An integrated location-inventory problem in a closed-loop supply chain with third-party logistics

Third-party logistics (3PL) is a fast growing business. Many large organisations are using 3PL services to reduce operating costs, simplify business processes, and enhance operations and supply chain flexibility. In this paper, we study location-inventory decisions jointly in a closed-loop system with 3PL. First, a model formulation is proposed to develop mixed-integer non-linear programming (MINLP) models for the location-inventory problem under study. Then, a novel heuristics based on differential evolution and the genetic algorithm is designed to solve the MINLP models efficiently. Last, numerical study is presented to illustrate and validate the solution approach.     

Material handling considerations in the FMS loading problem with full routing flexibility

This study exploits machining and routing flexibility to effectively deal with the material handling requirements resulting from a frequently changing demand mix in a manufacturing system where material handling is a bottleneck. For this purpose, the objective function of the operation and tool loading problem is selected as the minimisation of the total distance traveled by parts during their production. Versatile machines and the flexible process plans offer full routing flexibility that enable the same workpiece to be processed using alternative sequences of operations on alternative machines. Three mathematical programming (MP) models and a genetic algorithm (GA) are proposed to solve this problem. The proposed MP formulations include a mixed-integer nonlinear programming (MINLP) model and two mixed-integer programming (MIP) models, which offer different representations for the flexible process plans. The GA is integrated with linear programming for fitness evaluation and incorporates several adaptive strategies for diversification. The performances of these solution methods are tested through extensive numerical experiments. The MP models are evaluated on the basis of the exact solutions they yield as well as how they lend themselves for GA fitness evaluation. The GA–LP integration works successfully for this hard-to-solve problem.     

Connected Vehicle-Based Traffic Signal Coordination

This study presents a connected vehicles (CVs)-based traffic signal optimization framework for a coordinated arterial corridor. The signal optimization and coordination problem are first formulated in a centralized scheme as a mixed-integer nonlinear program (MINLP). The optimal phase durations and offsets are solved together by minimizing fuel consumption and travel time considering an individual vehicle’s trajectories. Due to the complexity of the model, we decompose the problem into two levels: an intersection level to optimize phase durations using dynamic programming (DP), and a corridor level to optimize the offsets of all intersections. In order to solve the two-level model, a prediction-based solution technique is developed. The proposed models are tested using traffic simulation under various scenarios. Compared with the traditional actuated signal timing and coordination plan, the signal timing plans generated by solving the MINLP and the two-level model can reasonably improve the signal control performance. When considering varies vehicle types under high demand levels, the proposed two-level model reduced the total system cost by 3.8% comparing to baseline actuated plan. MINLP reduced the system cost by 5.9%. It also suggested that coordination scheme was beneficial to corridors with relatively high demand levels. For intersections with major and minor street, coordination conducted for major street had little impacts on the vehicles at the minor street.     

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.     

CO-EVOLUTIONARY HYBRID DIFFERENTIAL EVOLUTION FOR MIXED-INTEGER OPTIMIZATION PROBLEMS

Evolutionary algorithms are promising candidates for obtaining the global optimum. Hybrid differential evolution is one or the evolutionary algorithms, which has been successfully applied to many real-world nonlinear programming problems. This paper proposes a co-evolutionary hybrid differential evolution to solve mixed-integer nonlinear programming (MINLP) problems. The key ingredients of the algorithm consist of an integer-valued variable evolution and a real-valued variable co-evolution, so that the algorithm can be used to solve MINLP problems or pure integer programming problems. Furthermore, the algorithm combines a local search heuristic (called acceleration) and a widespread search heuristic (called migration) to promote the search for a global optimum. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional MINLP optimization methods     

Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.     

A Novel Continuous-Time Modeling and Optimization Framework for Well Platform Planning Problems

The long-term planning problem for integrated gas field development is investigated. The key decisions involve both design of the production and transportation network structure and operation of the gas fields over time. A novel continuous-time modeling and optimization approach is proposed, which introduces the concept of event points and allows the well platforms to come online at potentially any time within the continuous horizon under consideration. A two-level formulation and solution framework is developed to take into account complicated economic calculations and results in mixed-integer nonlinear programming (MINLP) problems. As compared with the discrete-time model, the proposed approach leads to more compact mathematical models and significant reduction of the size of the resulting MINLP problems. Even though, the proposed approach in its current form cannot guarantee convergence to the optimal solution, computational results show that this approach can reduce the computational efforts required substantially and solve problems that are intractable for the discrete-time model.     

制造/再制造集成物流网络设施选址模型及算法

首先构建了一个制造/再制造集成物流网络:在该网络中,正向物流和逆向物流都是双层结构的,所有的物流设施均有能力限制,且假设再制造产品与新产品同质,都可以用来满足顾客的需求.在此基础上建立了一个混合整数非线性规划(MINLP)模型.然后提出了混合启发式算法求解.该算法用禁忌搜索法确定整型变量,用基于优先权的遗传算法解决多阶段运输问题.最后通过一个算例说明了模型和算法的有效性.     

A design model and a production–distribution and inventory planning model in multi-product supply chain networks

Supply chain network (SCN) design implicates decision-making at a strategic level. That includes selecting the right suppliers and determining the number and the location of plants, distribution centres and retailers. An apt design model of the supply chain is imperative for the proper function of the supply chain and consequently for making better operational decisions in an attempt of a continuous improvement. In this paper, we propose two models. The first model is a mixed-integer linear programming model which is concerned with the SCN design problem, whereas the second operational model is a mixed-integer non-linear programming model in respect to the production–distribution and inventory planning problem in a supply chain network. The number of customers and suppliers as well as their demand and capacities are assumed to be known in both models. Two steady-state genetic algorithms were implemented in MATLAB in order to solve both the design and the operational model. The results were compared with GAMS. Some examples were devised in order to demonstrate potential ways of use for the designer of the supply chain network, as well as for the supply chain manager.     

A multi-objective optimisation approach for order management: incorporating activity-based costing in supply chains

Most of the supply chain order management decision making models proposed in the literature are based mainly on the material flow and capacity constraints without any consideration to the profitability factor. In this paper, we develop a multi-objective mixed-integer programming (MIP) model which considers profitability in order to effectively manage order acceptance decisions in supply chains, subject to capacity constraints by using activity-based costing (ABC). While there are a numbers of decision-making models in literature integrating ABC in supply chains, this study expands the previous models with a more customer-oriented approach. The proposed model fulfils a desirable amount of orders completely and accepts selective number of orders partially with an objective of minimising the amount of residual capacity and increasing the profitability.     

Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.     

Improved mixed-integer linear programming model and heuristics for bi-objective single-machine batch scheduling with energy cost consideration

This article addresses bi-objective single-machine batch scheduling under time-of-use electricity prices to minimize the total energy cost and the makespan. The lower and upper bounds on the number of formed batches are first derived and a continuous-time mixed-integer linear programming model is proposed, which improves an existing discrete-time model in the literature. Two improved heuristics are proposed based on the improved model. Computational experiments demonstrate that the improved model and heuristics can run hundreds of times faster than the existing ones for large-size instances.     

A new DEA common-weight multi-criteria decision-making approach for technology selection

This paper addresses an advanced manufacturing technology selection problem by proposing a new common-weight multi-criteria decision-making (MCDM) approach in the evaluation framework of data envelopment analysis (DEA). We improve existing technology selection models by giving a new mathematical formulation to simplify the calculation process and to ensure its use in more general situations with multiple inputs and multiple outputs. Further, an algorithm is provided to solve the proposed model based on mixed-integer linear programming and dichotomy. Compared with previous approaches for technology selection, our approach brings new contributions. First, it guarantees that only one decision-making unit (DMU) (referring to a technology) can be evaluated as efficient and selected as the best performer while maximising the minimum efficiency among all the DMUs. Second, the number of mixed-integer linear programs to solve is independent of the number of candidates. In addition, it guarantees the uniqueness of the final optimal set of common weights. Two benchmark instances are used to compare the proposed approach with existing ones. A computational experiment with randomly generated instances is further proceeded to show that the proposed approach is more suitable for situations with large datasets.     

Mixed-integer nonlinear programming techniques for the synthesis of engineering systems

The development of new mixed-integer nonlinear programming (MINLP) algorithms, coupled with advances in computers and software, is opening promising possibilities to rigorously model, optimize, and automate the synthesis of engineering systems. A general overview of the MINLP approach and algorithms will be presented in this paper with the aim of gaining a basic understanding of these techniques. Strengths and weaknesses will be discussed, as well as difficulties and challenges which still need to be overcome. In particular, it will be shown how proper problem representations, effective modeling schemes, and solution strategies can play a crucial role in the successful application of these techniques. The application of MINLP algorithms in synthesis will be illustrated with several examples.     

A flower pollination algorithm for the double-floor corridor allocation problem†

This research explores the double-floor corridor allocation problem (DFCAP), which deals with the optimal arrangement of departments over two floors and then place them along both sides against a corridor. This problem is a natural extension of the corridor allocation problem (CAP) to additional floors; the layout of each floor can be regarded as an approximately independent CAP. The DFCAP is commonly observed in manufacturing and service buildings. In this study, a mixed-integer programming formulation for the DFCAP is developed, and it is able to reduce to the classical CAP model. Then a novel flower pollination algorithm is provided, which is discretised using swap pair set approach to solve the considered DFCAP. In addition, to ameliorate the algorithm, three constructive heuristic rules are developed to produce a reasonably good initial population; meanwhile, a variable neighbourhood search structure is presented to prevent prematurity in arrival at a poor local solution. Finally, several instances for the DFCAP with a size of 9?≤?n?≤?80 are employed in the algorithms, as well as in mixed-integer non-linear programming (MINLP) formulations, which are solved with GUROBI 7.0.1. Moreover, the above-mentioned instances are utilized to show that the proposed algorithm performs better in comparison to the state-of-the-art optimization algorithms.     

Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques

In the present paper a cutting plane approach to solve mixed-integer non-linear programming (MINLP) problems, containing pseudo-convex functions, is given. It is shown how valid cutting planes for pseudo convex functions can be obtained and, furthermore, it is shown how a class of non-convex MINLP problems with a pseudo-convex objective function and pseudo-convex constraints, can be solved to global optimality with the considered cutting plane technique. Finally the numerical efficiency of the procedure, when solving some example problems, is illustrated.     

Optimal solution for the flow path design problem of a balanced unidirectional AGV system

An optimal flow path layout (FPL) design method is introduced as a handy tool for an automated guided vehicle (AGV) system planing stage. The problem is analysed and formulated by linear mixed-integer programming. A procedure based on the branch-and-bound depth-first search technique is proposed to solve the FPL problem. The procedure is implemented as an efficient computer program and yields an optimal solution in a small number of iterations. Using the transportation model for calculating the required and optimal flow of empty vehicles, system balance is achieved. Finally, two examples are given. A simple illustrative example is discussed to demonstrate the procedure, and a realistic FPL problem with 23 nodes, 66 arcs and nine pick-up/delivery stations is solved.     

Investigating replenishment policies for centralised and decentralised supply chains using stochastic programming approach

In this paper, a multiple period replenishment problem based on (s, S) policy is investigated for a supply chain (SC) comprising one retailer and one manufacturer with uncertain demand. Novel mixed-integer linear programming (MILP) models are developed for centralised and decentralised decision-making modes using two-stage stochastic programming. To compare these decision-making modes, a Monte Carlo simulation is applied to the optimization models’ policies. To deal with demand uncertainty, scenarios are generated using Latin Hypercube Sampling method and their number is reduced by a scenario reduction technique. In large test problems, where CPLEX solver is not able to reach an optimal solution in the centralised model, evolutionary strategies (ES) and imperialist competitive algorithm (ICA) are applied to find near optimal solutions. Sensitivity analysis is conducted to show the performance of the proposed mathematical models. Moreover, it is demonstrated that both ES and ICA provide acceptable solutions compared to the exact solutions of the MILP model. Finally, the main parameters affecting difference between profits of centralised and decentralised SCs are investigated using the simulation method.     

A superior linearization method for signomial discrete functions in solving three-dimensional open-dimension rectangular packing problems

This article studies the three-dimensional open-dimension rectangular packing problem (3D-ODRPP) in which a set of given rectangular boxes is packed into a large container of minimal volume. This problem is usually formulated as a mixed-integer nonlinear programming problem with a signomial term in the objective. Existing exact methods experience difficulty in solving large-scale problems within a reasonable amount of time. This study reformulates the original problem as a mixed-integer linear programming problem by a novel method that reduces the number of constraints in linearizing the signomial term with discrete variables. In addition, the range reduction method is used to tighten variable bounds for further reducing the number of variables and constraints in problem transformation. Numerical experiments are presented to demonstrate that the computational efficiency of the proposed method is superior to existing methods in obtaining the global optimal solution of the 3D-ODRPP.     

Extension of the hybrid linear programming method to optimize simultaneously the design and operation of groundwater utilization systems

This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for solving practical groundwater management problems.