Süt toplama problemi için bütünleşik bir matematiksel model

Öz

Kalitelerine göre ayrılmış sütlerin içerikleri mikroorganizma sayısı, kimyasal değerleri birbirinden farklıdır. Farklı kaliteye sahip sütlerin karıştırılması durumunda oluşan sütün kalitesi, karışıma katılan sütler arasındaki en düşük kaliteye sahip olan süt tipinin kalitesine eşit kabul edilmektedir. Bu yüzden faklı kalitedeki sütler toplanırken karıştırılmamalıdır. Süt toplama problemi farklı noktalarda bulunan üreticilerden, kalite tiplerine göre ayrılmış çiğ sütlerin, çok tanka sahip tankerler aracılığı ile toplanması ile ilgilenmektedir. Bu çalışmada; farklı noktalarda bulunan farklı kalitede ki çiğ sütlerin, çok tanka sahip tankerler aracılığı ile belirlenen zaman limiti altında toplanmasını sağlayacak bütünleşik bir matematiksel model oluşturulmuştur. Varsayımsal bir vaka çalışmasının ILOG CPLEX ile çözülmesi ile elde edilen sonuçlar göstermektedir ki önerilen model farklı kalitedeki çiğ süt tiplerinin karıştırılmadan en etkin şekilde toplanmasına izin vermektedir. Böylece daha yüksek kalitede süt ürünleri üretilmesi mümkün olabilecektir.

Anahtar Kelimeler

• Süt toplama problemi,Araç rotalama problemi,Matematiksel model,Lojisitk

An integrated mathematical model for the milk collection problem

Öz

The number of microorganisms and chemical values of the milks separated according to their quality are different from each other. In case of mixing different quality types of milk, composed milk quality is considered equal to the lowest quality milk type among the types of milk added to the mixture. Therefore, different types of raw milk should not be mixed during collection. The problem of milk collection is related to the collection of raw milk, which is separated according to the quality types, from the producers at different points by multi-tank tankers. In this study, an integrated mathematical model has been developed to collect different quality types of raw milk at different points under the specified time limit by means of tankers having multiple tanks. The results obtained by solving a hypothetical case study with ILOG CPLEX show that proposed model allows to optimally collect different type of raw milks without mixing. Thus, it will be possible to produce higher quality dairy products.

Anahtar Kelimeler

• Milk collection problem,Vehicle routing problem,Mathematical model,Logistics

Kaynakça

1. Prodhon C, Prins C. "A survey of recent research on location-routing problems". European Journal of Operational Research, 238(1), 1-17, 2014.
2. Lahyani R, Khemakhem M, Semet F. "Rich vehicle routing problems: From a taxonomy to a definition", European Journal of Operational Research, 241(1), 1-14, 2015.
3. Cuda R, Guastaroba G, Speranza MG. "A survey on two-echelon routing problems". Computers & Operations Research, 55(0), 185-199, 2015.
4. Vásquez RR, Valencia MC. "Model of routing for raw milk collection using genetic algorithms". Sistemas & Telemática, 12(31), 77-87, 2014.
5. Lahrichi N, Gabriel Crainic T, Gendreau M, Rei W, Rousseau LM. "Strategic analysis of the dairy transportation problem". Journal of Operational Research Society, 66(1), 44-56, 2015.
6. Masson R, Lahrichi N, Rousseau LM. "A two-stage solution method for the annual dairy transportation problem". European Journal of Operational Research, 251(1), 36-43, 2016.
7. Hoff A, Løkketangen A. "A tabu search approach for milk collection in western Norway using trucks and trailers". TRISTAN VI: Sixth Triennial Symposium Transportation Analysis, Phuket Island, Thailand, 10-15 June 2007.
8. Pasha U, Hoff A, Løkketangen A. "A Hybrid Approach for Milk Collection Using Trucks and Trailers". Annals of Management Science, 3(1), 85, 2014.

9. Amiama C, Pereira JM, Carpente L, Salgado J. "Spatial decision support system for the route management for milk collection from dairy farms". Transportation Letters, 7(5), 279-288, 2015.
10. Chokanat P, Pitakaso R, Sethanan K. “Methodology to Solve a Special Case of the Vehicle Routing Problem: A Case Study in the Raw Milk Transportation System”. AgriEngineering, 1(1), 75-93, 2019.
11. Montero E, Canales D, Paredes-Belmar G, Soto R. “A Prize Collecting problem applied to a Real Milk Collection problem in Chile”. IEEE Congress on Evolutionary Computation (CEC), Wellington, New Zealand, 10-13 June 2019.
12. Polat O, Topaloğlu D. “Milk Collection Network Design İn A Fuzzy Environment”. Economy&Business, 13, 376-384, 2019.
13. Caramia M, Guerriero F. "A Milk Collection Problem with Incompatibility Constraints". Interfaces, 40(2), 130-143, 2010.
14. Laporte G, Nobert Y. “Exact algorithms for the vehicle routing problem”, North-Holland Mathematics Studies 132, 147-184, 1987.
15. Polat O, Kalaycı CB, Kulak O, Günther HO. "A perturbation based variable neighborhood search heuristic for solving the Vehicle Routing Problem with Simultaneous Pickup and Delivery with Time Limit". European Journal of Operational Research, 242(2), 369-382, 2015.
16. Polat O. “A Parallel Variable Neighborhood Search for the Vehicle Routing Problem with Divisible Deliveries and Pickups”. Computers & Operations Research, 85, 71-86, 2017.