PRODUCT MIX OPTIMIZATION OF FRUIT NECTAR WITH INTEGRATION OF ANALYTIC HIERARCHY PROCESS AND MATHEMATICAL PROGRAMMING

Year 2022, Volume: 33 Issue: 1, 96 - 114, 30.04.2022

Adem Erik , Burcu Dündar , Durmuş Can Acer

https://doi.org/10.46465/endustrimuhendisligi.978286

Abstract

Today, the competitiveness of companies is directly dependent on the quality and price of their products. This is because consumers have more options to buy a product than in previous years. In this study, two different mathematical models are developed to determine the best product mix according to different constraints for a fruit nectar producer. For a fruit nectar producer, 4 main and 9 sub-quality criteria were entered into the mathematical models whose importance levels were determined by the analytic hierarchy process (AHP) method. These models, created for optimum product mix, consider not only the integrated quality criteria but also different constraints such as capacity, labor, and raw material. Models aiming at breakeven and maximum profit have been run for different scenarios such as consumer demands, machine maintenance, and the increase in bottlenecks. The results have shown that the quality criteria change the production efficiency and sales quantities, and how much the existing production system can adapt if consumer demands change.

Keywords

Analytic Hierarchy Process Method, Optimization, Fruit Nectar Production, Breakeven Point, Mathematical Programming

Thanks

Adem Erik would like to extend thanks to the Scientific and Technological Research Council of Turkey (TÜB ̇ITAK) for supporting his Ph.D. studies (BIDEB-2211 Programme with Grant Application Number:1649B031905573).

ANALİTİK HİYERARŞİ PROSESİ VE MATEMATİKSEL PROGRAMLAMA ENTEGRASYONU İLE MEYVE NEKTARI ÜRÜN KARMASI OPTİMİZASYONU

Abstract

Günümüzde firmaların rekabet gücü doğrudan ürünlerinin kalitesine ve fiyatına bağlıdır. Bunun nedeni, tüketicilerin bir ürünü satın almak için önceki yıllara göre daha fazla seçeneğe sahip olmasıdır. Bu çalışmada, bir meyve nektarı üreticisi için farklı kısıtlara göre en iyi ürün karmasını belirlemek için iki farklı matematiksel model geliştirilmiştir. Bir meyve nektarı üreticisi için, analitik hiyerarşi süreci (AHP) yöntemi ile önem seviyeleri belirlenen matematiksel modellere 4 ana ve 9 alt kalite kriteri girilmiştir. Optimum ürün karması için oluşturulan bu modeller, sadece entegre kalite kriterlerini değil aynı zamanda kapasite, işçilik, hammadde gibi farklı kısıtları da dikkate almaktadır. Tüketici talepleri, makine bakımı, darboğazların artması gibi farklı senaryolar için başabaş ve maksimum karı hedefleyen modeller çalıştırılmıştır. Sonuçlar, kalite kriterlerinin üretim verimliliğini ve satış miktarlarını değiştirdiğini ve tüketici talepleri değiştiğinde mevcut üretim sisteminin ne kadar uyum sağlayabileceğini göstermiştir.

Keywords

Analitik Hiyerarşi Prosesi, Optimizasyon, Meyve Nektarı Üretimi, Başabaş Noktası, Matematiksel Modelleme

References

• Burdurlu, H. S., Koca, N., & Karadeniz, F. (2006). Degradation of vitamin C in citrus juice concentrates during storage. Journal of food engineering, 74(2), 211-216. https://doi.org/10.1016/j.jfoodeng.2005.03.026
• Chung, S. H., Lee, A. H., & Pearn, W. L. (2005). Analytic network process (ANP) approach for product mix planning in semiconductor fabricator. International journal of production economics, 96(1), 15-36. https://doi.org/10.1016/j.ijpe.2004.02.006
• Clegg K.M, (1964). Non‐enzymic browning of lemon juice. J. Sci. Food Agr. https://doi.org/10.1002/jsfa.2740151212
• Demirdöven, A., & Baysal, T. (2014). Optimization of ohmic heating applications for pectin methylesterase inactivation in orange juice. Journal of food science and technology, 51(9), 1817-1826.
• Dündar, B., Ağçam, E., & Akyıldız, A. (2019). Optimization of thermosonication conditions for cloudy strawberry nectar with using of critical quality parameters. Food chemistry, 276, 494-502. https://doi.org/10.1016/j.foodchem.2018.10.028.
• Galaverna, G., & Dall’Asta, C. (2014). Production processes of orange juice and effects on antioxidant components. In Processing and impact on antioxidants in beverages (pp. 203-214). Academic Press.
• Kokangul, A., & Susuz, Z. (2009). Integrated analytical hierarch process and mathematical programming to supplier selection problem with quantity discount. Applied mathematical modelling, 33(3), 1417-1429. doi: 10.1016/j.apm.2008.01.021
• Koshani, R., Ziaee, E., Niakousari, M., & Golmakani, M. T. (2015). Optimization of Thermal and Thermosonication Treatments on Pectin Methyl Esterase Inactivation of Sour Orange Juice (C itrus aurantium). Journal of food processing and preservation, 39(6), 567-573. https://doi.org/10.1111/jfpp.12262
• Laing, B. M., Schlueter, D. L., & Labuza, T. P. (1978). Degradation kinetics of ascorbic acid at high temperature and water activity. Journal of Food Science, 43(5), 1440-1443. https://doi.org/10.1111/j.1365-2621.1978.tb02515.x
• Lee, H. S., & Coates, G. A. (1999). Vitamin C in frozen, fresh squeezed, unpasteurized, polyethylene-bottled orange juice: a storage study. Food Chemistry, 65(2), 165-168. https://doi.org/10.1016/S0308-8146(98)00180-0
• Mehmood, Z., Zeb, A., Ayub, M., Bibi, N., Badshah, A., & Ihsanullah, I. (2008). Effect of pasteurization and chemical preservatives on the quality and shelf stability of apple juice. American Journal of Food Technology, 3(2), 147-153.
• Molina, M. G. (2018). Product mix optimization at minimum supply cost of an online clothing store using linear programming. International Journal of Applied Mathematics Electronics and Computers, 6(3), 33-38.
• Rajesh, R. (2020). Group decision-making and grey programming approaches to optimal product mix in manufacturing supply chains. Neural Computing and Applications, 32(7), 2635-2649. doi:10.1007/s00521-018-3675-y
• Rivas, A., Rodrigo, D., Martinez, A., Barbosa-Cánovas, G. V., & Rodrigo, M. (2006). Effect of PEF and heat pasteurization on the physical–chemical characteristics of blended orange and carrot juice. LWT-Food Science and Technology, 39(10), 1163-1170. https://doi.org/10.1016/j.lwt.2005.07.002
• Romauch, M., & Klemmt, A. (2015). Product mix optimization for a semiconductor fab: modeling approaches and decomposition techniques. Computers & Operations Research, 53, 338-352.
• Ross D.F, (2013). Competing through supply chain management: creating market-winning strategies through supply chain partnerships. Springer Science & Business Media, Berlin.
• Saaty T.L., (1980). The analytic hierarchy process. McGraw-Hill Book Co., New York.
• Saaty T.L., (2008). Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1(1), 83-98.
• Shapla, U. M., Solayman, M., Alam, N., Khalil, M. I., & Gan, S. H. (2018). 5-Hydroxymethylfurfural (HMF) levels in honey and other food products: effects on bees and human health. Chemistry Central Journal, 12(1), 1-18.
• Silva, F. V., & Silva, C. L. (1997). Quality optimization of hot filled pasteurized fruit purees: Container characteristics and filling temperatures. Journal of food Engineering, 32(4), 351-364. https://doi.org/10.1016/S0260-8774(97)00031-9
• Singh, S., Khemariya, P., & Rai, A. (2014). Process optimization for the manufacture of lemon based beverage from hydrolyzed whey. Journal of food science and technology, 51(4), 691-699. https://doi.org/10.1007/s13197-011-0563-1
• Sun, J., Chu, Y. F., Wu, X., & Liu, R. H. (2002). Antioxidant and antiproliferative activities of common fruits. Journal of agricultural and food chemistry, 50(25), 7449-7454. https://doi.org/10.1021/jf0207530.
• Tanhaie, F., & Nahavandi, N. (2017). Solving product mix problem in multiple constraints environment using goal programming. Journal of Industrial Engineering and Management Studies, 4(1), 1-12. https://doi.org/10.22116/JIEMS.2017.51960
• Tsai, J. T., Wang, J. L., & Tzeng, L. Y. (2010). On the optimal product mix in life insurance companies using conditional value at risk. Insurance: Mathematics and Economics, 46(1), 235-241.
• Tüfekci, H. B., & Fenercİoğlu, H. (2010). Conformation of some commercial fruit juices to Food Regulations in Turkey. Akademik Gida, 8(2), 11-17.
• Vasant, P., & Barsoum, N. N. (2006). Fuzzy optimization of units products in mix-product selection problem using fuzzy linear programming approach. Soft Computing, 10(2), 144-151.
• Vegara, S., Martí, N., Mena, P., Saura, D., & Valero, M. (2013). Effect of pasteurization process and storage on color and shelf-life of pomegranate juices. LWT-Food Science and Technology, 54(2), 592-596. https://doi.org/10.1016/j.lwt.2013.06.022
• Yıldız, O., Șahİn, H., Kara, M., Aliyazıcıoğlu, R., Tarhan, Ö., & Kolaylı, S. (2010). Maillard reactions and importance of reaction products in foods. Akademik Gida, 8(6), 44-51.
• Yu, C. M., Kuo, C. J., Chiu, C. L., Wen, W. C., & Zhang, M. (2018, December). Product mix optimization under required cycle time for semiconductor wafer fabrication. In 2018 International Symposium on Semiconductor Manufacturing (ISSM) (pp. 1-4). IEEE. https://l24.im/rpXBh