Based on several existing literatures that use mixed integer programming (MIP) to solve parallel machine scheduling problems, this study tests and compares three MIP models. Each order has its own ready date, due date...
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ISBN:
(纸本)9781509036653
Based on several existing literatures that use mixed integer programming (MIP) to solve parallel machine scheduling problems, this study tests and compares three MIP models. Each order has its own ready date, due date and processing time. The completion time of the order cannot over the its due date. If not, penalties for tardiness will occur. Formulation 1 used in immediate-precedence variables [1]. Formulation 2 is an improved version of immediate-precedence variables original proposed by [2]. Formulation 3 used linear ordering variables[1]. The results reveal that Formulation 2 has better computational performance than other does.
For many decades, solving the optimal architectural layout design is unattainable for the reasonable problem sizes. Architects have to settle foil acceptable layouts instead of the favourable optimal solution. With to...
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ISBN:
(纸本)1402034601
For many decades, solving the optimal architectural layout design is unattainable for the reasonable problem sizes. Architects have to settle foil acceptable layouts instead of the favourable optimal solution. With today technologies, various optimization techniques have been used to alleviate the optimal search according to diversified goals. This paper formulates the optimal architectural layout design as the multiobjective mixed integer programming model solved by the MIP solver. The main idea is to capture functional constraints, dimensional constraints and the objective function using only linear formulae with binary variables. Functional constraints are the connectivities, the unused grid cells, the fixed room location, the boundary and the fixed border location while dimension constraints are the non-intersecting, the overlapping, the length and the ratio constraints. The objective function is designed to minimize the absolute distance among rooms and maximize room spaces. Due to the nonlinearity of area computation, the linear approximation of width and height constraints have been utilized. Architects can control these different objectives within the model. By specifying the rigid restriction and the time limits, the problem can be solved within a reasonable amount of time.
This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the auth...
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This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the author formulated fundamental mathematical model for the assignment task in a mixed integer programming form and developed a prototype system based on spreadsheet software to derive an optimal assignment. In this study, the proposed mathematical model is extended and revised to deal with the conditions in the assignment task. Some solutions are discussed to improve practicality for system users.
In recent years, an operation planning of a district heating and cooling (DHC) plant has been arousing interest as a result of development of cooling load or heat demand prediction methods for district heating and coo...
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The investigated case is a vast country with a variety of climates. Due to this diversity in climate and therefore different farming conditions in different areas of the country, wheat is produced at different times o...
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ISBN:
(纸本)9781424448692
The investigated case is a vast country with a variety of climates. Due to this diversity in climate and therefore different farming conditions in different areas of the country, wheat is produced at different times of year all over the country. Therefore, wheat production rate is not constant during year all around the country. Lack of balance between wheat production and consumption in different provinces during different periods necessitates storage and transportation of wheat. In this paper, we intend to find the answer to the following question: "How much wheat in each month of year must be transported from each province to other provinces?" A mixed integer programming (MIP) model is developed for the problem and a genetic algorithm (GA) is designed because optimization solvers cannot solve the real-size problem in a reasonable time. To show efficiency, GA results are compared with those of LINGO 8.00 for randomly generated small-sized test problems.
This study aims to provide a systematic framework of the container selection and cargo loading problems, which are currently faced by a forwarding company in Hong Kong. The forwarding company first consolidates all go...
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ISBN:
(纸本)188933524X
This study aims to provide a systematic framework of the container selection and cargo loading problems, which are currently faced by a forwarding company in Hong Kong. The forwarding company first consolidates all goods that will be shipped to overseas markets into different types of cargos. Then the company is responsible for packing the cargos into containers, which arc rented from airlines a week in advance in order to obtain a cheap price from the airlines. The airlines can provide different types and numbers of containers. Therefore, the question of how to select containers from the airlines and how to pack cargos into the containers is a very important issue that the forwarding company faces every day. The decision-making process becomes complex because of the containers' volume and weight limits and the fact that the rental cost is the fixed cost for using the containers plus the variable cost that depend on the total weight that each container holds. The objective in this study is to minimize the total rental cost, which is the piece-wise function. We further change it into anther form, in which the piece-wise function can be expressed as a continue one. Therefore, a mixedinteger linear programming model is provided to determine the optimal container selection and cargo loading strategy. The application of the proposed model is illustrated by the practical problems from the forwarding company.
A mixedinteger approach for the least cost design or masonry bearing walls under a range of load cases is presented. The integer component of the formulation permits the selection of discrete block sizes and levels o...
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A mixedinteger approach for the least cost design or masonry bearing walls under a range of load cases is presented. The integer component of the formulation permits the selection of discrete block sizes and levels of grouting. The model is also capable of selecting reinforcement when it is necessary or more economical. The technique is appropriate for the design of walls for which the eccentricities are less than or equal to one third of the wall thickness. While the model has been developed to conform to the Canadian Code1, it can be adapted for use with other codes. The nature of the formulation minimizes the computational requirement of the branch-and-bound process used to solve the integer constraints.
mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indee...
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ISBN:
(纸本)9783319600451;9783319600444
mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indeed, they combine productions and they make a better use of biodiversity. These agroforestry systems are based on a complex set of interactions modifying the utilization of light, water and nutrients. Thus, designing such a system must optimize the use of these resources: by maximizing positive interactions (facilitation) and minimizing negative ones (competition). To attain these objectives, the system's design has to include the spatial and temporal dimensions, taking into account the evolution of above-and belowground interactions over a time horizon. For that, we define the mixed Fruit-Vegetable Crop Allocation Problem (MFVCAP) using a discrete representation of the land and the interactions between vegetable crops and fruit trees. First, we give a direct formulation as a binary quadratic program (BQP). Then we reformulate the problem using a Benders decomposition approach. The master problem has 0/1 binary variables and deals with tree positioning. The subproblem deals with crop quantities. The BQP objective function becomes linear in the continuous subproblem by exploiting the fact that it depends only on the quantity of crops assigned to land units having shade, root, or nothing. This problem decomposition allows us to reformulate the MFVCAP into a mixedinteger linear Program (MIP). The detailed spatial-temporal crop allocation plan is easy to obtain after solving the MIP. Experimental results show the efficiency of our approach compared to a direct solving of the original BQP formulation.
This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Thr...
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This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" by Chen. Van der Linden and Li made a strong statement calling for the cessation of test assembly heuristics development, and instead encouraged embracing mixed integer programming (MIP). This article points out the nondeterministic polynomial (NP)-hard nature of MIP problems and how solutions found using heuristics could be useful in an MIP context. Although van der Linden and Li provided several practical examples of test assembly supporting their view, the examples ignore the cases in which a slight change of constraints or item pool data might mean it would not be possible to obtain solutions as quickly as before. The article illustrates the use of heuristic solutions to improve both the performance of MIP solvers and the quality of solutions. Additional responses to the commentary by van der Linden and Li are included.
Lagrangian Relaxation (LR) and General mixed integer programming (MIP) are two main approaches for solving Unit Commitment (UC) problems. This paper compares the LR and the state of art general MIP method for solving ...
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ISBN:
(纸本)0780379896
Lagrangian Relaxation (LR) and General mixed integer programming (MIP) are two main approaches for solving Unit Commitment (UC) problems. This paper compares the LR and the state of art general MIP method for solving UC problems based on performance analysis and numerical testing. In this paper we have rigorously proved that UC is indeed an NP complete problem, and therefore it is impossible to develop an algorithm with polynomial computation time to solve it. In comparison with the general MIP methods, the LR methodology is more scaleable and efficient to obtain near optimal schedules for large scale and hard UC problems at the cost of a small percentage of deviation from the optimal solution. In particular, solving hydro generation sub-problems within the LR framework can take advantages of both LR and general MIP methods and provide a synergetic combination of both approaches.
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