jurnal teknologi maklumat dan sains kuantitatif

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Ruzzakiah Jenal, Amelia Natasya Abdul Wahab,. Suhaila Mohamed Yusof. Adopting a Common Mathematics Curriculum in a. Diverse Population: Is it a Wise ...
/ Maklumat dan Sains Kuantitatif

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UNIVERSITI TEKNOLOGI MARA

ISSN:1823-0822

Jilid 6, Bil. 1,2004

JURNAL TEKNOLOGI MAKLUMAT DAN SAINS KUANTITATIF Kandungan

Muka Surat

Measuring Outlier Effects in Bilinear Time Series Processes Mohamad Said Zainol, Ibrahim Mohamed, Azami Zaharim

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Orthogonal Latin Square Constructions Haslinda Ibrahim

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Pemeringkatan Kriteria Pemilihan Pelajar Matrikulasi ke Universiti Menggunakan Model Set Kabur Wan Rosmanira Ismail, Vmmul Khair Salma Hi.Din, Norngainy Mohd Tawil

19

A Case Study of Intrusion Signature Identifications Featuring SNORT Saadiah Yahaya, Abdul Hamid Osman, Nik Mariza

31

Optimization of Overtime in a Manufacturing System Ruzzakiah Jenal, Amelia Natasya Abdul Wahab, Suhaila Mohamed Yusof

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Adopting a Common Mathematics Curriculum in a Diverse Population: Is it a Wise Strategy? Mohd Sahar Sauian, Shukri Shamsudin

49

Universiti Teknoloei MARA

Jul 2g ^ ^

JurnaJ Tck. Maklumal & Sains Kuanlitalif Jilid 6. Bil. 1. 2004 (39-48)

Optimization Of Overtime In A Manufacturing System 'Ruzzakiah Jenal,2 Amelia Natasya Abdul Wahab and 3Suhaila Mohamed Yusuf Fakulti Teknologi Maklumat dan Sains Kuantitatif, 40450 UiTM Shah Alam Department of Industrial Computing, Faculty of Sciences and Information Technology, Universiti Kebangsaan Malaysia,. 43600 Bangi, Selangor, Malaysia

Abstract: This paper investigates the goal programming approach when applied to a manufacturing system with an intention to evaluate the trade-offs between the overtime hours and overtime costs/hour of the production environment under one objective function but allows re-run of the model with variations in their coefficients. The objective of this project is to determine the production level for each product that will maximize the net profit. The project also determines the optimal overtime limits in this manufacturing system, the number of units each product made and the number of extra hours overtime worked on each machine. The ease of use and interpretation make the proposed goal programming model a powerful communication tool to satisfy the goal of decision maker. Keywords: Goal programming, overtime costs/hour, overtime hours.

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Introduction

Manufacturing is a process concerned with changing raw materials into finished products. Thus, the bases of production line balance in manufacturing process are time and labor variables. These variables are interrelated and the way they are optimized will determine the overall cost of producing the product. Then, the optimum profit can also be determined from these variables. A successful manufacturing system usually can deal with the limitations of efficiency and flexibility, and to consider the real world resources limitations. However, it is often incorrectly structured due to the presence of multiple conflicting objectives. Therefore, new tools for manufacturing systems are required to handle such issue. The problem discussed here is about the manufacturing system environment. In this case we will consider three machines which use are to produce two different products. The machines operation is limited to eight hours daily but may be exceeded by up to four hours on an overtime e-mail: [email protected], 2 [email protected] 3 smy ©ftsm.ukm.my

40 Kuzzahah jenalelal

basis. But each of overtime hours will cost an additional $5. The production rates for the two products together with their profits per unit are summarized in Table 1-1. Therefore the objective required for this problem is to determine the production level for each product that will maximize the net profit. This manufacturing system has a set of objectives to maximize the net profit and to minimize the used of overtime. To realize these objectives, a goal programming model has been proposed in this paper. Table 1.1: Summary of the production rates for the two products together with their profits per unit.

Machine 1 2 3 Profit per unit 2.

Production Rate (units/hour) Product 1 Product 2 5 6 8 4 7 3 $6 $4

The Goal Programming Model

In a given production system, each machine will operate on an overtime basis that is limited to eight hours per day. However, it may be exceeded by a certain number of hours in order to increase the production rates and the profit. If the machine operates more than its limited hours, we will consider these as overtime hours. These overtime hours make the cost of production increase. It means we have to consider the cost of overtime hour to find the net profit of the products being produced. The approach we use to solve this problem is to utilize the goal programming method with penalty parameters. We will vary the overtime hours and overtime costs/hour to find the optimum revenue of these products. The details of variables, and the objective functions representing the various performance criteria are presented as follows. Notation Indices i = Product type (j = 1, 2) / = Machine type (/ = 1, 2, 3) Parameters stj = Production rates of product / from machine /' (units/hour). tt = Profit per unit for rth product. a = Overtime hours for machine 1 (equality model) and machine ,/'(non-equality model). b = Overtime hours for machine 2. c = Overtime hours for machine 3. p= Overtime costs/hour for machine 1 (equality model) and machine /(non-equality model). q = Overtime costs/hour for machine 2. r= Overtime costs/hour for machine 3. Decision Variables xt = Number of units of product i made. y( = Number of extra hours overtime worked on machine j . w = Max {0, y } where vc>= 0 and w >= y

Optimimtion Of Overtime In A Manufacturing System

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