A Structural Decomposition-Based Optimization Approach for the Integrated Scheduling of Blending Processes in Raw Material Yards

Logistics Equipment Scheduling (LES) problem in iron and steel industry is to select appropriate raw material piles and equipments for logistics equipment schedule with the objective of minimizing the operation cost of raw material yard, maximizing the utilization and the equilibrium ratio of reclaimers in the production process. Different from previous literatures, according to the characteristics of raw material yard, the LES problem is divided into two phases: the first one is how to select raw material piles, the other one is a reclaimer scheduling problem. The LES problem is formulated as a multi-targets mixed integer programming model by considering the practical requirements. The complexity of the model motivates us to develop a scatter search-based strategy algorithm to solve the problem approximately. Problem-oriented coding scheme and solution combination method are proposed in scatter search. The computational results on real data show that the cost is decreased by 25.85% in average compared with manual schedule.

Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems

A new, R-graph based, superstructure and corresponding MINLP model for designing conventional distillation columns are presented. A GDP representation (GR) of the superstructure is first constructed, then it is transformed to MINLP representation to which, in turn, additional trivial improvements are added. The new model has been tested on binary mixture examples, and the obtained results are compared to the results of an MINLP model which developed according to the GDP model of Yeomans and Grossmann. 9 The new model yields shorter computation time and provides better local optima. Additionally, the new model has been used for optimizing a complex multicomponent separation system consisting of several distillation columns. In order to handle such a complex system with a huge number of nonlinear equations, the outer approximation algorithm is modified to provide good initial values for the NLP subproblems. Distillation is one of the most widespread processes applied for separating multicomponent liquid mixtures. It is used for working up large volume or stream, and it requires high investment and operation outlays. The significance of the design of economically optimal distillation processes is of no question. Enormous interest has also been addressed to the area of designing optimal heat integrated distillation columns and distillation sequences. Minimizing the cost of a distillation process implies finding the optimal configuration of each individual column, as well. In the present article we consider staged column models only. The number of stages, and the stage numbers of the feed and side-stream points, are discrete decision variables. The total cost of a column may be modeled as the sum of the fix (capital) cost, depending on the number of stages and on the column diameter, and the variable (operation) cost related to the utility consumption. The objective of the design procedure is to find the optimal configuration of the column, which has the minimum total (annualized) cost. In order to model these processes, discrete decisions are required for calculating the number of stages. Optimizing single columns is a well-known procedure; all the basic textbooks outline how to do it in an easy manner. 1 After approximately determining the minimum and the estimated optimal number of theoretical stages, optimizing over the continuous variables is performed at varied values of the discrete variables. This is a 2-dimension discrete array of continuous optimization tasks in the case of a single-feed, two-product column, because there are merely two column sections in this case. This task becomes much more difficult if several feeds and side-products are to be taken into account. The real problem, however, is synthesizing a distillation sequence, or a system of advanced distillation columns, or a complex flowsheet containing distillation units when the number of distillation columns and their connections are not known in advance. In order to solve the complex synthesis problem outlined above, a proper superstructure for a single column, together with a proper generalized disjunctive programming (GDP) model or a proper mixed-integer nonlinear programming (MINLP) model, is a minimum requirement. Once such a model works well for a single column, the problem of more complex flowsheets may also be addressed. Mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) are the two exact methodologies commonly applied for solving process engineering problems with discrete decisions. The former includes algebraic equations describing the process, and binary variables related to discrete decisions. The latter method uses logic variables and expressions to represent the problem. 2 Both formulations have been successfully applied to rigorous models of distillation columns. Both methods apply a fixed maximum number of stages, and the actually used stages are selected from this set. Mathematical formulations that represent rigorous models of distillation column configurations fall into two categories: (i) one task-one equipment (OTOE) representations and (ii) variable task-equipment (VTE) representations. 3

PurposeThis paper aims to develop a bi-objective mixed integer non-linear programing model to optimize the supply chain networks consisting of raw material providers, final product manufacturers and distribution centers. Raw material substitution caused by varying raw material supply amounts, prices and carbon emissions and final product substitution due to different product prices and carbon emissions are considered.Design/methodology/approachThe proposed model aims to achieve total profit maximization and total carbon emission minimization. The objective function of carbon emissions is converted into a maximization problem by changing minimum to maximum. The composite objective function is the weighted sum of the bias value of each objective function. The model is then solved using software Lingo12.FindingsNumerical analysis results show that an increase in the number of alternate raw materials for original raw material helps improve supply chain network performance, and variation in that number causes detectable but not significant changes in downstream final product substitution results.Originality/valueThe major differences between this work and existing research are as follows: first, although previous research considered carbon emissions in supply chain network optimization, it has not considered the substitution effects of products or raw materials. This paper considers the substitution of both raw material and productions. Second, the item substitution considered by previous research is derived from inventory shortage or price difference of original items. However, the substitution considered in the present paper is a response to differences in purchase price, production cost and carbon emissions for items.

The Design and Synthesis of Batch/Semicontinuous Processes

A bi-level optimization model is proposed for locating billboards on road network links in cities. Since billboard locations are largely driven by the flow on the underlying network, factors that impact traffic considerations of users are accounted for, including link congestion and road link pricing. Safety aspects associated with billboard distraction to users of the network are also incorporated within the proposed Mixed Integer Non-Linear Programming (MINLP) model. The model is multi-objective in nature, and it is solved through adopting the augmented ε -constraint method to obtain a sample of non-dominated points on the Pareto front. Due to the non-convexity induced by the bi-level structure of the model, a model reformulation scheme based on the use of equilibrium conditions is presented. A linearization scheme is also adopted that involves the introduction of mixed integer variables.

Global optimization of multiscenario mixed integer nonlinear programming models arising in the synthesis of integrated water networks under uncertainty

A master–slave solving method with adaptive model reformulation technique for water network synthesis using MINLP

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.

Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solution of the problem to global optimality. The main objective of this research was to compare the intra-seasonal water allocation of a mixed integer nonlinear programming (MINLP) model with that of differential evolution (DE), to allocate a limited amount of water while considering irrigable area and the irrigation schedule that will maximise the total gross margin. Results show that both solution procedures adhere to economic theory of water allocation under limited water supply. The conclusion is that the MINLP model most likely achieved very near global optimality as the solutions of the two models were very close to each other. DE holds promise to solve more complex models involving risk and multiple crops.

The location-allocation problem of manifolds, which is a part of subsea field layout optimization, directly affects the flowline cost. This problem has always been studied as a mixed-integer nonlinear programming (MINLP) problem, or an integer linear programming (ILP) problem when there are location options for the facilities. Making a MINLP model is surely convenient to interpret the optimization problem. However, finding the global optimum of the MINLP model is very hard. Hence, practically, engineers use approximation algorithms to search a good local optimum or give several good location options based on their experience and knowledge to reduce the MINLP model into an ILP model. Nevertheless, the global optimum of the original MINLP model is no longer guaranteed. In this study, enlightened by the graphic theories, we propose a new method in which we reduce the MINLP model into an ILP model---more precisely, a binary linear programming (BLP) model---without compromise of achieving global optimum, but also with extremely high efficiency. The breakthrough in both efficiency and accuracy of our method for the location-allocation problem of manifolds and wellheads is well demonstrated in various cases with comparison to the published methods and the commercial MINLP solver from LINDO. Besides, we also provide our results for larger-scale problems which were considered infeasible for the commercial MINLP solver. More generally, our method can be regarded as a specific MINLP/NIP (nonlinear integer programming) solver which can be used for many other applications. This work is the second of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.

Monazite is a naturally occurring radioactive material that is processed for use in a variety of domestic applications. At present, there is little information available on potential radiation doses experienced by people working with monazite. The ambient dose rate and activity concentration of natural radionuclides in raw materials, products, and dust in work sites as well as the Rn and Rn concentrations in work sites were measured in a monazite processing plant in Japan. Dose estimations for plant workers were also conducted. The activity concentration of the U series in raw materials and products for the monazite processing plant was found to be higher than the relevant values described in the International Atomic Energy Agency Safety Standards. The ambient dose rates in the raw material yard were higher than those in other work sites. Moreover, the activity concentrations of dust in the milling site were higher than those in other work sites. The Rn concentrations in all work sites were almost the same as those in regular indoor environments in Japan. The Rn concentrations in all work sites were much higher than those in regular indoor environments in Japan. The maximum value of the effective dose for workers was 0.62 mSv y, which is lower than the reference level range (1-20 mSv y) for abnormally high levels of natural background radiation published in the International Commission of Radiological Protection Publication 103.

In this paper, we develop a mathematical model of a technician routeing and scheduling problem with time windows (TRSPTW) and overnight shifts, which we title the ‘overnight TRSPTW’. This problem is motivated by a real application in the telecommunications industry in Saskatchewan, Canada. A mixed-integer nonlinear programming (MINLP) model is employed to achieve two key objectives: (1) minimising the total costs associated with technicians and subcontractors, including travel costs, accommodation costs and penalty costs caused by late starts and (2) minimising imbalanced workloads. Furthermore, the present work aims to determine the daily assignment of technicians to communities, depots and routes; find a high-quality schedule for technicians’ start times in communities and lunch breaks and determine the daily assignment of tasks to the subcontractor. The bi-objective MINLP model used to solve the overnight TRSPTW is a typical NP-hard problem in combinatorial optimisation. As such, we introduce a new hybrid category of TRSPTW that combines centroid-based clustering, which is an unsupervised machine learning (ML) approach, with a bi-objective zebra optimisation algorithm (BOZOA). The resultant algorithm blends the advantages of the ZOA and ML to strike a balance between the exploration and exploitation of the solution region. Finally, we compare our results with those obtained using an exact solver for small-, medium-, and large-sized instances. The performance evaluation and validation results revealed that the proposed ML-based BOZOA provides very good performance in solving TRSPTWs at a variety of scales with respect to the optimality criteria, including, number of taken iterations, infeasibility, optimality error and complementarity compared with both an exact solver and two inspired algorithms from ZOA. Highlights An ML-based bi-objective zebra optimisation algorithm to treat large-scale TRSPs Centroid-based clustering on the population of zebras to avoid bias towards a specific search space Making a trade-off between exploration and exploitation of the feasible region in the developed algorithm A new MINLP model of a weighted bi-objective TRSP with limited capacity depots Workload function, penalty function for lateness, subcontracts, time windows for tasks and breaks Experiments using real data to show the performance of the model and solution method

An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach

This research studies the cellular manufacturing system (CMS) controlled by kanban mechanism which defective items are produced in any production run of each product and rework is carried out to transform them into serviceable items. We consider and compare two different policies for rework where in the first policy rework is completed within the same production cycle and in the second policy rework done after N production cycles. Recently Aghajani et al. (2012) explain policy 2 and proposed a mixed-integer nonlinear programming (MINLP) model for this policy. In order to minimize total cost, MINLP model was developed for policy 1 to find simultaneously the optimal number of kanban, batch size, and number of batches. The cost function includes the cost of setup, holding, and transportation. Due to the high combinatorial structure of the problem, particle swarm optimization (PSO), and simulated annealing (SA) algorithms as meta-heuristic methods are proposed to solve the problem and numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms. It is shown that both PSO and SA result are in a near optimal solution but the PSO algorithm gives a better performance than the SA method. Also, sensitivity analysis is carried out to study the effect of defective rate, holding cost, and setup cost variations on the total system cost is discussed the performance of these policies in different conditions.