Mixed Integer Goal Programming Model Research Articles

A MIXED INTEGER GOAL PROGRAMMING (MIGP) MODEL FOR DONATED BLOOD TRANSPORTATION PROBLEM – A PRELIMINARY STUDY

Blood Supply Chain (BSC) concerns with flow of blood products from blood collection by donors to transfusion of blood components to patients. BSC comprises of collection, testing, processing, storage, distribution and transfusion activities, which are normally responsibility of Blood Centre and hospitals. In Malaysia, National Blood Centre (PDN) is responsible to organize blood donation, collection and processing. Current procedure practised by PDN is to have vehicles sending staffs and equipment while one vehicle is assigned to collect donated blood from donation sites and transport the blood to PDN within six hours. As consequence, vehicles shortages are encountered and resources optimization unachieved especially when many blood donation sites involved per day. This paper presents the results of a preliminary study which aims at proposing blood collection optimal routes for blood collecting vehicles that adhere to all pre-determined time windows for blood collection at blood donation sites. A Mixed Integer Goal Programming (MIGP) model based on Vehicle Routing Problem with Time Windows (VRPTW) has been formulated. The MIGP model pursues four goals, namely, to minimize total distance travelled, to minimize total travel time, to minimize total waiting time of vehicles and to minimize number of vehicles (routes). The model was solved using preemptive goal programming approach and existing heuristics for the VRPTW. Based on the results, it can be concluded that the donated blood can be collected and transported using reduced number of vehicles as proposed by the MIGP model’s optimal compared to the total number of vehicles used by current practice, Thus, the proposed VRPTW based MIGP model has promising significant impact for donated blood transportation in terms of resources optimization and costs savings. The model and approach could be easily extended to solve larger problem involving large number of donation sites with variants of time windows for the sites.

Using Mixed Integer Goal Programming in Final Yield Harvest Planning: A Case Study from the Mediterranean Region of Turkey

A mixed integer goal programming model is developed to address the regeneration planning problems of even-aged forests in the Mediterranean region of Turkey. The unique aspect of the goal programming formulation is to minimize deviations in scheduled wood product volumes and the size of harvest areas within each time period, as these are important goals for the management area. About 98% of the forests in Turkey are considered even-aged, and 2% are uneven-aged. Therefore, an age class method is used for the planning of even-aged forests. For the areas where this method is applied, reaching the optimal age class structure is the first priority. This involves implementing final harvests (clearcuts) to regenerate an amount of forest area into each age class. To meet the local market’s needs, forest enterprises also require the final yield to be fairly equal each year. Further, it is desired that the harvest area (regeneration area) is relatively equal each year, to address operational considerations. A linear goal programming model is developed to address the problem. The minimization of deviations from both the harvest area and harvest volume targets are incorporated as goals in the objective function of the model. Several scenarios are solved using the extended version of Lingo 16. A scenario with weights of 0.8 for area and 0.2 for volume produces the best results. Here, the total deviation for 20 years is 3.8 ha in area and 2889 m3 in volume. In the actual regeneration plan, the area deviation for 10 years is 54.72 ha (6.2% of total regeneration area), and the volume deviation is 20,472 m3 (9.8% of harvest volume). The model described through this study can be developed further and integrated into forest management planning software and processes used for the planning of even-aged forests in the Mediterranean region.

Estimating the farm-level economic costs of spring cropping to manage Alopecurus myosuroides (black-grass) in UK agriculture

AbstractCrop rotation is a non-chemical strategy adopted by farmers to manage weeds. However, not all crops in a rotation are equally profitable. Thus, there is potentially a trade-off between the costs and benefits of this strategy. The objective of the current study is to quantify this trade-off for the rotational control of an important weed (Alopecurus myosuroides). Data from 745 farms were used to parameterize a farm-level mixed-integer goal-programming model of the economics of spring cropping for weed control in UK agriculture. On average, the short-term loss of profit from spring cropping is greater than the benefits in terms of reduced herbicide usage and yield increases. These costs are greater when weed densities are low, so that spring cropping is an expensive strategy in the early stages of an infestation. However, there is a great deal of farm-to-farm variation: factors such as soil type and farm size are important and the current study highlights that economic modelling at the farm level is important in enabling farmers to make informed decisions. In general, however, if spring cropping is to be a successful strategy then the benefits to farmers will be in terms of long-term reductions in weed densities, but this will be at the expense of short-term profitability.

Green fuzzy parallel machine scheduling with sequence-dependent setup in the plastic moulding industry

Job scheduling has always been a challenging task for production managers. It is of special importance if it involves multi-objectives and parallel machines. In this research, our direction is largely motivated by the uncertainty emerged in production systems, where processing times of jobs and setup times of machines are not fixed and they are subject to some uncertainties. Our paper presents a mixed-integer goal programming model considering fuzzy approach for parallel machines environments with separable jobs, sequence-dependent setup times and hazardous waste. Two fuzzy objectives are considered in the model to minimise the total tardiness and the total hazardous waste. Since the model is too complex to be solved using exact methods, we proposed a solution method based on genetic algorithm. To set the input parameters of the solution algorithm, Taguchi method is used. The results of the computational experiments indicate that the proposed algorithm is a proficient method and has efficiently found the optimal solutions for both objective functions.

Quality management in product recovery using the Internet of Things: An optimization approach

Internet of Things, by reducing or almost eliminating uncertainty regarding existence, types, conditions and remaining lives of components in an end-of-life product (EOLP), can mitigate planning of remanufacturing operations. Remaining useful life can be taken into account as a good measure of quality. Therefore, immediate determination of remaining useful life allows optimal recovery decisions to guarantee a minimum quality level on recovered products while satisfying various system criteria.In this paper, a multiple objective advanced remanufacturing-to-order and disassembly-to-order (ARTODTO) system is proposed as an order-driven component and product recovery (ODCPR) system. In ARTODTO, device embedded products are remanufactured and disassembled to meet the product and component demands, recycled to satisfy the materials demands, stored to be re-used later, or disposed of. The objective of the system is to achieve multiple conflicting financial, environmental and quality-based goals. The problem is formulated as a mixed integer goal programming model that utilizes the Internet of Things. A numerical case example is considered to illustrate its implementation.

Determining design requirements in QFD using fuzzy mixed-integer goal programming: application of a decision support system

In product development, the identification of critical design requirements (DRs) is key to satisfying customer needs because it helps produce more successful products in a shorter time. Quality function deployment (QFD) is a tool used in product development to systematically determine the DRs so as to attain higher customer satisfaction. In the QFD process, the simultaneous optimisation of more than one conflicting objective is generally required. However, it is very difficult for decision makers to determine the goal value of each objective in imprecise and uncertain environments. In order to overcome this problem, the present study proposes a fuzzy mixed-integer goal programming model that determines a combination of optimal DR values. Different from the existing fuzzy goal programming models, the values of the DRs in the proposed model are taken as discrete. Finally, a new Decision Support System is developed. The new system integrates QFD and mathematical programming, enabling the design team to effectively compare product design alternatives and make product development easier and faster. The proposed methodology is illustrated using a real-world application in the Turkish white goods industry.

Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Goal Programming (GP) is an important analytical approach devised to solve many realworld problems. The first GP model is known as Weighted Goal Programming (WGP). However, Multi-Choice Aspirations Level (MCAL) problems cannot be solved by current GP techniques. In this paper, we propose a Multi-Choice Mixed Integer Goal Programming model (MCMI-GP) for the aggregate production planning of a Brazilian sugar and ethanol milling company. The MC-MIGP model was based on traditional selection and process methods for the design of lots, representing the production system of sugar, alcohol, molasses and derivatives. The research covers decisions on the agricultural and cutting stages, sugarcane loading and transportation by suppliers and, especially, energy cogeneration decisions; that is, the choice of production process, including storage stages and distribution. The MCMIGP allows decision-makers to set multiple aspiration levels for their problems in which “the more/higher, the better” and “the less/lower, the better” in the aspiration levels are addressed. An application of the proposed model for real problems in a Brazilian sugar and ethanol mill was conducted; producing interesting results that are herein reported and commented upon. Also, it was made a comparison between MCMI GP and WGP models using these real cases.

An efficient hybrid meta-heuristic for aircraft landing problem

Aircraft landing problem is to assign an airport's runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts. In this paper, first a mixed integer goal programming model is developed. Then, due to the complexity of the problem, which is NP-hard, we design a hybrid meta-heuristic applying simulated annealing framework. The computational results show that the proposed algorithm can obtain the optimal solution for instances up to 100 aircrafts, and also it is capable of finding very high quality and comparable solutions for the problems with up to 500 aircrafts and 5 runways in a short time.

A mixed integer goal programming model for discrete values of design requirements in QFD

A main feature of quality function deployment (QFD) planning process is to determine target values for the design requirements (DRs) of a product, with a view to achieving a higher level of overall customer satisfaction. However, in real world applications, values of DRs are often discrete instead of continuous. Therefore, a mixed integer linear programming (MILP) model considering discrete data is suggested. As opposed to the existing literature, the fulfilment levels of DRs are assumed to have a piece-wise linear relationship with cost; because, constraints of technology and resource rarely provides a linear relationship in manufacturing systems. In the proposed MILP model, we considered customer satisfaction as the only goal. But, QFD process may be necessary to optimise cost and technical difficulty goals as well as customer satisfaction. Therefore, by developing the MILP model with multi-objective decision making (MODM) approach, a novel mixed integer goal programming (MIGP) model is proposed to optimise these goals simultaneously. Finally, MILP model solution turns out to be a more realistic approach to real applications because piece-wise linear relationship is taken into account. The solution of MIGP model provided different alternative results to decision makers according to usage of the lexicographic goal programming (LGP) approach. The applicability of the proposed models in practice is demonstrated with a washing machine development problem.

A fuzzy mixed integer goal programming approach for cooking and heating energy planning in rural India

In this study, a fuzzy mixed integer goal programming model (FMIGP) has been developed for rural cooking and heating energy planning in the Chikhli taluka of Buldhana district, Maharashtra, Central India. The model considers various scenarios such as economical, environmental, social acceptance and local resources to trade off between socio-economical and environmental issues related to cooking and heating energy in two villages namely Malshemba and Muradpur. Due to uncertainty involved in real world energy planning problems, exact input data is impossible to acquire. Hence FMIGP model is used to consider four fuzzy objectives. The solutions provide energy resource allocations at micro level with minimized cost, minimized emission, maximized social acceptance and maximized use of local resources. The proposed approach can handle fuzzy environmental realistic situation and can provide better solution to decision maker for rural energy planning.

Formulation of the Mixed-Integer Goal Programming Model for Flour Producing Companies

Formulation of the Mixed-Integer Goal Programming Model for Flour Producing Companies

Formulation of the Mixed-Integer Goal Programming Model for Flour Producing Companies

Formulation of the Mixed-Integer Goal Programming Model for Flour Producing Companies

A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the complexity of the above model and uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the parallel-machine scheduling problem with sequence-dependent set-up times under the hypothesis of fuzzy processing time's knowledge and two fuzzy objectives as the MIGP model. In addition, a quite effective and applicable methodology for solving the above fuzzy model are presented. At the end, the effectiveness of the proposed model and the denoted methodology is demonstrated through some test problems.

An MCDM model for media selection in the dual consumer/industrial market

An optimal advertising media selection is a strategic factor for the operations of both traditional and e-business environments. This paper presents a case study that considers two options: industrial and consumer products. In order to resolve the strategic decision-making about dual market high technology products, a mixed integer goal programming model is developed to facilitate the advertising media selection process. Preemptive priority ordering is established by the analytic hierarchy process. The problem is solved lexicographically using a software package, based on the data obtained from the e-business industry in Korea. The satisfying solution is identified and analyzed, and sensitivity analyses are performed for model flexibility.

Determination of master production schedule replanning frequency for various forecast window intervals

This paper examines the impact of forecast window intervals on replanning frequencies for a rolling horizon master production schedule (MPS). The problem environment for this study is an actual MPS operation of a paint company and includes features such as multiple production lines, multiple products, capacity constraints, minimum inventory requirements. A mixed integer goal programming model formulated for the MPS problem is used to analyze the impact of forecast window interval length on replanning frequencies and MPS performance in a rolling horizon setting. Given demand certainty, results indicate that the length of the forecast window interval influences the choice of replanning frequency for this company environment. A three‐month forecast window interval with a two‐month replanning frequency provided the best MPS performance in terms of total cost.

A nonlinear mixed integer goal programming model for the two-machine closed flow shop

This paper presents a nonlinear mixed integer goal programming model of the deterministic, static two-machine closed flow shop (CFS) problem. The model incorporates two sets of goals that are of importance to the production manager: cost goals and production goals. The cost goals are setup costs, finished goods holding costs, machine idle costs, and work-in-process inventory costs. The production goals are makespan, mean tardiness, mean flow time, capacity between runs and end shop capacity.

A Mixed-Integer Goal-Programming Formulation of the Standard Flow-Shop Scheduling Problem

Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance.This paper presents an extension of an earlier model developed by the authors, formulating the generalized N job, M machine standard flow-shop problem as a mixed-integer goal-programming model. The formulation was empirically tested through a comparison of the generated optimal solutions to their mathematically derived counterparts. For this, a special flow-shop problem with certain permutation properties was selected. In addition, a randomly chosen problem was solved to show the general applicability of the derived formulation.The model allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.

A new formulation and solution of the flowshop scheduling problem with no in-process waiting

To date, all models reported in the literature relating to the flowshop sequencing problem with no in-process waiting, have been based on single objective optimization. This paper presents a mixed integer goal programming model of the generalized N job, M machine standard flowshop problem with no in-process waiting, i.e. no intermediate queues. Instead of optimization being based on a single objective, the most satisfactory sequence is derived subject to user specified selection of the pre-emptive goals: makespan, flowtime, and machine idle time. Computational results of sample problems illustrating the advantage of a multiple criteria selection method are shown.

A mixed-integer goal programming model for nursing service budgeting.

This paper presents a mixed-integer goal programming model for expense budgeting in a hospital nursing department. The model incorporates several different objectives based upon such considerations as cost containment and providing appropriate nursing hours for delivering quality nursing care. Also considered are possible trade-offs among full-time, part-time and overtime nurses on weekdays as well as weekends. The budget includes vacation, sick leave, holiday, and seniority policies of a hospital and various constraints on a hospital nursing service imposed by nursing unions. The results are based upon data from a study hospital and indicate that the model is practical for budgeting in a hospital nursing department.

A mixed-integer goal programming model for capital budgeting within a police department

A difficult problem for most police departments is allocating limited dollars for capital expenditures in the most efficient manner possible. Because of the varied objectives of police services as perceived by police administrators, government officials and citizens, traditional allocation criteria, such as cost-benefit analysis, are not viable. As such, this paper proposes the use of mixed-integer goal programming as a methodology for selecting police expenditure items given a limited budget and multiple, conflicting objectives. In order to demonstrate this technique, a case example involving 18 potential expenditure items for a moderately-sized police department will be employed. This example model will be solved using a predetermined priority structure, and the results interpreted. Several alternative priority structures that reflect the objectives of different interest groups will then be tested in order to demonstrate the flexibility of this approach.