An application of Special Ordered Sets to a periodic milk collection problem

We present an OR-based approach to support a milk collection problem in a special branch of dairy industry. The annual growth of the sector and the continuous imbalance between milk supply and demand, has urged the sector to look for a different approach to their daily milk collection problem. Specific details of the problem environment (i.e., the continuous production on supply level and the delivery conditions on demand level) gave rise to choose for a short- to medium-term planning approach. The proposed decision support system has to be considered as an efficient tool for generating stable milk collection plans which in turn also serves as an effective starting point for the vehicle routing problem. From a computational point of view it turned out that the application of Special Ordered Sets type 1 (SOS1) was very useful. Although it appears from literature that the computational advantage of SOS1 is restricted to supplementary model conditions, this study shows that these conditions are not necessarily needed.     

Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.     

Part type selection problem in flexible manufacturing systems: tabu search algorithms

Production planning in flexible manufacturing systems is concerned with the organization of production in order to satisfy a given master production schedule. The planning problem typically gives rise to several hierarchical subproblems which are then solved sequentially or simultaneously. In this paper, we address one of the subproblems: the part type selection problem. The problem is to determine a subset of part types having production requirements for immediate and simultaneous processing over the upcoming period of the planning horizon, subject to the tool magazine and processing time limitation. Several versions of tabu search (TS) algorithm are proposed for solving the problem. A systematic computational test is conducted to test the performance of the TS algorithms. The best TS algorithm developed is compared to a simulated annealing algorithm.     

Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

In this paper some discrete-continuous project scheduling problems to minimize the makespan are considered. These problems are characterized by the fact that activities of a project simultaneously require for their execution discrete and continuous resources. A class of these problems is considered where the number of discrete resources is arbitrary, and one continuous, renewable, limited resource occurs. A methodology for solving the defined problems is presented. The continuous resource allocation problem is analyzed. An exact, as well as a heuristic approach to the problem is discussed. The idea of the continuous resource discretization is described, and a special case of the problem with identical processing rate functions is analyzed. Some computational experiments for evaluating the efficiency of the proposed heuristic approaches are presented. Conclusions and directions for future research are given.     

On solving stochastic production planning problems via scenario modelling

Summary Linear Porgramming models for stochastic planning problems and a methodology for solving them are proposed. A production planning problem with uncertainty in demand is used as a test case, but the methodology presented here is applicable to other types of problems as well. In these models, uncertainty in demand is characterized via scenarios. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield an implementable non-anticipative policy. Such an approach makes it possible to model correlated and nonstationary demand as well as a variety of recourse decision types. For computational purposes, two alternative representations are proposed. A compact approach that is suitable for the Simplex method and a splitting variable approach that is suitable for the Interior Point Methods. A crash procedure that generates an advanced starting solution for the Simplex method is developed. Computational results are reported with both the representations. Although some of the models presented here are very large (over 25000 constraints and 75000 variables), our computational experience with these problems is quite encouraging.     

基于在险价值的物流网络规划模糊两阶段模型与精确求解方法

针对物流网络规划问题中顾客需求和运输成本的不确定性,使用在险价值量化投资风险,建立了以投资损失的在险价值最小化为目标的模糊两阶段物流网络规划模型。对于模型中不确定参数均为规则模糊数的这一类模糊两阶段规划模型,本文通过理论分析和证明将其转化为等价的确定一阶段规划模型进行求解,从而将无穷维的优化问题转化为有限维的经典优化问题,降低了计算难度且得到了模型的精确解。不同规模的数值实验证实了所提出模型及其求解方法的有效性。     

On a continuous approach for the maximum weighted clique problem

This paper is focused on computational study of continuous approach for the maximum weighted clique problem. The problem is formulated as a continuous optimization problem with a nonconvex quadratic constraint given by the difference of two convex functions (d.c. function). The proposed approach consists of two main ingredients: a local search algorithm, which provides us with crucial points; and a procedure which is based on global optimality condition and which allows us to escape from such points. The efficiency of the proposed algorithm is illustrated by computational results.     

A multi-objective approach for solving a replacement policy problem for equipment subject to imperfect repairs

This paper proposes a multi-objective approach to model a replacement policy problem applicable to equipment with a predetermined period of use (a planning horizon), which may undergo critical and non-critical failures. Corrective replacements and imperfect repairs are taken to restore the system to operation respectively when critical and non-critical failures occur. Generalized Renewal Process (GRP) is used to model imperfect repairs. The proposed model supports decisions on preventive replacement intervals and the number of spare parts purchased at the beginning of the planning horizon. A Multi-Objective Genetic Algorithm (MOGA) coupled with discrete event simulation (DES) is proposed to provide a set of solutions (Pareto-optimum set) committed to the different objectives of a maintenance manager in the face of a replacement policy problem, that is, maintenance cost, rate of occurrence of failures, unavailability, and investment on spare parts. The proposed MOGA is validated by an application example against the results obtained via the exhaustive approach. Moreover, examples are presented to evaluate the behavior of objective functions on Pareto set (trade-off analysis) and the impact of the repair effectiveness on the decision making.     

Accessing feasible space in a generalized job shop scheduling problem with the fuzzy processing times: a fuzzy-neural approach

This paper presents a fuzzy-neural approach for constraint satisfaction of a generalized job shop scheduling problem (GJSSP) fuzzy processing times. Our study is an extension of recently developed research in a GJSSP where the processing time of operations was constant. Our paper assumes that the processing time of jobs is uncertain. The proposed fuzzy-neural approach can be adaptively adjusted with weights of connections based on sequence resource and uncertain processing time constraints of the GJSSP during its processing. The computational results show that the proposed neural approach is able to find good solutions in reasonable time.     

基于正弦型光滑打磨函数对0-1规划问题的连续化求解方法

传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.     

Capacitated replenishment and disposal planning for multiple products with resalable returns

We consider a replenishment and disposal planning problem (RDPP) that arises in settings where customer returns are in as-good-as-new condition. These returns can be placed into inventory to satisfy future demand or can be disposed of, in case they lead to excess inventory. Our focus is on a multi-product setting with dynamic demands and returns over a finite planning horizon with explicit replenishment and disposal capacities. The problem is to determine the timing of replenishment and disposal setups, along with the associated quantities for the products, so as to minimize the total costs of replenishment, disposal, and inventory holding throughout the planning horizon. We examine two variants of the RDPP of interest both of which are specifically motivated by a spare part kitting application. In one variant, the replenishment capacity is shared among multiple products while the disposal capacity is product specific. In the other variant, both the replenishment and disposal capacities are shared among the products. We propose a Lagrangian Relaxation approach that relies on the relaxation of the capacity constraints and develop a smoothing heuristic that uses the solution of the Lagrangian problem to obtain near-optimal solutions. Our computational results demonstrate that the proposed approach is very effective in obtaining high-quality solutions with a reasonable computational effort.     

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Solving the discrete-continuous project scheduling problem via its discretization

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.     

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

In this paper, we present a multicut version of the Benders decomposition method for solving two-stage stochastic linear programming problems, including stochastic mixed-integer programs with only continuous recourse (two-stage) variables. The main idea is to add one cut per realization of uncertainty to the master problem in each iteration, that is, as many Benders cuts as the number of scenarios added to the master problem in each iteration. Two examples are presented to illustrate the application of the proposed algorithm. One involves production-transportation planning under demand uncertainty, and the other one involves multiperiod planning of global, multiproduct chemical supply chains under demand and freight rate uncertainty. Computational studies show that while both the standard and the multicut versions of the Benders decomposition method can solve large-scale stochastic programming problems with reasonable computational effort, significant savings in CPU time can be achieved by using the proposed multicut algorithm.     

An augmented Lagrangian method for binary quadratic programming based on a class of continuous functions

In this paper, an augmented Lagrangian method is proposed for binary quadratic programming (BQP) problems based on a class of continuous functions. The binary constraints are converted into a class of continuous functions. The approach reformulates the BQP problem as an equivalent augmented Lagrangian function, and then seeks its minimizer via an augmented Lagrangian method, in which the subproblem is solved by Barzilai–Borwein type method. Numerical results are reported for max-cut problem. The results indicate that the augmented Lagrangian approach is promising for large scale binary quadratic programming by the quality of the near optimal values and the low computational time.     

A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-II and Monte Carlo simulation

The present study extends a multi-objective mathematical model in the context of industrial hazardous waste management, which covers the integrated decisions of three levels with locating, vehicle routing, and inventory control. Analyzing these decisions simultaneously not only may lead to the most effective structure in the waste management network, but also may reduce the potential risk of managing the hazardous waste. Furthermore, because of the inherent complexity of the waste management system, uncertainty is inevitable and should be acknowledged to guarantee reliability in the decision-making process. From this perspective, the proposed model is novel in the following three aspects: (1) shifting from a deterministic to stochastic environment; (2) considering a multi-period planning horizon; and (3) incorporating the inventory decisions into the problem. The problem is formulated as a multi-objective stochastic Mixed-Integer Nonlinear Programming (MINLP) model, which can be easily converted into a MILP one. In terms of methodological contribution, a new simheuristic approach that is an integration of Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and Monte Carlo simulation is developed to overcome the stochastic combinatorial optimization problem of this study. Our findings verify the efficiency of the proposed approach as it is able to find a high-quality solution within a relatively reasonable computational time.     

A combined ship scheduling and allocation problem

We present a bulk ship scheduling problem that is a combined multi-ship pickup and delivery problem with time windows (m-PDPTW) and multi-allocation problem. In contrast to other ship scheduling problems found in the literature, each ship in the fleet is equipped with a flexible cargo hold that can be partitioned into several smaller holds in a given number of ways. Therefore, multiple products can be carried simultaneously by the same ship. The scheduling of the ships constitutes the m-PDPTW, while the partition of the ships' flexible cargo holds and the allocation of cargoes to the smaller holds make the multi-allocation problem. A set partitioning approach consisting of two phases is proposed for the combined ship scheduling and allocation problem. In the first phase, a number of candidate schedules (including allocation of cargoes to the ships' cargo holds) is generated for each ship. In the second phase, we minimise transportation costs by solving a set partitioning problem where the columns are the candidate schedules generated in phase one. The computational results show that the proposed approach works, and optimal solutions are obtained on several cases of a real ship planning problem.     

An efficient computational approach for multiframe blind deconvolution

Obtaining high resolution images of space objects from ground based telescopes involves using a combination of sophisticated hardware and computational post-processing techniques. An important, and often highly effective, computational post processing tool is multiframe blind deconvolution (MFBD). Mathematically, MFBD is modeled as a nonlinear inverse problem that can be solved using a flexible, variable projection optimization approach. In this paper we consider MFBD problems that are parameterized by a large number of variables. The formulas required for efficient implementation are carefully derived using the spectral decomposition and by exploiting properties of conjugate symmetric vectors. In addition, a new approach is proposed to provide a mathematical decoupling of the optimization problem, leading to a block structure of the Jacobian matrix. An application in astronomical imaging is considered, and numerical experiments illustrate the effectiveness of our approach.     

Formation of a strategic manufacturing and distribution network with transfer prices

We propose a profit maximization model for the decision support system of a firm that wishes to establish or rationalize a multinational manufacturing and distribution network to produce and deliver finished goods from sources to consumers. The model simultaneously evaluates all traditional location factors in a manufacturing and distribution network design problem and sets intra-firm transfer prices that take account of tax and exchange rate differentials between countries. Utilizing the generalized Benders decomposition approach, we exploit the partition between the product flow and the cash allocation (i.e., the pricing and revenue assignment) decisions in the supply chain to find near optimal model solutions. Our proposed profit maximizing strategic planning model produces intuitive results. We offer computational experiments to illustrate the potential valuable guidance the model can provide to a firm's supply chain design strategic planning process.