Product mix optimization for a semiconductor fab

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al. 2006), this is essentially the only class of linear programs for which such an algorithm is known. In this work we provide a distributed algorithm for solving a different class of convex programs which we call “distance-bounded network design convex programs”. These can be thought of as relaxations of network design problems in which the connectivity requirement includes a distance constraint (most notably, graph spanners). Our algorithm runs in O((D/e) log n) rounds in the LOCAL model and with high probability finds a (1+e)-approximation to the optimal LP solution for any 0 < e ≤ 1, where D is the largest distance constraint. While solving linear programs in a distributed setting is interesting in its own right, this class of convex programs is particularly important because solving them is often a crucial step when designing approximation algorithms. Hence we almost immediately obtain new and improved distributed approximation algorithms for a variety of network design problems, including Basic 3- and 4-Spanner, Directed k-Spanner, Lowest Degree k-Spanner, and Shallow-Light Steiner Network Design with a spanning demand graph. Our algorithms do not require any “heavy” computation and essentially match the best-known centralized approximation algorithms, while previous approaches which do not use heavy computation give approximations which are worse than the best-known centralized bounds.

This paper establishes a framework for solving some optimization problems with linear constraints using simplex-type methods. The problems include those found in linear programs, linear fractional programs, and generalized linear fractional programs. In this study, these problems refer to a standard form of minimizing a single parameter subject to parameterized linear equations. Based on the analysis of parameterized basis-based solutions, a unified simplex-type approach is proposed. The adaptability of the parameterized model and that of the solution procedure are discussed. In particular, the proposed algorithm can prevent cycling when compared with the conventional simplex method used for solving linear programs.

A class of optimal shape design problems is studied in this paper. The boundary shape of a domain is determined such that the solution of the underlying partial differential equation matches, as well as possible, a given desired state. In the original optimal shape design problem, the variable domain is parameterized by a class of functions in such a way that the optimal design problem is changed to an optimal control problem on a fixed domain. Then, the resulting distributed control problem is embedded in a measure theoretical form, in fact, an infinite-dimensional linear programming problem. The optimal measure representing the optimal shape is approximated by a solution of a finite-dimensional linear programming problem. The method is evaluated via a numerical example.

Many planning problems involve choosing a set of optimal decisions for a system in the face of uncertainty of elements that may play a central role in the way the system is analyzed and operated. During the past decade, there has been a renewed interest in the modelling, analysis, and solution of such problems due to a remarkable development of both new theoretical results and novel computational techniques in stochastic optimization. A prominent approach is to develop upper and lower bounding approximations to the problem along with procedures to sharpen bounds until an acceptable tolerance is satisfied. The contributions of this dissertation are concerned with the latter approach. The thesis first studies the stochastic linear programming problem with randomness in both the objective coefficients and the constraints. A convex concave saddle property of the value function is utilized to derive new bounding techniques which generalize previously known results. These approximations require discretizing bounded domains of the random variables in such a way that tight upper and lower bounds result. Such techniques will prove attractive with the recent advances in large scale linear programming. The above results are also extended to obtain new upper and lower bounds when the domains of random variables are unbounded. While these bounds are tight, the approximating models are large-scale deterministic linear programs. In particular, with a proposed order-cone decomposition for the domains, these linear programs are well-structured, thus enabling one to use efficient techniques for solution, such as parallel computation. The thesis next considers convex stochastic programs. Using aggregation concepts from the deterministic literature, new bounds are developed for the problem which are computable using standard convex programming algorithms. Finally, the discussion is focused on a stochastic convex program arising in a certain resource allocation problem. Exploiting the problem structure, bounds are developed via the Karush-Kuhn-Tucker conditions. Rather than discretizing domains, these approximations advocate replacing difficult multidimensional integrals by a series of simple univariate integrals. Such practice allows one to preserve differentiability properties so that smooth convex programming methods can be applied for solution.

In this paper, we discusses the problem that involving the conflict fuzzy multi-objective in transportation planning which is one of special case in multi-objective linear programming. To find the simultaneously optimal solution of the problem, we use the Interactive Fuzzy Multi-Objective Linear Programming (IFMOLP) method. This method can reduce the fuzzy multi-objective linear programming problem into deterministic single objective linear programming which can be solved using simplex method. Beside that , with IFMOLP method, decision maker (DM) can establish interactively the goal from the objective function to produce the pareto optimal solution so that.

The fuzzy set theory is being applied massively in many fields these days. One of these is linear programming problems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzy linear programming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheirfam and Hasani. In this paper, those cases are considered and numerical examples are solved.

New South Wales Government's 1995 water reform proposals included several environmental flow policies aimed at improving water quality and the river ecosystems. In evaluating these policies a number of different river flow objectives were considered some of which resulted in a reduction in the water availability for irrigated agriculture. This paper discusses the methodology and modelling framework adopted to analyze the economic impacts of environmental flow policies on the Macquarie regional economy of NSW. An economic model (Catchment Economic Impact Model) was developed to estimate these impacts. This model combines hydrology, simulation, spreadsheet and linear programming applications. The objective function of the linear programming model is to maximize the total gross margins for the region. Constraints include prices, costs, land, labour, and water availability. The model provides economic impacts in the format of descriptive statistics of total gross margin, total irrigated regional gross margin, present value of total regional gross margin over a 30 year period and changes in crop areas under different environmental flow objectives. Four different river flow objectives represented by six hydrology scenarios were considered in this analysis. The results of the preliminary analysis of these objectives are also discussed in this paper.

This paper presents a linear programming (LP) model for simultaneously solving an operator staffing problem in a semiconductor fab. The problem is to determine the staffing level and assign operators to the staffing positions. The semiconductor fab has the following characteristics: it imposes a no-lay-off policy, but allows overtime; keeps high-quality shop floor operations; aims to control tightly the staffing costs; and faces frequent changes of product mix. The operator staffing problem in such a fab was not addressed in previous literature. The proposed LP model aims to minimize the operator staffing cost. The LP solutions have been examined and were found to be insensitive to stochastic demands modeled by various simulation replicates.

A system with several actors will increase the possibilities for collaboration and therefore, in many cases also increase the possibilities to affect the operation with economic and environmental benefits. In this paper a district heating system is studied with purpose to create economic and environmental operation guidelines in favour of the involved actors. The company LuleKraft owns a combined heat and power plant, while the four heating stations together with the DH network are owned by Luleå Energi. District heat is produced from the CHP plant and the four heating stations which are fired with process gases from an integrated steel plant, oil, wood pellets or electricity. The heat demand in the system is strongly depending on the outdoor temperature. In this paper, the system is modelled with Mixed Integer Non Linear Programming in order to optimise the profit and CO2 emission. A comparison between actual process data and modelled results is performed. A pareto front is derived to show the trade-off between economic benefits and CO2 emissions. It is found that the main suggestions, under conditions for optimised profit, are (1) to prioritize effective heat production instead of electricity production at cold outdoor temperatures and (2) redistribution of the accessible process gases between the CHP plant and one of the heating stations. This will lead to an improved operation strategy, resulting in increased profit and reduced energy consumption.

In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest enclosing ball and polytope distance, and set problems like hitting set and set cover. In the gossip model, a node can only push information to or pull information from nodes chosen uniformly at random. Protocols for the gossip model are usually very practical due to their fast convergence, their simplicity, and their stability under stress and disruptions. Our algorithms are very efficient (logarithmic rounds or better with just polylogarithmic communication work per node per round) whenever the combinatorial dimension of the given LP-type problem is constant, even if the size of the given LP-type problem is polynomially large in the number of nodes.

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

Over the past decade, organic farming has gained popularity among both consumers and producers. As producers consider the decision to shift from conventional to organic production, the farm management question asks under what price ratios can farmers be enticed to endure transition periods. Current rules require at least three years of organic production before the crop can be marketed as ‘organic’. Using a whole-farm linear programming (LP) model, these ‘non-productive’ transition years were modeled to examine the conditions that entice farmers to convert from conventionally grown corn. Results assist producers in making long term decisions with the objective to maximize returns to their operations. The LP base farm was parameterized using a central Illinois farm including local information on 1) production practices for a corn and soybean rotation, 2) yield penalties for plant and harvest date combinations, and 3) fieldwork probabilities. Preliminary results indicate that given expected price ratios of conventional commodities relative to a $11/bu organic corn price, producers would be willing to begin organic production.

We present an O â nL -iteration homogeneous and self-dual linear programming LP algorithm. The algorithm possesses the following features: â ¢ It solves the linear programming problem without any r...

Vendor Selection (VS) problem is considered as a critical decision that effects on the financial position for any firms. Hence the purchasing managers consider the selection process of the right vendors is a major function of the outsourcing process. Cost, quality, and services are three common criteria for VS problem. In the real cases the parameters of any problems are usually vague or not completely known, so that the Fuzzy Set Theory (FST) is one of the most powerful existing tools capable of addressing ambiguity and blurring information in parameters. A fuzzy parameters for VS problem are dealt with Linear Membership Function (LMF) through using cut that convert a fuzzy numbers to Interval Multiple Objective Linear Programming (IMOLP). The formulation of IMOLP is determined based on the value of , then IMOLP model is divided to upper and lower sub-models. A compromise interval solution will obtain from solving the sub-models as conventionally linear programming. The proposed approach is clarified with an illustrative example.

In this paper by using the lexicography method, we proposed a new model to solve fully fuzzy linear programming problem with L-R fuzzy number and find the fuzzy optimal solution of it. Our method has graceful structure and is easy to implement compared with some existing methods. To illustrate our method, a numerical example is solved.