We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of produc...
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We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up to C units of any mix of the items. In addition, an upper bound on the number of batches may be imposed. Under widely applicable conditions on the storage costs, namely that the production and storage costs are nonspeculative, and for any two items the one that has a higher storage cost in one period has a higher storage cost in every period, we show that there is a tight linear program with O(mT (2)) constraints and variables that solves the joint set-up multi-item lot-sizing problem, where m is the number of items and T is the number of time periods. This establishes that under the above storage cost conditions this problem is polynomially solvable. For the problem with backlogging, a similar linear programming result is described for the uncapacitated case under very restrictive conditions on the storage and backlogging costs. Computational results are presented to test the effectiveness of using these tight linear programs in strengthening the basic mixed integer programming formulations of the joint set-up problem both when the storage cost conditions are satisfied, and also when they are violated.
The aim of this paper is to transform a multi-choice linear programming problem to a standard mathematical programming problem where the right hand side goals of some constraints are 'multi-choice' in nature. ...
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The aim of this paper is to transform a multi-choice linear programming problem to a standard mathematical programming problem where the right hand side goals of some constraints are 'multi-choice' in nature. For each of the constraint there may exist multiple number of goals, out of which exactly one is to be chosen. The selection of goals should be in such a manner that the combination of choices for each constraint should provide an optimal solution to the objective function. There may be more than one combination which will provide an optimal solution. However the problem cannot be solved by standard linear programming techniques. In order to solve the present multi-choice linear programming problem, this paper proposes a new transformation technique. Binary variables are introduced in the transformation technique to formulate a non-linear mixed integer programming model. Using standard non-linear programming software optimal solution of the proposed model can be obtained. Finally, a numerical example is presented to illustrate the transformation technique and the solution procedure. (C) 2009 Elsevier Inc. All rights reserved.
This paper presents a stochastic coordination of generation and transmission expansion planning model in a competitive electricity market. The Monte Carlo simulation method is applied to consider random outages of gen...
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This paper presents a stochastic coordination of generation and transmission expansion planning model in a competitive electricity market. The Monte Carlo simulation method is applied to consider random outages of generating units and transmission lines as well as inaccuracies in the long-term load forecasting. The scenario reduction technique is introduced for reducing the computational burden of a large number of planning scenarios. The proposed model assumes a capacity payment mechanism and a joint energy and transmission market for investors' costs recovery. The proposed approach simulates the decision making behavior of individual market participants and the ISO. It is an iterative process for simulating the interactions among GENCOs, TRANSCOs and ISO. The iterative process might be terminated by the ISO based on a pre-specified stopping criterion. The case studies illustrate the applications of proposed stochastic method in a coordinated generation and transmission planning problem when considering uncertainties.
A mixed integer programming approach is proposed for a long-term, integrated scheduling of material manufacturing, material supply and product assembly in a customer driven supply chain. The supply chain consists of t...
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A mixed integer programming approach is proposed for a long-term, integrated scheduling of material manufacturing, material supply and product assembly in a customer driven supply chain. The supply chain consists of three distinct stages: manufacturer/supplier of product-specific materials (parts), producer where finished products are assembled according to customer orders and a set of customers who generate final demand for the products. The manufacturing stage consists of identical production lines in parallel and the producer stage is a flexible assembly line. The overall problem is how to coordinate manufacturing and supply of parts and assembly of products such that the total supply chain inventory holding cost and the production line start-up and parts shipping costs are minimized. A monolithic approach, where the manufacturing, supply and assembly schedules are determined simultaneously, is compared with a hierarchical approach. Numerical examples modeled after a real-world integrated scheduling in a customer driven supply chain in the electronics industry are presented and some computational results are reported. (C) 2009 Elsevier B.V. All rights reserved.
The paper investigates the effects of emissions constraints and Emissions Trading Scheme (ETS) on the generation scheduling outcome. ETS is a cap-and-trade market mechanism that has been introduced in European Union i...
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The paper investigates the effects of emissions constraints and Emissions Trading Scheme (ETS) on the generation scheduling outcome. ETS is a cap-and-trade market mechanism that has been introduced in European Union in order to facilitate CO(2) emissions management. This scheme gives generators certain amount of CO(2) allowances which they can use to cover emissions produced during energy generation, In a current setting, most of the allowances are given for free. However, under ETS generators also have an opportunity to buy and sell CO(2) allowances on the market. Since generation power outputs are bounded by the amount of CO(2) emissions that they are allowed to produce over time, it is becoming increasingly important for generating units to manage their allocations in the most profitable way and decide when and how much of permissions to spent to produce electricity. The method proposed here allows for modeling of this new limitation by including costs of buying and selling of CO(2) allowance in the generation scheduling procedure. It also introduces additional emissions constraints in the problem formulation. Although CO(2) permissions and energy are traded in separate markets, the proposed formulation permits analysis on how emission caps and emission market prices can influence market outcome. The method is illustrated on a 5-unit system. Given examples compare (i) a base-case when all generators have made a decision to use portions of their total free allocations that do not cause any shortfall during the investigated time period;(ii) two cases when the least expensive generators' decisions on the amount of free allowances they are willing to use during the considered period are insufficient. In all cases generators also submit prices at which they expect to be able to "top-up" or sell allowances on the market, however, only in the second and third case the "buying" option becomes active and affects generation scheduling and total costs. In addition, the pape
Transfer line balancing problems (TLBP) deal with the optimization of serial machining lines. At every machine, the operations are performed by blocks. The operations within each block are executed simultaneously by t...
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Transfer line balancing problems (TLBP) deal with the optimization of serial machining lines. At every machine, the operations are performed by blocks. The operations within each block are executed simultaneously by the same multi-spindle head. In the lines considered here, the spindle heads of each machine are activated sequentially. The objective of TLBP is to group the operations into blocks and to assign the blocks to machines in order to minimize the total amount of the required equipment (spindle heads and machines). This problem is described and all the most promising exact and heuristic algorithms, recently suggested for it, are compared via detailed computational experiments. (C) 2009 Elsevier B.V. All rights reserved.
In a semiconductor fabrication line (fab), high throughput often guarantees high revenue and profit since relatively constant operating cost is required throughout the year;however, maintaining high throughput has bee...
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In a semiconductor fabrication line (fab), high throughput often guarantees high revenue and profit since relatively constant operating cost is required throughout the year;however, maintaining high throughput has been a challenging task due to complicated operational variables in a modern high-end wafer fabrication line. To deal these variables, the industry has developed a fab scheduling system consisting of several functional modules that focus on different areas of decision making. WIP balancing, which aims to prevent starvation of bottleneck toolsets, has been an important component for fab scheduling. This research proposes a new WIP balancing concept, which directly considers load levels of bottleneck toolsets for higher throughput. Also, an MIP (mixed integer programming) model is developed for the new WIP balancing. A performance test shows that the new approach increases throughput, especially when WIP level and product routing flexibility are low.
In this article, we extend the classical maximal covering model in a competitive environment by including a price decision. We formulate a revenue maximization model and propose two procedures to solve it. By a carefu...
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In this article, we extend the classical maximal covering model in a competitive environment by including a price decision. We formulate a revenue maximization model and propose two procedures to solve it. By a careful examination of the relationships between the maximal covering problems for different prices, we reveal interesting properties of the deduced revenue maximization model, leading to a full enumeration solution approach. With the help of two more properties we develop a second, more intelligent solution procedure. Computational experiments show promising results for a small, medium and large case study.
With the increasing computing power of modern processors, exact solution methods (solvers) for the optimization of scheduling problems become more and more important. Based on the mixed integer programming (MIP) formu...
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With the increasing computing power of modern processors, exact solution methods (solvers) for the optimization of scheduling problems become more and more important. Based on the mixed integer programming (MIP) formulation of a scheduling problem, it will be analyzed how powerful the present solvers of this problem class are and up to which complexity real scheduling problems are manageable. initially some common benchmark problems are investigated to find out the boundaries for For this, practical application. Then, the acquired results will be compared with the results of a conventional simulation-based optimization approach under comparable time restrictions. As a next step, the general advantages and disadvantages of both approaches were analyzed. As the result, a coupling of the discrete event simulation system and an MIP solver is presented. This coupling automatically generates an MIP-formulation for the present simulation model which can be solved externally by an MIP solver. After the external optimization process follows a backward transformation of the results into the simulation system. All features of the simulation system (like Gantt-Charts, etc.) could be used to check or to illustrate these results. To perform the coupling for a wide range of simulation models, it has to be defined which general constraints the model has to satisfy. (C) 2009 Elsevier Ltd. All rights reserved.
This study follows the concept of set cover for proposing a refueling-station-location model using a mixed integer programming method, based on vehicle-routing logics. Its solution uses only the easy-obtain data of th...
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This study follows the concept of set cover for proposing a refueling-station-location model using a mixed integer programming method, based on vehicle-routing logics. Its solution uses only the easy-obtain data of the origin-destination distance matrix. A case study that focuses on the siting of refueling stations for achieving multiple origin-destination intercity travel via electric vehicles on Taiwan demonstrates the applicability of the model. Sensitivity analysis shows that greater vehicle range will result in a lower number of refueling stations that need to be sited. Range is crucial in reducing the facility-location costs, and therefore is an important issue in the development of alternative-fuel-vehicle technology. (C) 2009 Elsevier Ltd. All rights reserved.
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