Reference no: EM132927085
0508300 Quantitative Business Analysis - Al Ain University
Case Study: Linear Programming
Organic, vegan and eco-friendly have all become the most common terms in the personal care and cosmetic industry, but halal is the latest and emerging trend. Not so long ago, the word ‘halal' meant an activity permissible to undertake or the food that was safe to eat. However, in today's increasingly ethical and ecologically conscious world, the term has taken on a much broader meaning, and the concept is gradually taking over the cosmetic industry.
Halal cosmetics contain ingredients that are religiously permissible and not derived from cochineal or porcine, leading to the development of cosmetics such as creams, shampoos, and lotions that are free from non-Halal slaughtered animals. Halal cosmetic products are permitted under Shariah law and must fulfill certain conditions. Halal cosmetics have grown far beyond a novelty. A surge of cosmetic brands is capitalizing on the burgeoning halal cosmetic industry by producing halal certified products that contain no animal ingredients to meet the growing demand of consumers who just want to ensure that the beauty products they use are healthy and sustainably sourced.
Halal cosmetics are witnessing an upsurge in demand and popularity, not just from the Muslim population, but also from a rising number of health-conscious consumers on the global stage who are paying close attention to the cosmetic products they use on their bodies. In order to become a certified halal cosmetics brand, the companies in the beauty industry must avoid the use of alcohol and animal ingredients, while ensuring that the finished product isn't tested on animals.
The Ethical Beauty International (EBI) is creams, deodorants, toiletries, shampoos, lotions makeup and fragrances. The company provides product offerings through an e-commerce subscription model. Customers can select from different pricing plans and the products delivered to them at home monthly. The company was able to build brand loyalty with a stable income stream through the subscription model, particularly its three products A (day cream), B (anti-aging facial cream) and C (night cream).
The Annual sales about $150 million, EBI showed double digit growth over the few years. The estimated demand of the upcoming season were 12000, 8000, 18000 units of products A, B and C respectively. Each product passes through two production stages that use four ingredients: purified water, vegan oil, natural scents and colors, and emulsifiers. Stage I involved for material preparation and initial mixing while stage II focused for blending and packaging. EBI's available first-shift capacity for the next quarter was 15000 labor hours for stage I and 10000 hours for stage II. The first shift hourly rate was $8.5 for stage I and 9.25 for stage II. A second shift was available with 10 percent reduction in capacity and a 10 % increase in wage rate. The cost for raw material was $1 per pound for purified water, $1.5 per pound of vegan oil, $3 per pound for natural scents and colors and $2 per pound of emulsifiers. The production department had available 200000 pounds of purified water, 50000 pounds of vegan oil, 7500 pounds of natural scents and colors and 15000 pound of emulsifiers.
EBI could subcontract with a local supplier for product A and B at a cost of $40 and $ 55 per carton respectively. The vender is able to meet the demand requirements that were in excess of EBI capabilities. The vender will not be used for production of product C.
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Criteria/Vendor
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Product A
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Product B
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Product C
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Labor(hours/carton)
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Stage I
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1.5
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1.8
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1.0
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Stage II
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0.8
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1.0
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0.5
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Material (pounds/carton)
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Purified Water
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8.0
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6.0
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7.0
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Vegan Oil
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1.0
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3.0
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2.0
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Scents & colors
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0.5
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0.3
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0.4
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Emulsifiers
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0.5
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0.7
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0.6
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Managerial Report
Perform an analysis to EBI case, and prepare a report that summarizes your ?ndings and recommendations. Include the following items in your report:
1. Identify the problem in the EBI Case using the available information.
2. What are the key assumptions surrounding the business situation in this case?
3. Calculate the cost of producing the 3 products?
4. Develop the LP model for this problem.
5. Solve the LP model to find the optimal solution. What is the corresponding value of the objective function?
6. Analyze the results by trying to point to the following:
i. What production schedule that minimizes total cost?
ii. Which labor and material resources are used up completely, what is the shadow price?
7. Include the details of your analysis (using QM for Windows or Excel QM) as an appendix to your report. Do not include any output in the body of the report.
Attachment:- Quantitative Business Analysis.rar