scholarly journals Solution of Quadratic Programming with Interval Variables Using a Two-Level Programming Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimum Point ◽  
Interval Variables ◽  
Interval Coefficients ◽  
Optimum Solution

Quadratic programming with interval variables is developed from quadratic programming with interval coefficients to obtain optimum solution in interval form, both the optimum point and optimum value. In this paper, a two-level programming approach is used to solve quadratic programming with interval variables. Procedure of two-level programming is transforming the quadratic programming model with interval variables into a pair of classical quadratic programming models, namely, the best optimum and worst optimum problems. The procedure to solve the best and worst optimum problems is also constructed to obtain optimum solution in interval form.

scholarly journals Extension of Wolfe Method for Solving Quadratic Programming with Interval Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Programming Models ◽  
Interval Coefficients ◽  
Extension Process

Quadratic programming with interval coefficients developed to overcome cases in classic quadratic programming where the coefficient value is unknown and must be estimated. This paper discusses the extension of Wolfe method. The extended Wolfe method can be used to solve quadratic programming with interval coefficients. The extension process of Wolfe method involves the transformation of the quadratic programming with interval coefficients model into linear programming with interval coefficients model. The next step is transforming linear programming with interval coefficients model into two classic linear programming models with special characteristics, namely, the optimum best and the worst optimum problem.

A mathematical programming approach for walking-worker assembly systems

2014 ◽  
Vol 34 (1) ◽  
pp. 56-68 ◽  
Author(s):  
Emre Cevikcan
Keyword(s):  
Mathematical Programming ◽  
Task Allocation ◽  
Programming Model ◽  
Programming Models ◽  
Assembly System ◽  
Programming Approach ◽  
Assembly Systems ◽  
Mathematical Programming Model ◽  
Content Type ◽  
Mathematical Programming Approach

Purpose – It has become increasingly critical to design and maintain flexible and rapid assembly systems due to unpredictable and varying market conditions. The first stage of developing such systems is to restructure the existing assembly system. After designing the manufacturing system, efforts should be made for capacity adjustments to meet the demand in terms of allocating tasks to workers. Walking-worker assembly systems can be regarded as an effective method to achieve flexibility and agility via rabbit chase (RC) approach in which workers follow each other around the assembly cell or line and perform each task in sequence. In this paper, a novel mathematical programming approach is developed with the aim of integrating RC in assembly processes. Therefore, this study is thought to add value to industrial assembly systems in terms of effectively raising engineering control for task allocation activities. Design/methodology/approach – Two consecutive mathematical models are developed, since such a hierarchical approach provides computational convenience for the problem. The initial mathematical programming model determines the number of workers in each RC loop for each segment. In addition, the number of stations and the distribution of station times in the segments is essential. Therefore, the succeeding mathematical programming model generates stations in each segment and provides convenience for the workflow in RC loops. The output of mathematical programming models are the parameters of simulation model for performance assessment. Findings – The effectiveness of the proposed approach was validated by an application in a real-life chair production system. The application resulted in performance improvements for labour requirement (12.5 per cent) and production lead time (9.6 per cent) when compared to a classical assembly system design (CASD) where one stationary worker exists in each station. In addition, it is worth to note that RC leads to a reduced number of workers for a considerable number (39.4 per cent) of test problems. What is more, input as well as output factors have been determined via discriminant analysis and their impacts to the utilization of RC were analyzed for different levels. Practical implications – This study is thought to add value to the industry in terms of effectively providing convenience during production planning and task allocation in assembly lines and cells. Originality/value – To the best knowledge of the author, optimization models for RC considering a real industrial application have not yet been developed. In this context, this paper presents an approach which models RC by the use of mathematical programming in manual assembly processes to address this research gap. The contribution of the paper to the relevant literature is the development of hierarchical mixed integer linear programming models to solve RC problem for the first time.

scholarly journals A Constraint Programming Approach for Solving a Queueing Control Problem

2008 ◽  
Vol 32 ◽  
pp. 123-167 ◽  
Author(s):  
D. Terekhov ◽  
J. C. Beck
Keyword(s):  
Waiting Time ◽  
Constraint Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Problem Instances ◽  
Constraint Programming Model ◽  
Over Time

In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closed-form expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable run-time. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueing-based problems with constraint programming.

scholarly journals A Bilevel Stochastic Dynamic Programming Model to Assess the Value of Information on Actual Food Quality at Wholesale Markets

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Xiangyu Hou ◽  
Rene Haijema ◽  
Dacheng Liu
Keyword(s):  
Dynamic Programming ◽  
Programming Model ◽  
Market Price ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Wholesale Market ◽  
Dynamic Programming Approach ◽  
Additional Information ◽  
Similar Appearance ◽  
Inventory Decision

In the fresh produce wholesale market, the market price is determined by the total demand and supply. The price is stochastic, and either wholesaler or retailer has few influence on it. In the wholesaler’s inventory decision, the price’s uncertainty plays an important role as well as the uncertainty from the demand side: the wholesaler makes his decision based on the retailer’s ordering, which is influenced by the stochastic market price and the distribution of the consumer’s demand. In addition, when at the wholesale stage, the products show a similar quality of similar appearance. With more efforts being input, the wholesaler could detect and record more additional information than that reflected from the appearance. Based on this, he can classify the quality into different levels. No experience shows how the wholesaler could use the underlying quality information and how much this information could improve his profit. To describe and explore this problem, a bilevel dynamic programming approach is employed. We evaluate different strategies of using the underlying information, show the features of the optimal policy, develop heuristics, and discuss the influence of factors such as quality and market price. We also develop the managerial principles for the practical use.

scholarly journals Applying Simulation Modelling in Quantifying Optimization Results

2021 ◽  
Vol 15 (4) ◽  
pp. 518-523
Author(s):  
Ratko Stanković ◽  
Diana Božić
Keyword(s):  
Linear Programming ◽  
Simulation Model ◽  
Input Data ◽  
Optimization Problems ◽  
Programming Model ◽  
Optimal Solution ◽  
Simulation Modelling ◽  
Simulation Software ◽  
Programming Models ◽  
Freight Forwarding

Improvements achieved by applying linear programming models in solving optimization problems in logistics cannot always be expressed by physically measurable values (dimensions), but in non-dimensional values. Therefore, it may be difficult to present the actual benefits of the improvements to the stake holders of the system being optimized. In this article, a possibility of applying simulation modelling in quantifying results of optimizing cross dock terminal gates allocation is outlined. Optimal solution is obtained on the linear programming model by using MS Excel spreadsheet optimizer, while the results are quantified on the simulation model, by using Rockwell Automation simulation software. Input data are collected from a freight forwarding company in Zagreb, specialized in groupage transport (Less Than Truckload - LTL).

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