Optimal priority ordering in PHP production of multiple part-types in a failure-prone machine

This note deals with the problem of minimising the expected sum of quadratic holding and shortage inventory costs when a single, failure-prone machine produces multiple part-types. Shu and Perkins (2001) introduce the problem and, by restricting the set of control policies to the class of prioritised hedging point (PHP) policies, establish simple, analytical expressions for the optimal hedging points provided that the priority ordering of the part-types is given. However, the determination of an optimal priority ordering is left by the authors as an open question. This leaves an embedded sequencing problem which we focus on in this note. We define a lower bound for the problem, introduce a test bed for future developments, and propose three dynamic programming approaches (with or without the lower bound) for determining the optimal priority orderings for the instances of the test bed. This is an initial step in a research project aimed at solving the optimal priority ordering problem, which will allow evaluating the performance of future heuristic and metaheuristic proceduresPeer ReviewedPostprint (published version

Optimal priority ordering in optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

Shu and Perkins deals with the problem of minimising the expected sum of quadratic buffer cost when a single, failure-prone machine produces multiple part-types. They restrict the set of control policies to the class of prioritised hedging point (PHP) policies and determine simple, analytical expressions for the optimal hedging points, provided that the priority ordering of the part-types is given. This paper addresses the determination of the optimal priority ordering for PHP policies, and reports the results of a computational experiment. The conclusions are that instances of up to approximately twenty-five part-types can be solved to optimality in short computing times, that it is worthwhile to use dominance relations and that the influence of the values of some parameters is insignifican

Manufacturing systems with a production dependent failure rate: structure of optimality

This report provides the structure of a policy minimizing a long term, average, expected, backlog/inventory cost for a fluid model, single machine, single product manufacturing system subject to a failure/repair Markov process, where the failure rate is a piecewise constant function of the production rate. This policy generalizes previous results and confirms several conjectures reported in the literature, providing an interesting insight into the problem

Computation of production control policies by a dynamic programming technique

"September, 1982."Bibliography: leaves 16-17.National Science Foundation Grant DAR78-17826 National Science Foundation Grant ECS 79-20834by Joseph Kimemia, Stanley B. Gershwin, Dimitri Bertsekas

On Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Backlog-Dependent Demand

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, the customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's own production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system when it is managed according to this policy is evaluated. The subcontractors represent a set of capacity options, and we calculate the values of these options

A model for FMS of unreliable machines

Fulltext link (Conference paper): http://www.wseas.us/e-library/conferences/athens2000/Papers2000/170.pdfDocument Type: ArticleThis paper studies Markovian queueing model for flexible manufacturing system. The manufacturing system consists of multiple unreliable machines. Hedging point policy is applied to the system as production control. We model the machine states and inventory levels of the system as a multi-server queueing system. Fast numerical algorithm is presented to solve the steady state probability distribution of the system. Using the probability distribution, the system performance and the effect of machine reliability and maintainability can be evaluated.link_to_subscribed_fulltex

Corporate Demand for Liquidity

This paper proposes a theory of corporate liquidity demand and provides new evidence on corporate cash policies. Firms have access to valuable investment opportunities, but potentially cannot fund them with the use of external finance. Firms that are financially unconstrained can undertake all positive NPV projects regardless of their cash position, so their cash positions are irrelevant. In contrast, firms facing financial constraints have an optimal cash position determined by the value of today's investments relative to the expected value of future investments. The model predicts that constrained firms will save a positive fraction of incremental cash flows, while unconstrained firms will not. We also consider the impact of Jensen (1986) style overinvestment on the model's equilibrium, and derive conditions under which overinvestment affects corporate cash policies. We test the model's implications on a large sample of publicly-traded manufacturing firms over the 1981-2000 period, and find that firms classified as financially constrained save a positive fraction of their cash flows, while firms classified as unconstrained do not. Moreover, constrained firms save a higher fraction of cash inflows during recessions. These results are robust to the use of alternative proxies for financial constraints, and to several changes in the empirical specification. We also find weak evidence consistent with our agency-based model of corporate liquidity.

Scheduling Manufacturing Systems With Work-in-Process Inventory Control: Single-Part-Type Systems

In this paper, a real-time feedback control algorithm is developed for scheduling single-part-type production lines in which there are three important classes of activities: operations, failures, and starvation or blockage. The scheduling objectives are to keep the actual production as close to the demand as possible, and to keep the level of work-in-process inventory as low as possible. By relating the starvation and blockage to the system capacity, the buffer sizes and the target buffer levels are chosen according to the demands and machine parameters. The processing time for each operation is deterministic. Failure and repair times are random. Whenever a machine fails or is starved or blocked, the scheduling system recalculates short term production rates. To begin with, we study a very simple case, a two machine and one part type system, to get insight into the buffer effects and production control policies. Using the relationship between system capacity and starvation or blockage, we find desirable buffer levels and buffer sizes. The production control policy is determined to meet the system performance requirements concerning low WIP inventory and tardiness. The results from the simple case are extended to N-machine, one-part-type systems