LINGO Solver Research Articles

Integrating resilience and reliability in semiconductor supply chains during disruptions

The semiconductor industry, a cornerstone of modern technology, has been crucial in driving globalization and supporting various sectors, from consumer electronics to automotive industries. However, in recent years, the industry has faced substantial challenges threatening its ability to meet the surging demand for semiconductor chips. Disruptions at any point in the supply chain, from raw material sourcing to end-product delivery, can substantially influence the semiconductor ecosystem. The intricate nature of such SCs makes them highly vulnerable to various disruptions, emphasizing the critical need for building resilient and reliable supply chain strategies. This article presents comprehensive research aimed at addressing critical gaps in the understanding and management of resilience and reliability within the semiconductor supply chain (SSC). This study proposes a multi-objective mixed-integer non-linear programming (MO-MINLP) model to configure an SSC while considering reliability and resilience measures. It emphasizes and draws attention to the importance of resilience and reliability in managing SSC disruptions during a pandemic and potential future epidemic outbreak. Exploring the precise breakdown of batch transportation between two sites shows how disruption can affect product flow along the SC. The applicability of the proposed method is demonstrated through a numerical example of an SSC, solved using the LINGO solver. Finally, a sensitivity analysis is conducted on the model's parameters to assess the capability and effectiveness of the results from managerial viewpoints.

A Comparative Study of Time and Cost Optimization in Project Management: Primavera P6 & Linear Programming with Lingo Solver

In an effort to boost efficiency and reduce costs, computer-based solutions have become more popular for project management. Although Primavera P6 and other traditional tools have proved essential for project planning and control, difficulties still arise with complicated projects. An innovative approach is provided by the development of mathematical optimization techniques, especially Linear Programming (LP) with programmes like Lingo Solver. The purpose of this study is to compare the time and cost optimization of Primavera P6 and Lingo Solver's LP. The goals are to analyse the advantages and disadvantages, evaluate the effectiveness and adaptability, and offer useful information to decision-makers. Application of Lingo Solver's LP is found to significantly reduce project duration, with a significant impact on cost trends. On the other hand, Primavera P6 shows that project duration can be reduced while maintaining the same level of cost. The study highlights how the duration of the project, additional indirect expenses, and costs interplay dynamically throughout the duration of the project. This research provides useful insights to the continuing discussion on project management methodologies by bridging the gap between conventional project management tools and advanced optimization techniques. This will help decision-makers overcome the complexities of project optimization for optimal results in practical applications. Key Words: Optimization, Construction project, Linear programming, Primavera p6, Lingo, Project management, Mathematical model, Time-cost trade-off.

A pentagonal type-2 fuzzy variable defuzzification model with application in humanitarian supply chains

Disasters can be caused by humans or natural hazards, and they impact the vulnerability of communities worldwide. This study considers disasters caused by humans, including the rescue operation taken post-accidents. The objective of the research is to minimise time and cost to save people’s lives in the early stages of rescue operations from the fuzzy logic perspective by proposing a novel pentagonal type-2 fuzzy variable (PT2FV) defuzzification method. The multi-objective multi-modal services at the crucial early hours of a disaster solve a solid transportation problem mathematically using a weighted sum method and neutrosophic compromise programming in Lingo solver software. The novelty of the research has been justified by the sensitivity analysis test on various levels of credibility at different intervals of PT2FV. The various credibility level intervals have also been discussed, and the best possible interval is suggested. The outcome suggests an effective plan for humanitarian relief in difficult areas using multiple modes of transit for delivery of reliefs, availing rescue team and saving of victims along with a notion of an efficient contingency planning.

Cost Effective Maintenance and Machine Reliability for Food Manufacturing Industries using Optimal Maintenance Strategy

An optimal maintenance strategy for cost effective maintenance and machine reliability in food manufacturing industries was developed in this study. Maintenance and cost parameters were employed to develop cost-reliability based model in terms of an optimal maintenance using lingo solver. The developed cost-reliabilitybased model considered system’s reliability, cost of equipment failure, preventive maintenance, corrective maintenance and downtime cost associated with - equipment maintenance. A case of a food manufacturing company in Nigeria was observed and the data wasused to evaluate the model. It is imperative to know that, the developed optimal maintenance strategy provided better cost savings and improved system reliability than the current maintenance cost and machine reliability of the industrial case study.

Sustainable multi-products delivery routing network design for two-echelon supplier selection problem in B2B e-commerce platform

This paper examines the environmental impact produced by multi-vehicle transportation on a sustainable supply chain (SC) network. The relevance of green principles is gaining momentum day by day, which has forced the governments to introduce carbon emission schemes for the transportation associated with the firms. Various countries around the globe are introducing carbon-pricing schemes, in which a carbon tax is imposed based on the amount of anthropogenic emissions. A firm, which sets environmental standards for the emission associated with its operational activities, should design a transportation network based on the trade-off between its economic efficiency and the carbon emission. In this paper, the main focus is to design a sustainable supply chain network. A mixed-integer-non-linear-programming (MINLP) model is formulated to minimize the overall cost incurred in a multi-vehicle, multi-product sustainable transportation network. The meta-heuristic approach i.e., Hybrid Chemical Reaction Optimization Algorithm with Tabu search (CRO-TS) and LINGO solver have been used to solve the proposed model. This analysis can guide the government to encourage the logistics service providers to capitalize on anthropogenic gas emission systems and simultaneously design the tax policy on carbon emission.

Solving the mixed-model assembly line balancing problem type-I using a Hybrid Reactive GRASP

ABSTRACT One of the most recent challenges that manufacturers confront is to respond on time to the variety of customers’ demands for different products. The Assembly line is the main element responsible for assembling products in manufacturing systems, and it requires good management to avoid several problems that could lead to production failures. The mixed-model assembly line balancing problem type-I (MiMALBP-I) occurs in the step of designing a new assembly line in which different models of one product are assembled in an intermixed sequence; it aims to optimize the number of workstations for a fixed known cycle time. In this paper, the authors propose a Hybrid Reactive Greedy Randomized Adaptive Search Procedure (HRGRASP) to solve this problem. The performance of the proposed algorithm is compared with those of the basic GRASP, heuristics based approach, and the Lingo solver using seven problems of different sizes.

Reconfiguring a multi-period facility model—An empirical test in a dynamic setting

Facility location is an important problem faced by companies in many industries. Finding an optimal location for facilities and determining their size involves the consideration of many factors, including proximity to customers and suppliers, availability of skilled employees and support services, and cost-related factors, for example, construction or leasing costs, utility costs, taxes, availability of support services, and others. The demand of the surrounding region plays an important role in location decisions. A high population density may not necessarily cause a proportional demand for products or services. The demography of a region could dictate the demand for products, and this, in turn, affects a facility’s size and location. The location of a company’s competitors also affects the location of that company’s facilities. Another important aspect in facility location modeling is that many models focus on current demand and do not adequately consider future demand. However, while making location decisions in an industry in decline, carefully and accurately considering future demand is especially important, and the question in focus is whether to shrink or close down certain facilities with the objective of keeping a certain market share or maximizing profit, especially in a competitive environment. This paper develops a model which enables companies to select sites for their businesses according to their strategy. The model analyzes the strategic position of the company and forms a guideline for the decision. It investigates which facilities should be closed, (re)opened, shrunk, or expanded. If facilities are to shrink or expand, the model also determines their new capacities. It depicts the impact on market share and accounts for the costs of closure and reopening. A number of papers deal with location theory and its applications, but few have been written for modeling a competitive environment in the case of declining demand. Existing papers in this area of research are mostly static in nature, do not offer multi-period approaches, nor do they incorporate the behavior of competitors in the market. To demonstrate the validity of the model, it is first solved using a small problem set–three facilities, three demand locations, and three periods–in LINGO solver. To get a better understanding of the model’s behavior, several additional scenarios were constructed. First, the number of demand locations was extended to 10. Our findings show that the model presented provides an extension of existing facility location models that can be applied to a variety of location problems in commercial and industry sectors that need to make their decisions considering future periods and competitors. The developed heuristic shows multiple options for solving the problem, including their advantages and disadvantages, respectively. The Java code and LINGO fragments thus developed can be used to provide easy access to related problems.

MODEL OF VEHICLE ROUTING PROBLEM WITH SPLIT DELIVERY, MULTI TRIPS, MULTI PRODUCTS AND COMPARTMENTS FOR DETERMINING FUEL DISTRIBUTION ROUTES

The industrial development in Indonesia encourages companies to have high sensitivity in competing to meet consumer demands promptly by considering minimum distribution costs. One of the factors that can affect distribution costs is route determination. Determining the distribution route is the Vehicle Routing Problem (VRP). The purpose of VRP is to arrange the order of distribution routes to produce a minimum total distance. This study aims to determine the fuel distribution route at TBBM Rewulu in one delivery period to obtain the optimal distribution route and minimize the vehicle mileage. Delivery is carried out using three types of tanker trucks with heterogeneous capacities. This study uses a mathematical model of Mixed Integer Linear Programming (MILP) by considering split delivery, multi trips, multi-products, and compartments.The branch and bound method in the LINGO solver has been used to solve this problem. This model was tested on a simple case using data of 8 customers with different distances and demand shipped by truck. The results obtained indicate that no boundaries are violated, and all consumers are served. The mathematical model built is still general, so it can solve similar cases. A model can be developed for further research by adding VRP variants such as time windows and adding the product types to represent the entire existing system.

ANALISIS MODEL TRANSSHIPMENT DALAM PROSES DISTRIBUSI PRODUK SEMEN DI CV BANGUN KREASI ABADI

Bangun Kreasi Abadi is one of the distributors working with PT. Jui Shin Indonesia in marketing and distributing Garuda cement products to several regions in West Java, especially the city of Bandung. In the distribution process, CV Bangun Kreasi Abadi does not send its cement products directly to consumers, but CV. Bangun Kreasi Abadi uses two warehouses as transit points for the delivery of cement products for several regions. The transshipment method has several problems because in the distribution process, products are not sent directly to consumers but must pass through several transit points first. This will result in large costs because the delivery process will be twice as long and will also result in a longer lead time. This study aims to determine the optimal allocation of Garuda cement distribution to produce minimum transportation costs from distributors to warehouses and from warehouses to service points (retailers) using the Transshipment method with the help of Lingo Solver Software. The result of transportation costs from distributors to warehouses is Rp. 25,655,900 and transportation costs from warehouses to retailers of Rp. 26,140,220, the total cost of Garuda cement distribution is Rp. 51,796,120.

Reconfiguring a Multi-period Facility Model – An Empirical Test in a Dynamic Setting

Facility location is an important problem faced by companies in many industries. Finding an optimal location for facilities and determining their size involves the consideration of many factors, including proximity to customers and suppliers, availability of skilled employees and support services, and cost-related factors, for example, construction or leasing costs, utility costs, taxes, availability of support services, and others. The demand of the surrounding region plays an important role in location decisions. A high population density may not necessarily cause a proportional demand for products or services. The demography of a region could dictate the demand for products, and this, in turn, affects a facility’s size and location. The location of a company’s competitors also affects the location of that company’s facilities. Another important aspect in facility location modeling is that many models focus on current demand and do not adequately consider future demand. However, while making location decisions in an industry in decline, carefully and accurately considering future demand is especially important, and the question in focus is whether to shrink or close down certain facilities with the objective of keeping a certain market share or maximizing profit, especially in a competitive environment.<br /> This paper develops a model which enables companies to select sites for their businesses according to their strategy. The model analyzes the strategic position of the company and forms a guideline for the decision. It investigates which facilities should be closed, (re)opened, shrunk, or expanded. If facilities are to shrink or expand, the model also determines their new capacities. It depicts the impact on market share and accounts for the costs of closure and reopening. A number of papers deal with location theory and its applications, but few have been written for modeling a competitive environment in the case of declining demand. Existing papers in this area of research are mostly static in nature, do not offer multi-period approaches, nor do they incorporate the behavior of competitors in the market. To demonstrate the validity of the model, it is first solved using a small problem set – three facilities, three demand locations, and three periods – in LINGO solver. To get a better understanding of the model’s behavior, several additional scenarios were constructed. First, the number of demand locations was extended to 10. Our findings show that the model presented provides an extension of existing facility location models that can be applied to a variety of location problems in commercial and industry sectors that need to make their decisions considering future periods and competitors. The developed heuristic shows multiple options for solving the problem, including their advantages and disadvantages, respectively. The Java code and LINGO fragments thus developed can be used to provide easy access to related problems.

Risk Analysis Method of Cascade Plants Operation in Medium Term Based on Multi-Scale Market and Settlement Rules

Due to the distribution of runoff is uneven and uncertain in time and space, there are huge differences between the electricity markets dominated by hydropower and thermal power. Therefore, how to evaluate the risk of cascade plants participating in electricity market is an urgent problem to be solved. Based on the rules of the market in southwest China which hydropower plays a leading role, this paper proposes a risk analysis method for cascade hydropower to participate in market which is coupled with monthly market and day-ahead market: Copula-Monet Carlo is used to generate the combined scenario of daily runoff and daily clearing price, and the LINGO solver is used to calculate the generation income of all scenarios, and the corresponding conditional value-at-risk value(CVaR) of portfolio is obtained according to the confidence level. The method takes into account the uncertainty of runoff and electricity price in the meantime, as well as the settlement order and deviation assessment of each market in the settlement rules, and can directly solve the income and risk value. The process is simple and the physical meaning is clear. Using the actual data of a grid cascade hydropower participating in the electricity market as an example, the simulation analysis of the results shows that the proposed method can easily solve the portfolio risk value, and can more reasonably evaluate the risk value compared with the considering runoff and day-ahead market clearing prices separately.

Greedy iterative genetic algorithm for the volume-based cross dock transportation problem associated with fixed charge

Cross docking is a distribution method wherein the products from inbound vehicles are loaded directly onto outbound vehicles with a minor or no storage in between. The fixed charge cross dock transportation problem (FCCDTP) involves determining the optimal method of loading and routing the vehicles in a cross dock system with minimal fixed and variable cost of transportation. In this paper, the FCCDTP with the volume-based quantification of products is formulated as a mixed integer linear programming model. The model is solved using the optimisation software LINGO solver, the proposed GA with variable neighbourhood search (GA-VNS) meta-heuristic and the proposed greedy iterative genetic algorithm (GIGA) meta-heuristic. The data for the problems are obtained from a real-life logistics company. The analysis of results reveals that the proposed GIGA meta-heuristic provides lesser total transportation cost as compared to the GA-VNS meta-heuristic.

Greedy iterative genetic algorithm for the volume based cross dock transportation problem associated with fixed charge

Cross docking is a distribution method wherein the products from inbound vehicles are loaded directly onto outbound vehicles with a minor or no storage in between. The fixed charge cross dock transportation problem (FCCDTP) involves determining the optimal method of loading and routing the vehicles in a cross dock system with minimal fixed and variable cost of transportation. In this paper, the FCCDTP with the volume-based quantification of products is formulated as a mixed integer linear programming model. The model is solved using the optimisation software LINGO solver, the proposed GA with variable neighbourhood search (GA-VNS) meta-heuristic and the proposed greedy iterative genetic algorithm (GIGA) meta-heuristic. The data for the problems are obtained from a real-life logistics company. The analysis of results reveals that the proposed GIGA meta-heuristic provides lesser total transportation cost as compared to the GA-VNS meta-heuristic.

Research on Multi-Time Scale Optimization Strategy of Cold-Thermal-Electric Integrated Energy System Considering Feasible Interval of System Load Rate

The integrated energy system coupling multi-type energy production terminal to realize multi-energy complementarity and energy ladder utilization is of great significance to alleviate the existing energy production crisis and reduce environmental pollution. In this paper, the topology of the cold-thermal-electricity integrated energy system is built, and the decoupling method is adopted to analyze the feasible interval of load rate under the strong coupling condition, so as to ensure the “source-load” power balance of the system. Establishing a multi-objective optimization function with the lowest system economic operation and pollution gas emission, considering the attribute differences and energy scheduling characteristics of different energy sources of cold, heat and electricity, and adopting different time scales to optimize the operation of the three energy sources of cold, heat and electricity, wherein the operation periods of electric energy, heat energy and cold energy are respectively 15 min, 30 min and 1 h; The multi-objective problem is solved by standard linear weighting method. Finally, the mixed integer nonlinear programming model is calculated by LINGO solver. In the numerical simulation, the hotel summer front load parameters of Zhangjiakou, China are selected for simulation and compared with a single time scale system. The simulation results show that the multi-time scale system reduces the economic operation cost by 15.6% and the pollution gas emission by 22.3% compared with the single time scale system, it also has a wider feasible range of load rate, flexible time allocation, and complementary energy selection.

An upper bound of radio k-coloring problem and its integer linear programming model

For a positive integer k, a radio k-coloring of a simple connected graph G = (V(G), E(G)) is a mapping $$f:V(G) \to \{ 0,1,2, \ldots \}$$ such that $$|f(u) - \,f(v)| \ge k + 1 - d(u, \, v)$$ for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer assigned by it to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this paper, we propose an improved upper bound of radio k-chromatic number for a given graph against the other which is due to Saha and Panigrahi (in: Arumugan, Smyth (eds) Combinatorial algorithms (IWOCA 2012). Lecure notes in computer science, vol 7643, Springer, Berlin, 2012). The computational study shows that the proposed algorithm overcomes the previous algorithm. We introduce a polynomial algorithm [differs from the other that is due to Liu and Zhu (SIAM J Discrete Math 19(3):610–621, 2005)] which determines the radio number of the path graph Pn. Finally, we propose a new integer linear programming model for the radio k-coloring problem. The computational study between the proposed algorithm and LINGO solver shows that the proposed algorithm overcomes LINGO solver.

The consideration of opened facilities' operational volumes in designing supply chain network

In this paper, we deal with single-item, multi-period, two-echelon capacitated facility location problems where manufacturing plants and distribution centres (DCs) are decided to be opened or not at the pre-determined potential sites. At each opened facility, our model controls operational level over or under its minimum requirement volume. To do that, we use the big M technique to detect running status. If the opened facility runs at lower minimum requirement volume, penalty cost will occur and add to objective value, which should be as low as possible. This information helps the investors and managers to evaluate performance of their supply chain (SC) network system. The problem is formulated as a mixed integer linear programming (MILP) model with the objective to minimise the total cost including transportation costs, production costs, inventory holding costs, fixed costs for opening facilities, and penalty costs. Based on the specific structure of the developed model, we need one additional constraint set before using Lagrangian relaxation algorithm to solve the problem. Numerical experiments are then conducted to compare the solution of the proposed approach and the optimal solution obtained by the commercial lingo solver.

Economic order quantity for joint complementary and substitutable items

In real-world situations, substitution may occur in the event of a product stock-out, and some products are complements with others. However, the classical inventory models ignore these conditions. This paper addresses an economic order quantity (EOQ) model to determine the joint ordering policy for two products under completion and substitution conditions. The proposed model determines order quantities for two products in order to optimize the total cost of inventory, including setup and holding costs. To formulate the problem, two special cases are discussed and analyzed in detail. Furthermore, the pseudo-convexity of the total cost functions is derived, and then a solution procedure is suggested. Numerical examples are presented and an analysis of sensitivity is conducted, using Matlab and Lingo solver, in order to investigate the impact of input parameters on the optimal policy. The results show that proposed model saves the costs as opposed to the traditional EOQ model.

A mixed-integer linear formulation for a capacitated facility location problem in supply chain network design

In this research, we deal with a multi-item, multi-period, two-echelon capacitated facility location problem. With every period in horizon planning, manufacturing plants and distribution centres are decided to open or not at predetermined potential sites. The developed model is formulated as a mixed integer linear programming (MILP) model with the objective of minimising the total cost, including transportation cost, inventory holding cost, and fixed costs for opening facilities. We employ a Lagrangian relaxation algorithm for solving the developed model. Before decomposition into sub-problems, the initial structure of developed model is modified, three additional constraint sets add to two sub-problems, and these are the key differences of our algorithm. For validation testing, some numerical experiments are used for solving, and the solutions obtained from the Lagrangian relaxation algorithm are respectively compared with the solutions obtained by the LINGO solver. With good achievements of this research, our proposed model can be applied and the proposed approach is an advantage for getting the specific solutions.

Design and development of a hybrid ant colony-variable neighbourhood search algorithm for a multi-depot green vehicle routing problem

The traditional distribution planning problem in a supply chain has often been studied mainly with a focus on economic benefits. The growing concern about the effects of anthropogenic pollutions has forced researchers and supply chain practitioners to address the socio-environmental concerns. This research study focuses on incorporating the environmental impact on route design problem. In this work, the aim is to integrate both the objectives, namely economic cost and emission cost reduction for a capacitated multi-depot green vehicle routing problem. The proposed models are a significant contribution to the field of research in green vehicle routing problem at the operational level. The formulated integer linear programming model is solved for a set of small scale instances using LINGO solver. A computationally efficient Ant Colony Optimization (ACO) based meta-heuristic is developed for solving both small scale and large scale problem instances in reasonable amount of time. For solving large scale instances, the performance of the proposed ACO based meta-heuristic is improved by integrating it with a variable neighbourhood search.

A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem

Abstract To better reflect the uncertainty existing in the actual disassembly environment, the multi-objective disassembly line balancing problem with fuzzy disassembly times is investigated in this paper. First, a mathematical model of the multi-objective fuzzy disassembly line balancing problem (MFDLBP) is presented, in which task disassembly times are assumed as triangular fuzzy numbers (TFNs). Then a Pareto improved artificial fish swarm algorithm (IAFSA) is proposed to solve the problem. The proposed algorithm is inspired from the food searching behaviors of fish including prey, swarm and follow behaviors. An order crossover operator of the traditional genetic algorithm is employed in the prey stage. The Pareto optimal solutions filter mechanism is adopted to filter non-inferior solutions. The proposed model after the defuzzification is validated by the LINGO solver. And the validity and the superiority of the proposed algorithm are proved by comparing with a kind of hybrid discrete artificial bee colony (HDABC) algorithm using two test problems. Finally, the proposed algorithm is applied to a printer disassembly instance including 55 disassembly tasks, for which the computational results containing 12 non-inferior solutions further confirm the practicality of the proposed Pareto IAFSA in solving the MFDLBP.