This paper develops a mixed-integer programming model to design the cellular manufacturing systems (CMSs) under dynamic environment. In dynamic environment, the product mix and part demand change under a multi-period ...
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This paper develops a mixed-integer programming model to design the cellular manufacturing systems (CMSs) under dynamic environment. In dynamic environment, the product mix and part demand change under a multi-period planning horizon. Thus, the best designed cells for one period may not be efficient for subsequent periods and reconfiguration of cells is required. Reconfiguration may involve adding, removing or relocating machines;it may also involve a change in processing rout of part types from a period to another. The advantages of the proposed model are as follows: considering the batch inter/intra-cell material handling by assuming the sequence of operations, considering alternative process plans for part types, and considering machine replication. The main constraints are maximal cell size and machine time-capacity. The objective is to minimize the sum of the machine constant and variable costs, inter- and intra-cell material handling, and reconfiguration costs. An efficient hybrid meta-heuristic based on mean field annealing (MFA) and simulated annealing (SA) so-called MFA-SA is used to solve the proposed model. In this case, MFA technique is applied to generate a good initial solution for SA. The obtained results show that the quality of the solutions obtained by MFA-SA is better than classical SA, especially for large-sized problems. (C) 2007 Elsevier B.V. All rights reserved.
A leading manufacturer of forest products with several production facilities located in geographical proximity to each other has recently acquired a number of new production plants in other regions/countries to increa...
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A leading manufacturer of forest products with several production facilities located in geographical proximity to each other has recently acquired a number of new production plants in other regions/countries to increase its production capacity and expand its national and international markets. With the addition of this new capacity, the company wanted to know how to best allocate customer orders to its various mills to minimize the total cost of production and transportation. We developed mixed-integer programming models to jointly optimize production allocation and transportation of customer orders on a weekly basis. The models were run with real order files and the test results indicated the potential for significant cost savings over the company's current practices. The company further customized the models, integrated them into their IT system and implemented them successfully. Besides the actual cost savings for the company, the whole process from the initial step of analyzing the problem, to developing, testing, customizing, integrating and finally implementing the models provided enhanced intelligence to sales staff. (C) 2008 Elsevier Ltd. All rights reserved.
When products are sold by multiple vendors in various locations, the purchaser must decide what to order from each vendor and where to send it. To solve this decision problem, a novel optimization model is developed a...
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When products are sold by multiple vendors in various locations, the purchaser must decide what to order from each vendor and where to send it. To solve this decision problem, a novel optimization model is developed and applied to a situation involving the nationwide wholesale distribution of grocery products. Comparing the model's solution with the actual record of shipments reveals instances in which the model selected higher-priced vendors in order to capitalize on truckload cost savings, which are seen to be an important factor in vendor selection. Additional models are developed to reduce computation time and assign shipments to vehicles. (c) 2007 Elsevier Ltd. All rights reserved.
An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried Out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MI...
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An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried Out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to Supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case Studies to illustrate the proposed solution Strategy. (C) 2007 Elsevier B.V All rights reserved.
In 1990, Cook, Kannan and Schrijver [W. Cook, R. Kannan, A. Schrijver, Chvatal closures for mixedintegerprogramming problems. Mathematical programming 47 (1990) 155-174] proved that the split closure (the 1st 1-bran...
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In 1990, Cook, Kannan and Schrijver [W. Cook, R. Kannan, A. Schrijver, Chvatal closures for mixedintegerprogramming problems. Mathematical programming 47 (1990) 155-174] proved that the split closure (the 1st 1-branch Split Closure) of a polyhedron is again a polyhedron. They also gave an example of a mixed-integer polytope in R2+1 whose 1-branch split rank is infinite. We generalize this example to a family of high-dimensional polytopes and present a closed-form description of the kth 1-branch split closure of these polytopes for any k >= 1. Despite the fact that the m-branch split rank of the (m + 1)-dimensional polytope in this family is 1, we show that the 2-branch split rank of the (m+1)-dimensional polytope is infinite when m >= 3. We conjecture that the t-branch split rank of the (m + 1)-dimensional polytope of the family is infinite for any 1 <= t <= m-1 and (c) 2008 Elsevier B.V. All rights reserved.
The scheduling of multi-product, multi-stage batch processes is industrially important because it allows us to utilize resources that are shared among competing products in an optimal manner. Previously proposed metho...
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The scheduling of multi-product, multi-stage batch processes is industrially important because it allows us to utilize resources that are shared among competing products in an optimal manner. Previously proposed methods consider problems where the number and size of batches is known a priori. In many instances, however, the selection and sizing (batching) of batches is or should be an optimization decision. To address this class of problems we develop a novel mixed-integer linear programming (MILP) formulation that involves three levels of discrete decisions: selection of batches, assignment of batches to units and sequencing of batches in each unit. Continuous decision variables include sizing and timing of batches. We consider various objective functions: minimization of makespan, earliness, lateness and production cost, as well as maximization of profit, an objective not addressed by previous multi-stage scheduling methods. To enhance the solution of the proposed MILP model we propose symmetry breaking constraints, develop a preprocessing algorithm for the generation of constraints that reduce the number of feasible solutions, and fix sequencing variables based upon time window information. The model enables the optimization of batch selection, assignment and sequencing decisions simultaneously and is shown to yield solutions that are better than those obtained by existing sequential optimization methods. (C) 2007 Elsevier Ltd. All rights reserved.
The continuous mixing set is S = R {(s, r, z) is an element of R x R-+(n) x Z(n) : s + r(j) + w(j)z(j) >= f(j), j = 1,..., n}, where w(1),..., m(n) > 0 and f(1),....f(n) is an element of R. Let m = vertical bar{...
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The continuous mixing set is S = R {(s, r, z) is an element of R x R-+(n) x Z(n) : s + r(j) + w(j)z(j) >= f(j), j = 1,..., n}, where w(1),..., m(n) > 0 and f(1),....f(n) is an element of R. Let m = vertical bar{w(1),....w(n)}vertical bar. We show that when w(1) vertical bar...broken vertical bar w(n,) optimization over Scan be performed in time O(n(m+1)), and in time O(n log n) when w(1) =... = w(n) = 1. (C) 2008 Elsevier B.V. All rights reserved.
Golf teams at most public universities derive much of their support for player scholarships from external donors. Relationships with current and potential donors are often created and maintained via annual golf tourna...
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Golf teams at most public universities derive much of their support for player scholarships from external donors. Relationships with current and potential donors are often created and maintained via annual golf tournaments that pair donors with varsity players and team coaches in a scramble format tournament. This paper introduces a new spreadsheet-based DSS tool for optimizing the formation of teams for multi-round, unique-team, golf scramble tournaments. The DSS uses mixed-integer programming to create unique teams for each round of play while considering the handicaps of all teams and individual players to ensure a reasonable level of fairness in the tournament. (C) 2008 Elsevier B.V. All rights reserved.
The importance of ensuring short set-up times in manufacturing has been well-documented in the literature over the past years. However, this body of work largely addresses situations involving a single machine with no...
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The importance of ensuring short set-up times in manufacturing has been well-documented in the literature over the past years. However, this body of work largely addresses situations involving a single machine with no specific worker-related issues. In practice, there exist multiple machines or workstations that form a machine line, and that need set-up operations to be performed by multiple workers. The existing literature does not provide adequate methodologies for set-up reduction in such cases. This paper describes a quantitative modeling and algorithmic approach for scheduling activities or tasks in order to minimize the set-up time in such situations, also taking into account relevant secondary objectives such as balancing the workload amongst the workers, concentrating slack toward the end of the set-up process, and minimizing the movement costs of the workers performing the different set-up tasks. Three real-life examples are used to demonstrate the efficacy of the proposed approach. (C) 2006 Elsevier B.V. All rights reserved.
This paper describes the development and experimental validation of a multi-layer hybrid controller for optimizing energy management in a solar air conditioning plant. The hybrid nature of the process is clue to its m...
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This paper describes the development and experimental validation of a multi-layer hybrid controller for optimizing energy management in a solar air conditioning plant. The hybrid nature of the process is clue to its multi-mode structure: the refrigeration circuit can be fed by flat solar collectors, a storage system, by an auxiliary gas heater, or by a combination of them. The selection of the operating mode is obtained by switching electrovalves, pumps, and three-way mixing valves. The proposed multi-layer hybrid controller consists of a high-level supervisor that decides on-line the optimal operating mode through a hybrid model predictive control strategy, a static lower-level controller defining proper set-points for the chosen mode, and existing standard low-level controllers that ensure robust tracking of such set-points. The overall controller was designed in Matlab/Simulink using the Hybrid Toolbox, and then tested experimentally a real process, showing the effectiveness of the approach.
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