Product Mix Optimization at Minimum Supply Cost of an Online Clothing Store using Linear Programming

International Journal of Applied Mathematics Electronics and Computers ISSN:2147-82282147-6799 http://dergipark.gov.tr/ijamec Original Research Paper Product Mix Optimization at Minimum Supply Cost of an Online Clothing Store using Linear Programming Marivic G. Molina*1 Accepted : 01/08/2018 Published: 30/09/2018 DOI: 10.1039/b000000x Abstract: Starting a small business with little capital can be very challenging to new business owners. Oftentimes, they resort to using trial and error in managing their finances especially when it comes to purchasing products from their suppliers. This study considered an online clothing store as a case study. The data provided by the online clothing store owners were used to estimate the parameters of the linear programming model. The LP model was solved using QM for Windows software to determine the most economical product mix to be purchased by the online clothing store owners from their suppliers and therefore provide an optimum solution. It was recommended that the owners should continue using linear programming in determining the number of each product to be purchased from the suppliers while minimizing the overall supply cost. Likewise, as their online clothing store grows, they must also explore the possibility of using linear programming to determine the optimal product mix for maximum profit. Keywords: Linear Programming, Online Clothing Store, Optimization, Product Mix, Simplex Method, Supply Cost, 1. Introduction Starting a small business need not involve a big amount of money. Instead, the business owners should have the ability to use and manage as little capital as possible to put up the business. Moreover, with good money management abilities, any venture could develop into a success story. However, not all business owners are good at handling finances. Oftentimes, since most businesses consist of several product lines – groups of items featuring similar characteristics – challenges in handling finances usually happen in product mix determination. Product mix is the combination of the total product lines that a company offers [1]. Woubante [2] enumerated four important reasons that make product mix determination essential to the success of a business. First, it provides the best opportunity of meeting customers’ needs. Second, it shapes the company’s image and its brand. Third, it keeps the company to stay focus on its core business. Lastly, it limits the company in the number of products it is able to offer. To be able to determine what mix of product lines produces output at lowest cost while maintaining the desired level of quality, a cost minimization technique must be utilized. A technique that involves either minimization or maximization of a quantity is called linear programming (LP). In fact, one of the most common linear programming applications is the product mix problem [3]. According to Shaheen and Ahmad [4], in determining an optimal solution among alternatives to meet a specified objective function limited by various constraints, the best method to be used is linear programming. Minimization of costs can also be attained if the business is done online. Creating a website or a page can easily be done due to a variety of free or affordable programs and ready-made templates in the internet. Furthermore, with the advancement of technology, _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 1 College of Science, Pamantasan ng Lungsod ng Maynila, Gen. Luna cor. Muralla St.,Intramuros, Manila, Philippines 1002 * Corresponding Author: Email: promoting the products becomes easier and cheaper since thousands of people can easily be reached through social networking sites. In this connection, this study focused on product mix determination by considering an online clothing store as a case study with the aim of applying linear programming in determining the most economical product mix. 2. Problem Statement A budding online clothing store that has been operating for two months as of the writing of this study is currently selling two product lines: dresses and blouses. Each product was obtained from four suppliers: two dress suppliers (A and B) and two blouse suppliers (C and D). Each supplier offers a fixed price on their products for a corresponding minimum number of pieces to be purchased. However, the price depends on the size of the blouse or dress. Furthermore, the four suppliers offer policy in charging shipping fees. For the soft opening of the online clothing business, the clothes they sold were obtained from the four suppliers through trial and error. With this, the problem addressed here was to determine how many of each product should be obtained from the four suppliers while minimizing the overall supply cost. 3. Objective of the Study The objective of this study was to apply linear programming in determining the most economical product mix. 4. Literature Review Linear programming has numerous real-life applications [5]. Some of the enumerated, with corresponding examples provided, basic applications of linear programming techniques are: (a) Financial International Journal of Applied Mathematics Electronics and Computers (IJAMEC) 2018, 6(3), 33–38 | 33 Applications which were discussed under three sections – Portfolio Selection problem, Financial Mix, and Investment Strategies; (b) Marketing Application which was discussed under two sections – Media Selection and Marketing Strategy; (c) Management Applications which considered the Production Scheduling and Manpower Planning Application; (d) Transportation Model; (e) Assignment Model; (f) Urban Planning; (g) Diet Problem; (h) Currency Arbitrage; (i) Blending Model; and (j) Environmental Protection. However, they argued that despite the aforementioned real-life applications, the general public does not seem to give the desired level of recognition and acceptance to linear programming techniques. Hence, a reconciliation between the seemingly apathy to linear programming techniques and the benefits derived therein was deemed necessary. Furthermore, they recommended that the main thrust of the study become a national policy, that is, to make the teaching and learning of operations research and its applications a national priority. Consistently, Miller [6] regarded linear programming as a generalization of linear algebra which is used to successfully model an overwhelming number of real life problems ranging from scheduling airline routes to shipping oil from refineries to cities for meeting the minimum daily requirements through finding inexpensive diets. Similar with Kanu et. al. [5], they described several types of problem that can be handled by linear programming and solved them (...truncated)