregation and Optimization

Complexity has been a long standing obstacle to efficient buffer assignment in transfer lines. For fixed buffer sizes, an approximate transfer line decomposition/aggregation algorithm is developed and its ability to predict line performance is demonstrated via Monte-Carlo simulations. It equates the line with a collection of isolated, unreliable multi-state machines with recursively related statistical parameters. For scalability enhancement, state merging is used to reduce the number of machine states from up to 6 down to 2. An efficient dynamic programming based buffering optimization algorithm which minimizes a combined measure of storage and backlog costs in the transfer line is then presented. Numerical results and comparisons with alternative algorithms are reported.

A characterization of the maximum throughput of unreliable transfer lines

Given an unreliable transfer line with fixed size finite buffer zones for work in process, the objective is to determine the maximum, if it exists, of the production rate sustainable by the line when the first machine is never starved and the last machine is either never blocked, or if it is, an infinite backlog is allowed. A recent single machine based, transfer line under fixed demand rate decomposition method, is used to rigorously establish the existence of a maximum sustainable demand, and to characterize such a demand level via a set of necessary and sufficient conditions. The foundation of the analysis is a recursive procedure called the iterated demand algorithm (IDA). It is shown to generate a sequence that geometrically converges to a limit point, later precisely identified as the required transfer line maximum throughput. IDA becomes our computational tool. For a collection of transfer lines, numerical performance of the proposed algorithm is compared with that obtained based on other alternatives, as well as Monte Carlo based line throughput maximization results.

Unreliable transfer lines throughput maximization

Given a transfer line with individual machines reliability data, and given fixed size buffer zones for work in process across the transfer line, the objective is to determine the transfer line maximal sustainable mean production rate. We present a recursive algorithm based on a recently developed transfer line decomposition technique to evaluate a maximal sustainable throughput. The algorithm derived provably converges. Numerical results are compared with those obtained based on other competing algorithms in the literature for similar transfer lines.

Two Approximations as a Basis for the Optimization of Production in Unreliable Markovian Long Transfer Lines

Optimizing buffer sizes in manufacturing transfer lines has been a long standing problem. By providing some amount of decoupling between various production stages, parts buffering can significantly help increasing manufacturing productivity in the face of potential individual machine failures and part processing time variability. However, buffering comes at a cost, both in terms of occupied space and frozen capital within the plant. Transfer line decomposition methodologies have aimed, among other goals, at simplifying the analysis of this question. Two approximations, the machine decoupling approximation and the socalled demand averaging principle, are presented. They lead to a characterization of the transfer line, when controlled via a class of KANBAN like production policies, as a collection of isolated failure prone machines with random failures described by recursively coupled statistical parameters. Subsequently, the well developed single machine theory can be used as a building block in the analysis and optimization of the line. The approximations are tested via regenerative Monte Carlo simulation, and illustrative dynamic programming based transfer line optimization results are reported.