Solving mixed integer programming production planning problems with setups by shadow price information

Algorithms developed to solve linear programming (LP) problems and advances in computer speed have made large-scale LP problems solvable in time for implementation. Solving an LP is relatively easier than solving an MIP for modern production planning problems. In this study, we propose a heuristic iterative algorithm between LP solution phases and setup decision computations for solving these difficult MIP production planning problems. By utilizing the shadow price information provided by the LP solution of the previous iteration, the setup decision computation converts an MIP problem into an LP problem, which can be efficiently solved in the current iteration. Extensive experiments show that the proposed heuristic algorithm performs well.     

Analysis of integer programming algorithms with L-partition and unimodular transformations

We study algorithms for solving integer linear programming problems, in particular, set packing and knapsack problems. We pay special attention to algorithms of lexicographic enumeration of L-classes and their combinations with other approaches. We study the problems of using unimodular transformations in order to improve the structure of the problems and speed up the algorithms. We construct estimates on the number of iterations for the algorithms that take into account the specific structure of the problems in question. We also show experimental results.     

Multi-stage multi-objective production planning using linguistic and numeric data-a fuzzy integer programming model

This paper introduces a methodology to solve a multi-stage production planning problem having multiple objectives, which are conflicting, non-commensurable and fuzzy in nature. The production process consists of multiple stages having one or more machines in each stage. Every processing stage produces work-in-process, semi-finished items as an output, which becomes an input to the subsequent stage either fully or partially depending on the cycle times of the machines. Events of machine breakdowns and imbalances in input–output relations in one or more stages may affect both work-in-process (WIP) and final production targets. Our paper provides a methodology based on fuzzy logic to maintain the desired balanced input–output relation at each stage and the targeted production output at the final stage. This is done by procurement of work-in-process inventory (WIP) and installation of new machines at appropriate stages. The objectives or goals expressed in linguistic terms are represented as fuzzy sets. The Induced Ordered Weighted Averaging (IOWA) operator is used to aggregate the objectives as per their priorities and finally to formulate the production process as a Mixed Integer Programming (MIP) problem. The solution to MIP shows the degrees of achievements of the production process objectives. The methodology is illustrated with a real life application of crankshaft productions in an automobile industry.     

Operation planning of district heating and cooling plants using genetic algorithms for mixed integer programming

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 cooling systems. In this paper, we formulate an operation planning of a district heating and cooling plant as a mixed integer linear programming problem. Since the formulated problem involves hundreds of variables, we anticipate that it is difficult to strictly solve it by enumeration-based methods. Thereby, we propose an approximate solution method based on genetic algorithms for mixed integer programming problems. Furthermore, we show the feasibility and effectiveness of the proposed method by comparison with the branch-and-bound method through numerical experiments using actual plant data.     

Dynamic programming algorithms for scheduling parallel machines with family setup times

We address the problem of scheduling jobs with family setup times on identical parallel machines to minimize total weighted flowtime. We present two dynamic programming algorithms — a backward algorithm and a forward algorithm — and we identify characteristics of problems where each algorithm is best suited. We also derive two properties that improve the computational efficiency of the algorithms.Scope and purposeWhile most production schedulers must balance conflicting goals of high system efficiency and timely completion of individual jobs, consideration of this conflict is underdeveloped in the scheduling literature. This paper examines a model that incorporates a fundamental cause of the efficiency/timeliness conflict in practice. We propose solution methodologies and properties of an optimal solution for the purpose of exposing insights that may ultimately be useful in research on more complex models.     

A Hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization

Hybrid methods are promising tools in integer programming, as they combine the best features of different methods in a complementary fashion. This paper presents such a framework, integrating the notions of genetic algorithm, linear programming, and ordinal optimization in an effort to shorten computation times for large and/or difficult integer programming problems. Capitalizing on the central idea of ordinal optimization and on the learning capability of genetic algorithms to quickly generate good feasible solutions, and then using linear programming to solve the problem that results from fixing the integer part of the solution, one may be able to obtain solutions that are close to optimal. Indeed ordinal optimization guarantees the quality of the solutions found. Numerical testing on a real-life complex scheduling problem demonstrates the effectiveness and efficiency of this approach.     

WSN中基于混合整数非线性规划的功率分配算法

近期协作路由协议的研究受到广泛关注.然而,现多数协作路由协议是以减少能量消耗为目的,它们并没有考虑在协作路由中的数据包碰撞概率最小化问题.为此,针对无线传感网WSNs(Wireless Sensor Networks)的协作路由,提出基于最小化碰撞概率的功率分配CMPA(Collision Minimization-based Power Allocation)算法.首先,推导了碰撞概率数学模型,并形成了混合整数非线性规划问题.然后,为了降低复杂度,将功率分配和路由选择进行独立处理,同时利用分支界定空间缩小BBSR(Branch-and-Bound Space Reduced)算法求解.仿真结果表明,提出的CMPA算法能够有效地降低碰撞概率和总的传输功率.与OKCR算法相比,CMPA算法的碰撞概率下降了近82%,总的传输功率下降了0.1 dB.     

Transmission planning for Indian power grid: a mixed integer programming approach

The paper presents a modeling framework to analyze some important issues associated with operation planning of a power system. Major activities involved in operations planning of large integrated power systems are considered simultaneously to ensure optimal utilization of generation and transmission capacity. The model also examines optimal transmission expansion plans vis-à-vis fuel supply issues. A mixed integer programming model is developed for this purpose and the Indian power system considered. Specific emphasis is on spatial transmission expansion plan for the existing Indian inter-state transmission grid and new transmission links, coordinated operation of the isolated regional grids and system benefits accruing from transmission expansion, enhanced fuel production and supply rescheduling to ensure efficient operation of various generating stations.     

Stochastic programming problems associated with adaptive production planning

Cybernetics and Systems Analysis -     

Computer-based algorithms for multiple criteria and multiple constraint level integer linear programming

This paper investigates algorithm development and implementation for multicriteria and multiconstraint level (MC²) integer linear programming problems. MC² linear programming is an extension of linear programming (LP) and multiple criteria (MC) linear programming and a promising computer-aided decision technique in many applications. Here, we present two of the most recent techniques, the MC² branch-and-partition algorithm and the MC² branch-and-bound algorithm, to solve MC² integer linear programs. We describe the design and implementation of a C++ software library for these approaches, and then conduct a comparison study in terms of computational efficiency and complexity through a series of empirical tests.     

基于混合整数规划的智能网联车冲突区时序优化模型

智能网联车的大规模应用为交通冲突区域的优化与管理提供了新的机遇和挑战.为保证冲突区域车辆的汇入安全,提高冲突区域车流的运行效率,引入优化时间区间的概念,以车辆平均延误为优化目标,车辆通过冲突区域的最小安全时间间隔为约束条件,构建车辆进入冲突区域时序的混合整数线性规划模型.为研究不同流量状态对模型结果的影响,设计不同流量...     

Random decomposition of 0-1 linear integer programming problems and automatic choice of algorithms

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 149–158, March–April, 1994.     

Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.     

A multi-plant production planning model considering non- repeated setup and aperiodic shipment

A new model for multi-plant production planning is developed. As the important actual features of some manufacturers, non-repeated setup and aperiodic shipment are appropriately introduced into the multi-plant production planning model and the corresponding constraints are accurately linearized. The new model is also applicable in the case of periodic shipment or backorder prohibition. Its effectiveness is examined by an instance which simulates many real characteristics. The experimental results indicate that the new model achieves the optimal profit. The sensitivity of unit setup cost and unit shipment cost is analyzed. The significance of backorder and the limitation of shipment at a time are discussed in detail.     

A fuzzy mixed integer goal programming approach for cooking and heating energy planning in rural India

In this study, a fuzzy mixed integer goal programming model (FMIGP) has been developed for rural cooking and heating energy planning in the Chikhli taluka of Buldhana district, Maharashtra, Central India. The model considers various scenarios such as economical, environmental, social acceptance and local resources to trade off between socio-economical and environmental issues related to cooking and heating energy in two villages namely Malshemba and Muradpur. Due to uncertainty involved in real world energy planning problems, exact input data is impossible to acquire. Hence FMIGP model is used to consider four fuzzy objectives. The solutions provide energy resource allocations at micro level with minimized cost, minimized emission, maximized social acceptance and maximized use of local resources. The proposed approach can handle fuzzy environmental realistic situation and can provide better solution to decision maker for rural energy planning.     

A linearized polynomial mixed integer programming model for the integration of process planning and scheduling

This paper presents a linearized polynomial mixed-integer programming model (PMIPM) for the integration of process planning and scheduling problem. First, the integration problem is modeled as a PMIPM in which some of the terms are of products of up to three variables, of both binary and continuous in nature. Then, an equivalent linearized model is derived from the polynomial model by applying certain linearization techniques. Although the linearized models have more variables and constraints than their polynomial counterparts, they are potentially solvable to the optimum in comparison to their equivalent polynomial models. Experiments show that the linearized model possesses certain characteristics that are absent from other models in the literature, and provides a fundamental framework for further research in this area.     

Optimizing returns with stock option strategies: An integer programming approach

The paper develops an integer programming model for obtaining the optimum number of call and put stock options to buy in order to maximize the expected profitability from the resulting straddle. Option values are obtained using the Black and Scholes model [1].The objective function of the model is based on probabilistic estimates rather than on an empirical utility function, as has been done in the past [7].All the input parameters to the model are observable with the exception of break even points, which are based on the subjective judgement of the investor and the historical behavior of the underlying security.     

A goal programming model for aggregate production planning with resource utilization constraint

This paper addresses the aggregate production planning problem with different operational constraints, including production capacity, workforce level, factory locations, machine utilization, storage space and other resource limitations. Three production plants in North America and one in China are considered simultaneously. A pre-emptive goal programming model is developed to maximize profit, minimize repairing cost and maximize machine utilization of the Chinese production plant hierarchically. A set of data from a surface and materials science company is used to test the effectiveness and the efficiency of the proposed model. Results illustrate the flexibility and the robustness of the proposed model by adjusting goal priorities with respect to importance of each objective and the aspiration level with respect to desired target values.     

New mixed integer approach to solve a multi-level capacitated disassembly lot-sizing problem with defective items and backlogging

The disassembly process has attracted mounting interest due to growing green concerns. This paper addresses the capacitated dynamic lot-sizing problem with external procurement, defective and backordered items, setup times, and extra capacity. The problem is to determine how many end-of-life products to disassemble during each period. We propose a new mixed-integer programming (MIP) approach to formulate the problem under study in order to maximize the disassembly-process gain, which is obtained as the difference between the revenue achieved by resale of the items recovered after disassembly and the costs tied to operating the disassembly tasks. Several numerical tests using the well-known CPLEX solver proved that this new model can find the optimal disassembly schedule for most test instances within an acceptable computational time. Furthermore, we led sensitivity studies on disassembly capacity, setup time and procurement cost. Test results validate the power of the suggested model and provide helpful insights for industry practitioners.