Nonlinear Goal Programming Model Research Articles

Nonpre-Emptive Integer Nonlinear Goal Programming Model for Multi-Item Inventory Problem: Case Study of a Car Retail Centre in Lagos State.

Most of the real-world optimization problems involve multiple objectives with constraint resources. Retailers oftentimes anticipate demand, they stock, and maintain warehouses with different variety of products at high cost to meet prospecting customers' demand. In this paper, a Non-preemptive Integer Nonlinear Goal Programming (NINGP) model was developed for obtaining Economic Order Quantities (EOQ) of multi-item inventory problems that satisfy the multiple and conflicting objectives of the Decision Maker (DM). The particular case considered was that of a motor vehicle dealer who sells 10 brands of Tokunbo vehicles and wants to determine the EOQ for each brand such that the deviations from the aspiration level are minimized. Using LINGO 17.0 Software to solve the NINGP model, the EOQ allocated to each brand type from 1 through 10 are 2, 2, 5, 2, 2, 3 3, 3, 3, and 3 cars respectively. The optimal number of cars was 28 with the associated cost of ₦53,825,915. Compared to the estimated budget of ₦60,000,000, the NINGP approach was able to achieve a 10% (₦6,174,085) below budget. With proper modifications considering the associated constraints, related inventory problems can be solved using the NINGP model.

Introducing a New Approach in Stand Tending Planning and Thinning Block Designation by Using Mixed Integer Goal Programming

Long-term management plans have been developed for nearly all of the forests in Turkey. These plans are applied at a sub-district management unit level and may contain guidance for both intermediate yield and final yield harvests. To implement an intermediate yield plan, which involves the scheduling of forest thinnings (stand tending), consideration in Turkey is given to the advantages of working in the same terrain and the same general area each year. Therefore, compartments are often clumped together to create thinning blocks, taking into consideration the thinning priority of the stands, road conditions, site index, age, and proximity of the compartments. Further, when preparing annual budgets and planning to meet the market’s needs, forest enterprises require an even flow of intermediate wood volume each year. In this paper, we introduce a new approach in stand tending planning designed to schedule an equal amount of intermediate wood volume each year and to create thinning blocks by minimizing the distance to pre-defined ramps (landings). We developed both linear and nonlinear goal programming models to minimize both the deviations from a harvest volume (annual intermediate yield allowable cut) target and the deviations from a target value determined for the distances (total and average) of the centroid of each compartment to the hypothetical forest ramps. By using the extended version of Lingo 16, we solved the problem with different weights for the deviations in volume and distance that ranged from 0.0 to 1.0, in 10% intervals, which created 11 scenarios. We carefully analyzed the results of each scenario by taking into consideration the wood volume and distance of compartments to the ramps. The best scenario using the linear model produced a deviation in volume scheduled for the entire decade of 6 m3, while the deviation in total distance between harvest areas and ramps was 59.7 km. Scenario 5, with weights of 0.6 for volume and 0.4 for distance, produced these results, where compartments were closest to one another. The best scenario using the nonlinear model also produced a deviation in volume of 0 m3 and the total average deviation in distance between harvest areas and ramps was 8.7 km. Scenario 3, with weights of 0.8 for volume and 0.2 for distance, produced these results. The approach and models described through this study may be appropriate for further integration into forest management planning processes developed for the planning of Mediterranean forests.

Operational mine planning in block cave mining: a simulation-optimisation approach

ABSTRACT Block cave mining operations face challenges to meet daily operational production targets. The optimistic long-term and medium-term plans along with uncertainty and the synergistic effect of the mechanical and structural failures in operational levels of the mine cause a significant deviation from production plan targets. The on-site tuning of the mining production targets in real time are neither the best practice nor the optimum approach to compensate for shortfalls in production. The objective of this paper is to develop a methodology that generates practical and near-optimal short-term mine plans for block caving operations in the presence of operational uncertainty. To accomplish this goal, we propose a simulation-optimisation approach using a Monte Carlo simulation model and a multi-objective non-linear goal programming model that takes into consideration operational constraints and uncertainties. In a case study, we compare the results of the proposed methodology against the mine plan and the historical production data of a copper block cave operation. The strengths and weaknesses of the model are presented and discussed.

A decision support model for risk management of hazardous materials road transportation based on quality function deployment

Risk management of hazardous materials (hazmats) road transportation has long been a concern because of the potential hazards that poses to society and the environment. In this work, a systematic and semi-quantitative decision support framework for risk management of hazmats road transportation based on the combination of quality function deployment (QFD), fuzzy analytic hierarchy process (F-AHP), fuzzy failure mode and effect analysis (F-FMEA), and nonlinear goal programming is proposed. The QFD is used innovatively to construct the overall framework, which contains three main components of general risk management: risk identification, risk assessment, and risk control. The F-AHP is used to build a hierarchical risk assessment system and determine the importance rating of each risk factor. The F-FMEA is used to evaluate the potential risks of risk control measures and determine the risk adjustment coefficient of each risk measure, which is used subsequently to modify the fulfillment level of risk measure in the nonlinear goal programming model. To address the inherent vagueness and uncertainty contained in the risk management process, the fuzzy set theory is introduced as an effective tool. An empirical case on risk management of a hazmats transportation company is presented to demonstrate the effectiveness and feasibility of the proposed methodology. Some managerial implications on risk management of hazmats road transportation are provided based on the obtained findings.

Mathematical Nonlinear Goal Programming in Quality Control

This paper concerned with applying suggested mathematical programming and nonlinear goal programming models to determine the producer's risk (α), consumer's risk (β) and acceptance level (c) simultaneously. The suggested nonlinear goal programming model allowed α and β values to be free and determined their values more accurately which make balance between the power of a statistical test (1-β) and level of significance α. Real quality control data are used to evaluate the performance of the suggested models . This enables decision makers in quality control to develop more accurate and free acceptance sampling plans.

Weapon target assignment optimization for land based multi-air defense systems: A goal programming approach

This study addressed the issue of allocating the air defense missiles to incoming air targets to maximize the air defense effectiveness of land-based air defense systems. A constraint based nonlinear goal programming (multi-objective) model for weapon assignment problem to minimize survival probability was developed. The model not only gave optimum assignment but also resulted in engagement times and defense success for multi-defense sites. The model utilized parameters belonging to defense systems such as engagement duration, setup duration between engagements, command and control structures, fire doctrines, and defense strategies and parameters belonging to target such as probability of kill values, position, orientation, weapon load, target type, and course of actions inferred by current detection information. The simulation model has two-way usages. In the first usage, it obtains solution for the parameters given above under limited number of missiles. In the second usage, the model shows the amount of missile to be used to achieve the possible highest success with the parameters given above. To be able to use the optimization model in a simulation environment, a simulation model as an optimizer agent is developed and located in air defense simulation scenarios. The model collects input data, optimize assignments, calculates fire times, and schedules fire orders. This solution is exemplified by a land-based air defense example.

A nonlinear goal programming model for determining the bias parameters of Liu-type estimator with application to construction sector in Egypt

A nonlinear goal programming model for determining the bias parameters of Liu-type estimator with application to construction sector in Egypt

An Evolutionary Firefly Algorithm, Goal Programming Optimization Approach for Setting the Osmotic Dehydration Parameters of Papaya

An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established via a response surface technique with the resulting optimization formulation being a non-linear goal programming model. For optimization, a computationally efficient, FA-driven method is employed and the resulting solution is shown to be superior to those from previous approaches for determining the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this evolutionary metaheuristic approach over a range of the two key parameters that most influence its running time-the number of iterations and the number of fireflies. This sensitivity analysis revealed that for intermediate-to-high values of either of these two key parameters, the FA would always determine overall optimal solutions, while lower values of either parameter would generate greater variability in solution quality. Since the running time complexity of the FA is polynomial in the number of fireflies but linear in the number of iterations, this experimentation shows that it is more computationally practical to run the FA using a “reasonably small” number of fireflies together with a relatively larger number of iterations than the converse.

A Multistage Procedure for Optimal Distribution of Preparatory-Year Students to Faculties and Departments: A Mixed Integer Nonlinear Goal Programming Model with Enhanced Differential Evolution Algorithm

A Multistage Procedure for Optimal Distribution of Preparatory-Year Students to Faculties and Departments: A Mixed Integer Nonlinear Goal Programming Model with Enhanced Differential Evolution Algorithm

A nonlinear goal-programming-based DE and ANN approach to grade optimization in iron mining

This study proposes a combined `nonlinear goal-programming'-based `differential evolution' (DE) and `artificial neural networks' (ANN) methodology for grade optimization in iron mining production processes. The nonlinear goal-programming model has decision variables of `cutoff grade,' `dressing grade' and `concentrate grade,' with the goals being `concentrate output,' `resource utilization rate' and `economic benefit (profit).' The model, which contains three unknown functions, the `loss rate,' the `ore-dressing metal recovery rate' and the `total cost,' is subsequently converted into an unconstrained optimization problem, to be solved by our integrated DE---ANN approach. DE is used to search for the optimum combination of the cutoff, dressing and concentrate grades, with the crossover rate in the DE analysis being dynamically adjusted within the evolutionary process. The loss rate is calculated by a regression model, whilst the ore-dressing metal recovery rate and the total cost functions are, respectively, calculated using `back-propagation' and `radial basis function' neural networks. We subsequently go on to analyze a case study of the Daye iron mine in China to demonstrate the reliability and efficiency of our proposed approach. Our study provides a novel approach for decision makers to guide production and management in iron mining.

Generalized Linguistic Ordered Weighted Hybrid Logarithm Averaging Operators and Applications to Group Decision Making

In this paper, we develop the generalized linguistic weighted logarithm averaging (GLWLA) operator and the generalized linguistic ordered weighted logarithm averaging (GLOWLA) operator in the group decision making under the linguistic surrounding. Then some properties of the families of the GLOWLA operator by different weighting vector are investigated. Furthermore, we present the generalized linguistic ordered weighted hybrid logarithm averaging (GLOWHLA) operator, which extends the GLOWLA operator. We also construct a nonlinear goal programming model to determine GLOWHLA weights from observational linguistic variable values under partial weight information. Finally, a numerical example is given to illustrate the new approach to evaluating university faculty for tenure and promotion, which indicates the feasibility and effectiveness of the new approach.

Using mixed integer multi-objective goal programming for stand tending block designation: A case study from Turkey

Sustainable forest management is a key to maintaining the economic, social, environmental and cultural benefits and services of forests for the long term. In Turkey, all forestry activities, such as regeneration and stand tending, are carried out according to forest management plans, which are used as a tool for achieving sustainable forest management goals. An intermediate yield harvest plan, which is a part of management plan, is used for stand tending. Every year, the compartments (stands) within the same stand tending block are thinned. Decision support systems have not been used so far in order to designate the size and location of these stand tending blocks. In this study, we used multi-objective goal programming to designate stand tending blocks for an entire decade. We developed two models: a linear goal programming model and a nonlinear goal programming model. To design these models, we only considered wood flow and distance between the centroids of compartments as the objectives. Then, we used a working circle of the Golcuk forest sub-district, which is a planning unit in Turkey, as a case study. The linear model worked very well, and for reference scenarios, the deviation in volume scheduled for the entire decade was only 16.8m3 and the deviation in total distance between compartments was 172km. Scenario 3, with weights of 0.2 for distance and 0.8 for volume, produced the best results. The nonlinear model, which in theory would better represent the problem, was not as useful due to a combination of the time required to produce a solution and the quality of the solutions. The linear model can be developed by including other factors and used by forest planners.

A Nonlinear Goal Programming Model for University Admission Capacity Planning with Modified Differential Evolution Algorithm

This paper proposes a nonlinear Goal Programming Model (GPM) for solving the problem of admission capacity planning in academic universities. Many factors of university admission capacity planning have been taken into consideration among which are number of admitted students in the past years, total population in the country, number of graduates from secondary schools, desired ratios of specific specialties, faculty-to-students ratio, and the past number of graduates. The proposed model is general and has been tested at King Abdulaziz University (KAU) in the Kingdom of Saudi Arabia, where the work aims to achieve the key objectives of a five-year development plan in addition to a 25-year future plan (AAFAQ) for universities education in the Kingdom. Based on the results of this test, the proposed GPM with a modified differential evolution algorithm has approved an ability to solve general admission capacity planning problem in terms of high quality, rapid convergence speed, efficiency, and robustness.

A Simulation-Based Nonlinear Goal Programming Model for Groundwater Remediation Systems Design

A Simulation-Based Nonlinear Goal Programming Model for Groundwater Remediation Systems Design

A Parametric Testing Of The Firefly Algorithm In The Determination Of The Optimal Osmotic Drying Parameters Of Mushrooms

Abstract The Firefly Algorithm (FA) is employed to determine the optimal parameter settings in a case study of the osmotic dehydration process of mushrooms. In the case, the functional form of the dehydration model is established through a response surface technique and the resulting mathematical programming is formulated as a non-linear goal programming model. For optimization purposes, a computationally efficient, FA-driven method is used and the resulting optimal process parameters are shown to be superior to those from previous approaches. The final section of this study provides a computational experimentation performed on the FA to analyze its relative sensitivity over a range of the two key parameters that most influence its running time.

Logistic Planning with Nonlinear Goal Programming Models in Spreadsheets

This is a case study of a coal mining company to demonstrate how algebra principles and nonlinear goal programming can be applied for logistics planning using spreadsheet software. The paper asserts that mathematical programming techniques are not well-accepted by managers because the models are difficult to understand due to abstract notational conventions yet alternative commercial software is inflexible (and sometimes inaccurate). The relevant operations research literature was reviewed, highlighting techniques applicable for analyzing quantitative and qualitative logistics data. A practical supply-demand transportation logistics model was built which included determinist constraints and stochastic costing theories, while applying both linear and nonlinear calculus slope principles. The formulae were explained in algebraic standard form (citing corresponding spreadsheet functions). The logistics problem was optimized, illustrating how 6 mining sites could supply 4 countries with sufficient coal to meet different electricity demand levels, surpassing the break-even goal and projecting annual revenue of over $34 billion.

A weighted goal programming approach for replenishment planning and space allocation in a supermarket

We propose a mixed integer non-linear goal programming model for replenishment planning and space allocation in a supermarket in which some constraints on budget, space, holding times of perishable items, and number of replenishments are considered and weighted deviations from two conflicting objectives, namely profitability and customer service level, are minimized. We apply a minimum–maximum approach to introduce demand where the maximum demand is a function of price change and allocated space. Each item is presented in the form of multiple brands, probably exposed to price changes, competing to obtain more space. In addition to inventory investment costs, replenishment costs, and inventory holding costs we also include costs related to non-productive use of space. The order quantity, the amount of allocated showroom and backroom spaces, and the cycle time of joint replenishments are key decision variables. We also propose an extended model in which price is a decision variable. Finally we solve the model using LINGO software and provide computational results.

A fuzzy goal programming approach for mid-term assortment planning in supermarkets

We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.

Method for multi-attribute group decision-making based on the compromise weights

Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete. In group decision analysis, if preference information about alternatives is provided by participants, it should be verified whether there exist compromise weights that can support all the preference relations. The different compromise weight vectors may differ for the ranking of the alternatives. In the case that compromise weights exist, the method is proposed to find out all the compromise weight vectors in order to rank the alternatives. Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences, dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation. The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences. A final ranking of the alternatives can be obtained by aggregating these dominance relations.

A multiobjective model for forest planning with adjacency constraints

This work presents a nonlinear goal programming model with binary variables used to plan the management of a tree plantation, taking economic and environmental objectives into account. The aims are to stay within the limits of a given harvesting volume, limit the age of basic units targeted for clearcutting, obtain a forest with a balanced age distribution, and surpass the minimum net present value set at each planning period. This has to be achieved bearing in mind technical restrictions regarding treatments, and spatial adjacency constraints that limit the maximum adjacent surface area to which clearcutting can be applied. The outcome is a highly complex problem that is solved by applying a metaheuristic method based on Scatter Search. The proposed model has been validated by applying it to a Cuban plantation located in the region of Pinar del Rio.