LINGO Solver Research Articles

Lot streaming in [N-1](1)+N(m) hybrid flow shop

This paper deals with N-stage hybrid flow shop (HFS) lot streaming problem to develop a schedule that minimises the makespan. The HFS considered consists of one machine in each of the first (N-1) stages and m machines in stage N. A mixed integer linear programming (MILP) model is proposed and solved using LINGO solver. For large size problems, the LINGO solver takes longer time and hence an algorithm is proposed. The heuristic approach consists of splitting the lots and then sequencing. The lot splitting is based on the average processing time of jobs in the first (N-1) stages and cycle time of stage N. The sum of processing time of all jobs in each stage of the first (N-1) stages is considered for sequencing. Numerical illustrations are carried out to show the percentage deviation of solution obtained using the algorithm from the MILP model. The results show that the algorithm gives near optimal solution to the problems within a very small computational time compared to the MILP model.

Development of a Joint Economic Lot Size Model with Stochastic Demand Within non-equal shipments

The majority of the researches in the integrated vendor-buyer inventory problem assume that the shipments are equal. In this paper, shipments are considered to be non-equal. Both demand and delivery times are also assumed to be stochastic. Moreover, unsatisfied demand can be backordered and lost, as well asconsidering a service level constraint. The objective is to minimize both buyer and vendor costs at the same time. The problem is solved by an exact heuristic algorithm. To validate the algorithm’s performance, the results are compared with that of LINGO solver. Finally, a set of numerical problems is applied to compare the result in the integrated and independent forms.

Modelling and Analysis of Multi-period Distribution-Allocation Problem in a Two-Stage Supply Chain

A supply chain has a network structure and all the production-distribution decisions involve several variables and constraints which vary both quantitatively and qualitatively. Mostly, production and distribution functions are managed independently, with little or no coordination which results in huge inventory holding costs and backorder costs. Hence, supply chains are exploring strategies to reduce the inefficiencies and the redundancies along the manufacturing/ distribution channel, which can eventually lead to a closer coordination between the various supply chain partners. One such strategy is to effectively allocate the downstream entities to the upstream entities. Hence, this paper considers a multi-period distribution- allocation problem(MPDAP) subjected to backorder and inventory constraints. It's mathematical formulation is difficult to solve due to the presence of fixed costs which causes nonlinearities in the objective function. The MPDAP is known to be Non-deterministic Polynomial-time hard problem. The complexity of the problem increases as and when more constraints are imposed into the model and problem size increases. In this work, an MPDAP is solved using an Ant colony optimization based heuristic to get a near-optimal solution. The proposed heuristic has been evaluated for the solution robustness by comparing it with that obtained using LINGO solver. A range of problem instances were considered in which suppliers, customers and time-periods were varied from 2-8. The percentage deviation of ACO cost from optimal solution obtained from LINGO was around 2%.

Planning a Capacitated Road Network with Flexible Travel Times: A Genetic Algorithm

We are concerned with a capacitated location-multi allocation-routing problem in a road network with flexible travel times. It is assumed that all links are two-way and capacities of the server nodes and arcs for accepting of population are limited. The aim of our work is to find numbers and locations of server nodes, allocation of the existing population in existing demand nodes on the network to the servers and the allocation of existing population in each node to different routes to determine the decided server for each member so that total transportation time is minimized. Here, two basic concepts are considered: multi allocation and flexible travel times. The concept of multi allocation arises from the possibility of allocating the existing population in a demand node to more than one server node. Also, flexible travel times concentrate on impact of traveling population on the times of links simultaneously, that is, depending on how the population is distributed on the network, the travel times on links may be increased. So, to have the least increase in the time of each link, it is necessary to decide upon the distribution of population in the network. We formulate the proposed problem as a mixed-integer nonlinear programming model and then present a genetic algorithm (GA) for solving large problems Finally, we make two sets of numerical experiments and analyze the obtained results by LINGO solver and GA. Numerical results show the proposed GA to be highly efficient.

A model for the layout of bike stations in public bike‐sharing systems

SummaryThe problem of designing a layout of bike stations for public bike‐sharing systems entails selecting a number of stations and then constructing them within a planning area having many bike traffic zones and candidate bike stations. In this paper, we proposed a mathematical model to formulate the layout of public bike stations with the objective of minimizing users' total travel time and investment budget constraints. The model can guarantee that the needs for picking up and dropping off bikes amidst all bike travel demands are satisfied. Using this model, the number and locations of bike stations and the number of bikes and parking lockers at each bike station can be simultaneously determined. A typical example solved by lingo solver is created to illustrate the proposed model. Copyright © 2015 John Wiley & Sons, Ltd.

Multi-item solid transportation problem with type-2 fuzzy parameters

In this paper, a multi-item solid transportation problem with parameters, e.g., transportation costs, supplies and demands as type-2 triangular fuzzy variables is formulated. In this problem there are restrictions on some items and conveyances so that some specific items cannot be transported through some particular conveyances. With the critical value (CV)-based reductions of type-2 fuzzy variables, a chance-constrained programming model is formulated for the problem and then this model is converted to an equivalent deterministic form. Here, we propose a method to find nearest interval approximations for continuous type-2 fuzzy variables. A deterministic form for the problem is also obtained by applying interval analysis using the interval approximations of continuous type-2 fuzzy variables. The reduced deterministic problems are solved using a gradient based optimization – Generalized Reduced Gradient (GRG) technique (using LINGO solver) and Genetic Algorithm. Numerical example is provided to illustrate the problem and methods.

Design and optimization of machining fixture layout for end-milling operation

High product quality and productivity are the important objectives of manufacturing industries. They are greatly affected by the fixture layout design, and it requires modeling and analysis of fixture-workpiece interactions. In particular, the position of fixture elements has explicit influence on the deformation of the workpiece which needs to be minimized during machining. In order to ensure effective fixture layout design, the relationship between the position of fixture elements and workpiece deformation has to be modeled and optimized. In this research paper, workpiece deformation is modeled using response surface methodology. The developed model is tested for model adequacy, and the results obtained are matched with the simulated data. Then, it is used to minimize the workpiece deformation by determining the appropriate positions of locators and clamps using sequential approximation optimization and LINGO solver. It is found that integration of response surface methodology, with sequential approximation optimization, produces better results than LINGO solver.

Solving fuzzy p-hub center problem by genetic algorithm incorporating local search

The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel times, in which value-at-risk (VaR) criterion is adopted in the formulation of objection function. For trapezoidal and normal fuzzy travel times, we first turn the original VaR p-hub center problem into its equivalent parametric mixed-integer programming problem, then develop a hybrid algorithm by incorporating genetic algorithm and local search (GALS) to solve the parametric mixed-integer programming problem. In our designed GALS, the GA is used to perform global search, while LS strategy is applied to each generated individual (or chromosome) of the population. Finally, we conduct two sets of numerical experiments and discuss the experimental results obtained by general-purpose LINGO solver, standard GA and GALS. The computational results show that the GALS achieves the better performance than LINGO solver and standard GA.

Application of a hybrid simulated annealing-mutation operator to solve fuzzy capacitated location-routing problem

In the field of supply chain management and logistics, using vehicles to deliver products from depots to customers is one of the major operations. Before using vehicles, optimizing the location of depots is necessary in a location-routing problem (LRP). Also, before transportation products, optimizing the routing of vehicles is required so as to provide a low-cost and efficient service for customers. In this paper, the mathematical modelling of LRP is developed according to the existing condition and constraint in the real world. Maximum travelling time constraint is added, and we apply fuzzy numbers to determine customer demands, travelling time and drop time. The objective is to open a subset of depots to assign customers to these depots and to design vehicle routes, in order to minimize both the cost of open depots and the total cost of the routes. The proposed problem is modelled as a fuzzy linear programming (FLP), by applying the fuzzy ranking function method; the proposed FLP is converted to an exact linear programming (LP). A Lingo solver is used to solve this LP model in very small size. LRP is an non-deterministic polynomial-time hard (NP-Hard) problem, and because of the limitation of Lingo solver in solving medium, and large-size numerical examples, a hybrid algorithm including simulated annealing and mutation operator is proposed to solve these numerical examples. Also, a heuristic algorithm is proposed to find a suitable initial solution which is used in hybrid algorithm. At the end, a different analysis of the applied algorithm and a proposed model are introduced.

Genetic Algorithm Approach to a Multiobjective Land Allocation Model

Optimal land allocation plays a vital role for the development of agriculture sector. Development toward optimal utilization of land under cultivation and increasing the production of crops and profit with less fertilizer consumption must be taken into consideration in agriculture planning. In this paper, a weighted additive model is formulated with net profit, production of crops, and fertilizer consumption as objectives and availability of cultivable land, agriculture labour, agriculture machinery, and water as constraints for optimal land allocation. Weighted additive model takes care of relative priority of objectives laid by the agriculture planners. To illustrate the model, a case study of Visakhapatnam district, Andhra Pradesh, India is presented. The results of GA approach are compared with LINGO solver and observed that there is an improvement in the utilization of land.

Optimal Machining Parameters for Achieving the Desired Surface Roughness in Turning of Steel

Due to the widespread use of highly automated machine tools in the metal cutting industry, manufacturing requires highly reliable models and methods for the prediction of output performance in the machining process. The prediction of optimal manufacturing conditions for good surface finish and dimensional accuracy plays a very important role in process planning. In the steel turning process the tool geometry and cutting conditions determine the time and cost of production which ultimately affect the quality of the final product. In the present work, experimental investigations have been conducted to determine the effect of the tool geometry (effective tool nose radius) and metal cutting conditions (cutting speed, feed rate and depth of cut) on surface finish during the turning of EN-31 steel. First and second order mathematical models are developed in terms of machining parameters by using the response surface methodology on the basis of the experimental results. The surface roughness prediction model has been optimized to obtain the surface roughness values by using LINGO solver programs. LINGO is a mathematical modeling language which is used in linear and nonlinear optimization to formulate large problems concisely, solve them, and analyze the solution in engineering sciences, operation research etc. The LINGO solver program is global optimization software. It gives minimum values of surface roughness and their respective optimal conditions.

Solving a mixed-integer linear programming model for a multi-skilled project scheduling problem by simulated annealing

Article history: Received July 20, 2011 Received in Revised form October, 12, 2011 Accepted 15 October 2011 Available online 20 October 2011 A multi-skilled project scheduling problem (MSPSP) has been generally presented to schedule a project with staff members as resources. Each activity in project network requires different skills and also staff members have different skills, too. This causes the MSPSP becomes a special type of a multi-mode resource-constrained project scheduling problem (MM-RCPSP) with a huge number of modes. Given the importance of this issue, in this paper, a mixed integer linear programming for the MSPSP is presented. Due to the complexity of the problem, a metaheuristic algorithm is proposed in order to find near optimal solutions. To validate performance of the algorithm, results are compared against exact solutions solved by the LINGO solver. The results are promising and show that optimal or near-optimal solutions are derived for small instances and good solutions for larger instances in reasonable time. © 2012 Growing Science Ltd. All rights reserved.

A genetic algorithm based heuristic to the multi-period fixed charge distribution problem

This paper proposes a genetic algorithm (GA) based heuristic to the multi-period fixed charge distribution problem associated with backorder and inventories. The objective is to determine the size of the shipments, backorder and inventories at each period, so that, the total cost incurred during the entire period towards transportation, backorder and inventories is minimum. The model is formulated as pure integer nonlinear programming and 0–1 mixed integer linear programming problems, and proposes a GA based heuristic to provide solution to the above problem. The proposed GA based heuristic is evaluated by comparing their solutions with lower bound, LINGO solver and approximate solutions. The comparisons reveal that the GA generates better solutions than the approximate solutions, and is capable of providing solutions equal to LINGO solutions and closer to the lower bound value of the problems.

A genetic algorithm for simultaneous optimisation of lot sizing and scheduling in a flow line assembly

This paper considers flexible flow line assembly, which assembles various models of a single product. Lot sizing in procurement and production scheduling are considered as the two critical factors to control the cost of production in those units. The simultaneous optimisation of procurement lot sizing, and the assembly scheduling offer many benefits. Literature review has shown that only a little consideration is given to setup time dependent production system with order backlog. An integrated cost model including setup time dependency and order backlog is developed to handle both procurement lot sizing and production scheduling simultaneously. This paper proposes a genetic algorithm (GA) based heuristic to evolve optimal or near optimal solution for flow line assembly problem. LINGO Solver, an integer programming tool, is used to evaluate the performance of the proposed algorithm under independent setup time considerations. The comparison reveals that the proposed GA is able to give optimal or closer to optimal solutions. But the significance of GA is its capability of optimising the production sequence and the production quantity simultaneously under the setup dependent environment.

The research of online price quotation for the automobile parts exchange programme

With the lack of virgin materials and the growing concerns for the environment, there has been an ever growing interest in reusing old products. In this paper, an online price quotation model (OPQM) for the ‘exchange the new part with the old one’ is proposed. The main aim of OPQM is to minimise the exchange price, based on jointly optimising the disassembly and remanufacturing plan for the used part throughout the supply chain. The disassembly and remanufacturing plan problem, however, resembles a combinatorial problem, whose computation time to obtain an optimal solution increases exponentially in proportion to the size of the problem. Therefore, the authors propose an enhanced particle swarm optimisation (EPSO) method to generate a relatively good solution within a given time. Through a series of experiments with several benchmark methods, the proposed EPSO method is found to be superior to the conventional optimisation methods, such as LINGO solver, in time, and preferable to the traditional particle swarm optimisation (PSO) and genetic algorithm (GA) in quality.

Lumped Approach to a Multi-Period–Multi-Reservoir Cyclic Storage System Optimization

Cyclic storage system (CSS) refers to the joint development and operation of surface impoundment and subsurface subsystems with natural and physical interaction and a prespecified operating rule which manages the inter-relation between different components of the system. This paper presents a lumped modeling approach to a generalized large scale cyclic storage system. The model is capable to optimally design and operate a cyclic system in an irrigable area. The excitation units with pronounced impact and a complexity of the semi-distributed model are replaced with approximated lumped functions, while maintaining a desirable level of accuracy in the system’s performance in a long-term planning horizon. The proposed model has a MINLP structure, which is solved using powerful well-known LINGO solver. Design capacities of different components of the system and the associated operating rules parameters are considered as decision variables that minimize total cost of operating costs over the planning horizon. Extensive simulation runs show that the derived operating rules perform quite satisfactory with non-significant deficits over the entire horizon.

A GOAL PROGRAMMING MODEL FOR OPTIMIZING RELIABILITY, MAINTAINABILITY AND SUPPORTABILITY UNDER PERFORMANCE BASED LOGISTICS

Reliability, Maintainability and Supportability (R, M and S) are the main drivers of the system operational effectiveness (SOE). New procurement strategies have been developed by both public and private sectors to focus on the R, M and S characteristics inherent to the design of a system. One such strategy known as Performance Based Logistics (PBL) has gained popularity due to its success in improving the operational effectiveness of the system. In a PBL contract the customer buys performance, typically measured using R, M and S metrics, instead of contracting for a specified collection of resources defining the underlying support infrastructure. In this paper we have developed a mathematical model, using Goal Programming to optimize multiple performance measures of a design. We show how the best design is chosen from competing design alternatives when systems engineering principles are considered in defining the evaluation measures. The proposed mathematical model simultaneously considers multiple system engineering metrics during the design stage of the product development. The engineering metrics considered are a representation of the system's operational availability, reliability, maintainability, supportability and total cost of ownership. The Goal Programming model developed in the paper can be easily solved using software such as LINDO, LINGO and Excel Solver.