A heuristic approach for the truck and trailer routing problem

In this paper, we propose an approach based on mathematical programming and local search to cope with the truck and trailer vehicle routing problem. The mathematical programming framework models two subproblems that are solved sequentially, that is, the customer-route assignment problem (CAP), with the objective of minimizing the fleet size used to service clients, and the route definition problem, with the objective of minimizing the total tour length given the set of clients assigned to each vehicle. Since the route assignment model can return infeasible solutions, the local search plays the role of possibly retrieving a feasible solution. The mathematical formulations and the local search work iteratively, embedded in a multiple restarting mechanism able to diversify solutions by (i) identifying additional constraints for the CAP formulation to be taken into account during the algorithm progress, (ii) using a tabu like customer-route matrix to avoid assignments already analysed in the previous iterations of the algorithm. Also a lower bound to assess the solution quality is given. Experiments and comparison with competing approaches suggest that the results of the proposed machinery are promising, producing, on average,a smaller total tour lengths on benchmarks.     

A mathematical immunochemoradiotherapy model: A multiobjective approach

This study developed a near optimization immunochemoradiotherapy model, which has three objectives; maximizing total weighted damage of cancer cells, minimizing total weighted side effect and minimizing total dose related therapy costs, originated from the Weapon–Target Assignment problem (WTA) of military operations research. The multi-objective structure is transformed into a single-objective format via goal programming. The presented model is a mixed-integer nonlinear goal programming model. A non-clinical hypothetical illustrative example is solved using MS Excel's Solver tool as a powerful spreadsheet tool. The theoretical result is extremely impressive especially compared with result of the single-objective program. The model facilitates cancer therapists to act in a multi-objective frame. However, the model is extremely needed to have clinical experiments to validate its theoretical power. This theoretical model is a virtuous synthesis of military and medical operations research.     

A mathematical model and two-stage heuristic for hot rolling scheduling in compact strip production

This paper addresses a new hot rolling scheduling problem from the compact strip production process, which is the mainstream production technology that is used worldwide for sheet strips. The problem is modeled as a combination of two coupled sub-problems. One sub-problem is a sheet strip assignment problem that assigns sheet strips to rolling turns with the constraints of safe values of different gauge levels, and the other is a sheet strip sequencing problem that decides the rolling sequence for all of the sheet strips in a rolling turn to form a particular parabolic shape in thickness. To solve this hot rolling scheduling problem, we present a novel approach that consists of a sheet strip assignment heuristic and a sheet strip sequencing heuristic. The sheet strip assignment heuristic minimizes the number of virtual sheet strips by generating rolling turns according to the ordered sheet strips with maximum gauge level and their safe values. The sheet strip sequencing heuristic minimizes the average change of the thickness of adjacent sheet strips by arranging a certain number of duplicate sheet strips to the increasing stage of a rolling turn. Extensive experiments based on both synthetic and real-world instances from a compact strip production process show the effectiveness of the proposed two-stage heuristic in solving the hot rolling scheduling problem.     

A new VRPPD model and a hybrid heuristic solution approach for e-tailing

We analyze a business model for e-supermarkets to enable multi-product sourcing capacity through co-opetition (collaborative competition). The logistics aspect of our approach is to design and execute a network system where “premium” goods are acquired from vendors at multiple locations in the supply network and delivered to customers. Our specific goals are to: (i) investigate the role of premium product offerings in creating critical mass and profit; (ii) develop a model for the multiple-pickup single-delivery vehicle routing problem in the presence of multiple vendors; and (iii) propose a hybrid solution approach. To solve the problem introduced in this paper, we develop a hybrid metaheuristic approach that uses a Genetic Algorithm for vendor selection and allocation, and a modified savings algorithm for the capacitated VRP with multiple pickup, single delivery and time windows (CVRPMPDTW). The proposed Genetic Algorithm guides the search for optimal vendor pickup location decisions, and for each generated solution in the genetic population, a corresponding CVRPMPDTW is solved using the savings algorithm. We validate our solution approach against published VRPTW solutions and also test our algorithm with Solomon instances modified for CVRPMPDTW.     

Freight transportation in railway networks with automated terminals: A mathematical model and MIP heuristic approaches

In this paper we propose a planning procedure for serving freight transportation requests in a railway network with fast transfer equipment at terminals. We consider a transportation system where different customers make their requests (orders) for moving boxes, i.e., either containers or swap bodies, between different origins and destinations, with specific requirements on delivery times. The decisions to be taken concern the route (and the corresponding sequence of trains) that each box follows in the network and the assignment of boxes to train wagons, taking into account that boxes can change more than one train and that train timetables are fixed.The planning procedure includes a pre-analysis step to determine all the possible sequences of trains for serving each order, followed by the solution of a 0-1 linear programming problem to find the optimal assignment of each box to a train sequence and to a specific wagon for each train in the sequence. This latter is a generalized assignment problem which is NP-hard. Hence, in order to find good solutions in acceptable computation times, two MIP heuristic approaches are proposed and tested through an experimental analysis considering realistic problem instances.     

A mathematical model and a metaheuristic approach for a memory allocation problem

Memory allocation in embedded systems is one of the main challenges that electronic designers have to face. This part, rather difficult to handle is often left to the compiler with which automatic rules are applied. Nevertheless, an optimal allocation of data to memory banks may lead to great savings in terms of running time and energy consumption. This paper introduces an exact approach and a vns-based metaheuristic for addressing a memory allocation problem. Numerical experiments have been conducted on real instances from the electronic community and on dimacs instances expanded for our specific problem.     

A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services

This study investigates a multi-visit flexible-docking vehicle routing problem that uses a truck and drone fleet to fulfill pickup and delivery requests in rural areas. In this collaborative truck–drone system, each drone may serve multiple customers per trip (multi-visit services), dock to the same or different truck from where it launched (flexible docking), and perform simultaneous pickup and delivery. These characteristics complicate the temporal, spatial, and loading synchronization for trucks and drones, making the decisions of order allocation and vehicle routing highly interdependent and intractable. This problem is formulated as a mixed-integer linear programming model and solved by a tailored adaptive large neighborhood search metaheuristic. Numerical experiments are conducted on sparse rural networks to demonstrate the efficiency of the proposed method. We observe that the proposed truck–drone system shows an average cost saving of 34% compared to the truck-only case. Moreover, deep insights into the impacts of multi-visit services, flexible docking, and simultaneous pickup and delivery on the performance of the truck–drone system are discussed.     

A heuristic algorithm for the free newspaper delivery problem

This paper addresses the problem of finding an effective distribution plan to deliver free newspapers from a production plant to subway, bus, or tram stations. The overall goal is to combine two factors: first, the free newspaper producing company wants to minimize the number of vehicle trips needed to distribute all newspapers produced at the production plant. Second, the company is interested in minimizing the time needed to consume all newspapers, i.e., the time needed to get all the newspapers taken by the final readers. The resulting routing problem combines aspects of the vehicle routing problem with time windows, the inventory routing problem, and additional constraints related to the production schedule. We propose a formulation and different heuristic approaches, as well as a hybrid method. Computational tests with real world data show that the hybrid method is the best in various problem settings.     

A new heuristic approach for the P-median problem

The Euclidean p-median problem is concerned with the decision of the locations for public service centres. Existing methods for the planar Euclidean p-median problems are capable of efficiently solving problems of relatively small scale. This paper proposes two new heuristic algorithms aiming at problems of large scale. Firstly, to reflect the different degrees of proximity to optimality, a new kind of local optimum called level-m optimum is defined. For a level-m optimum of a p-median problem, where m<p, each of its subsets containing m of the p partitions is a global optimum of the corresponding m-median subproblem. Starting from a conventional local optimum, the first new algorithm efficiently improves it to a level-2 optimum by applying an existing exact algorithm for solving the 2-median problem. The second new algorithm further improves it to a level-3 optimum by applying a new exact algorithm for solving the 3-median problem. Comparison based on experimental results confirms that the proposed algorithms are superior to the existing heuristics, especially in terms of solution quality.     

A mathematical model for unemployment

In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results.     

A mathematical programming approach to clusterwise regression model and its extensions

The clusterwise regression model is used to perform cluster analysis within a regression framework. While the traditional regression model assumes the regression coefficient (β) to be identical for all subjects in the sample, the clusterwise regression model allows β to vary with subjects of different clusters. Since the cluster membership is unknown, the estimation of the clusterwise regression is a tough combinatorial optimization problem. In this research, we propose a “Generalized Clusterwise Regression Model” which is formulated as a mathematical programming (MP) problem. A nonlinear programming procedure (with linear constraints) is proposed to solve the combinatorial problem and to estimate the cluster membership and β simultaneously. Moreover, by integrating the cluster analysis with the discriminant analysis, a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis. The cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model.     

Robotic disassembly line balancing problem: A mathematical model and ant colony optimization approach

The use of robots is significantly increasing day by day in manufacturing systems, and especially improving the efficiency of the lines. Robots can be used to complete disassembly tasks, and each of the robots can need different operation times to perform the tasks. In this paper, the balancing of the robotic disassembly line problem has been studied to develop efficient solution techniques. Firstly, a mixed-integer linear mathematical model is proposed to determine and solve the problem optimally. A case study from literature is addressed to assess and show the efficiency and effectiveness of the model to minimize cycle time. Secondly, a heuristic algorithm based on ant colony optimization is also proposed to discover a solution for especially the large-size test problems due to the complexity of the problem. The performance of the proposed heuristic algorithm is verified and compared with the different heuristic on data sets. The computational results indicate that the proposed mathematical model and the algorithms are promising for the small and large-size test problems, respectively. Finally, it should be stated that robots have great potential to use in the area of disassembly line and useful solutions provide according to test results.     

A heuristic decomposition approach to optimal control in a water supply model

The optimal pump control problem in a water supply system can be formulated as a mixed integer programming problem. In general, this problem is very difficult to solve by conventional integer programming algorithms, because the number of decision variables is as large as the total number of combinations of pump stations and control periods. However, it possesses a certain block triangular structure, which offers an attractive computational scheme. Taking advantage of this structure, this paper proposes a heuristic decomposition algorithm for finding a good feasible solution to this type of mixed integer programming problems. Numerical results for an actual pump control problem are also reported.     

A unifying approach to heuristic search

We present the General Search Procedure (GSP) that provides a unifying way of describing search algorithms. The GSP captures both constructive and iterative search algorithms. We demonstrate as an exercise that various well-known heuristic search procedures can be obtained as instances of the GSP. The introduced formalism provides a solid ground to prove theoretical properties of search methods. Furthermore, by the formal approach we obtain a framework that can serve as the basis of implementing a search based problem solver.     

A heuristic approach for capacity expansion of packet networks

We address the problem of expanding transmission capacity of an existing packet network over a multiperiod planning horizon, the objective being low total cost of expansion. Discrete capacity choices, interaction with routing decisions, and economy of scale in the cost of capacity make it extremely difficult to decide when, where and how much capacity to add. A fast heuristic solution method is developed based on the well established Flow Deviation routing algorithm. The heuristic begins by making myopic expansion decisions, which are then subsequently adjusted to account for economies of scale in the cost of capacity. Heuristic solutions are compared to a benchmark which approximates the real cost function by its linear lower envelope. Since the number of possible expansion plans is an exponential function of the number of edges, capacity choices, and periods in the planning horizon, a fast heuristic allows one to look beyond small problems at more realistically sized ones.     

A heuristic approach for the double row layout problem

Annals of Operations Research - In the double row layout problem, we wish to position n machines on two parallel rows in order to minimize the cost of material flow among machines. The problem is...     

A heuristic algorithm for a pseudo-cyclic delivery problem under window constraints

The scheduling problem for pseudo-cyclic deliveries under window constraints is presented. The problem is formulated as a linear integer programming problem, where the objective function represented the minimization of the centralized supplier capacity needed to satisfy all user requests over a discretized planning horizon of infinite length. A heuristic algorithm running in polynomial time is illustrated and an experimental analysis of its efficiency is presented.     

A mathematical model for asset pricing

Asset price dynamics is studied by using a system of ordinary differential equations which is derived by utilizing a new excess demand function introduced by Caginalp [4] for a market involving more information on demand and supply for a stock rather than their values at a particular price. Derivation is based on the finiteness of assets (rather than assuming unbounded arbitrage) in addition to investment strategies that are based on not only price momentum (trend) but also valuation considerations. For this new model and the older models which were extracted using the classical excess demand function by Caginalp and Balenovich [2] and [3], time evolutions of asset price are compared through numerical simulations.     

A mathematical model for continuous crystallization

J. Banasiak We discuss a mixed‐suspension, mixed‐product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.