Abstract
Large-scale feed factories may have multiple production and storage facilities. Any production facility uses its own available raw materials while performing feed formulation. However, ensuring a reasonable cost is achieved, and the desired quality criteria are met, may require obtaining a certain amount of raw material from other facilities. Selecting a specific amount of raw materials among many raw materials in different facilities requires many combinations to be tried out. Providing solutions, especially when there is a large amount of the raw material, may be costly and take more time. A new mixed-integer linear programming (MILP) model that specifies the type of material and the amount of the material to be selected from external facilities has been proposed in this study. When deterministic methods like MILP are used, only one solution result is obtained. However, when the decision-maker would like to see alternative results, solution constraints can be mitigated and a solution provided within the same or similar time. A new method named hybrid-linear binary PSO (H-LBP) has been proposed in this study for the problems that the decision-maker had limited time for and for which the solution results were required in a shorter time. Continuous particle swarm optimization, which works as a hybrid with linear programming, has been used in this method. The new model proposed in this study was tested on the mixed feeds for sheep, cattle and rabbit species by using both MILP and the proposed H-LBP methods. Raw materials determined by the model were added to the mixture, and the cost in each of the three species was observed to go down. In addition, different alternative solutions at reasonable cost and similar quality were presented to the producer/decision-maker in a shorter time.
Similar content being viewed by others
References
Waugh FV (1951) The minimum-cost dairy feed (an application of “linear programming”). J Farm Econ 33:299–310
Barbieri MA, Cuzon G (1980) Improved nutrient specification for linear programming of penaeid rations. Aquaculture 19(4):313–323. doi:10.1016/0044-8486(80)90080-0
De Kock HC, Sinclair M (1987) Multi-mix feedstock problems on microcomputers. J Oper Res Soc 38(7):585–590. doi:10.2307/2582395
Chappell AE (1974) Linear programming cuts costs in production of animal feeds. J Oper Res Soc 25(1):19–26
Munford AG (1989) A microcomputer system for formulating animal diets which may involve liquid raw materials. Eur J Oper Res 41(3):270–276. doi:10.1016/0377-2217(89)90248-8
Munford AG (1996) The use of iterative linear programming in practical applications of animal diet formulation. Math Comput Simul 42(2–3):255–261. doi:10.1016/0378-4754(95)00115-8
Chakeredza S, Akinnifesi FK, Ajayi OC, Sileshi G, Simon M, Gondwe FMT (2008) A simple method of formulating least-cost diets for smallholder dairy production in sub-Saharan Africa. Afr J Biotechnol 7(16):2925–2933
Glen JJ (1980) A mathematical programming approach to beef feedlot optimization. Manage Sci 26(5):524–535. doi:10.1287/mnsc.26.5.524
Htun MS, Thein TT, Tin TP (2005) Linear programming approach to diet problem for black tiger shrimp in shrimp aquaculture. In: 2005. APSITT 2005 proceedings. 6th Asia-Pacific symposium on information and telecommunication technologies, 10–10 Nov 2005, pp 165–170. doi:10.1109/APSITT.2005.203650
Mohr GM (1972) The bulk constraint and computer formulations of leastcost feed mixes. Rev Mark Agric Econ 40(1):15–28
O’Connor JD, Sniffen CJ, Fox DG, Milligan RA (1989) Least cost dairy cattle ration formulation model based on the degradable protein system. J Dairy Sci 72(10):2733–2745. doi:10.3168/jds.S0022-0302(89)79417-0
Rehman T, Romero C (1984) Multiple-criteria decision-making techniques and their role in livestock ration formulation. Agric Syst 15(1):23–49. doi:10.1016/0308-521X(84)90016-7
Rehman T, Romero C (1987) Goal programming with penalty functions and livestock ration formulation. Agric Syst 23(2):117–132. doi:10.1016/0308-521X(87)90090-4
Zhang F, Roush WB (2002) Multiple-objective (goal) programming model for feed formulation: an example for reducing nutrient variation. Poult Sci 81(2):182–192. doi:10.1093/ps/81.2.182
Lara P, Romero C (1992) An interactive multigoal programming model for determining livestock rations: an application to dairy cows in Andalusia, Spain. J Oper Res Soc 43(10):945–953. doi:10.2307/2584548
Tozer PR, Stokes JR (2001) A multi-objective programming approach to feed ration balancing and nutrient management. Agric Syst 67(3):201–215. doi:10.1016/S0308-521X(00)00056-1
Pomar C, Dubeau F, Létourneau-Montminy MP, Boucher C, Julien PO (2007) Reducing phosphorus concentration in pig diets by adding an environmental objective to the traditional feed formulation algorithm. Livest Sci 111(1–2):16–27. doi:10.1016/j.livsci.2006.11.011
Mitani K, Nakayama H (1997) A multiobjective diet planning support system using the satisficing trade-off method. J Multi Criteria Decis Anal 6(3):131–139. doi:10.1002/(SICI)1099-1360(199705)6:3<131:AID-MCDA129>3.0.CO;2-S
Glen JJ (1986) A linear programming model for an integrated crop and intensive beef production enterprise. J Oper Res Soc 37(5):487–494. doi:10.2307/2582671
Polimeno F, Rehman T, Neal H, Yates CM (1999) Integrating the use of linear and dynamic programming methods for diary cow diet formulation. J Oper Res Soc 50(9):931–942. doi:10.2307/3010190
Cadenas JM, Pelta DA, Pelta HR, Verdegay JL (2004) Application of fuzzy optimization to diet problems in Argentinean farms. Eur J Oper Res 158(1):218–228. doi:10.1016/S0377-2217(03)00356-4
Furuya T, Satake T, Minami Y (1997) Evolutionary programming for mix design. Comput Electron Agric 18(2–3):129–135. doi:10.1016/S0168-1699(97)00025-2
Altun AA, Şahman MA (2013) Cost optimization of mixed feeds with the particle swarm optimization method. Neural Comput Appl 22(2):383–390. doi:10.1007/s00521-011-0701-8
Li F-C, Jin C-X (2008) Study on fuzzy optimization methods based on principal operation and inequity degree. Comput Math Appl 56(6):1545–1555. doi:10.1016/j.camwa.2008.02.042
Genova K (2011) A heuristic algorithm for solving mixed integer problems. Cybern Inf Technol 11(2):3–12
Garey MR, Johnson DS (1979) A guide to the theory of NP-completeness. In: Klee V (ed) Computers and intractability. W H Freeman and Company, New York, pp 1–15
Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization: algorithms and complexity. Dover Publications Inc, Mineola, pp 156–190
Gendreau M, Potvin J-Y (2005) Metaheuristics in combinatorial optimization. Ann Oper Res 140(1):189–213. doi:10.1007/s10479-005-3971-7
Wilbaut C, Hanafi S (2009) New convergent heuristics for 0–1 mixed integer programming. Eur J Oper Res 195(1):62–74. doi:10.1016/j.ejor.2008.01.044
Kıran MS, İşcan H, Gündüz M (2012) The analysis of discrete artificial bee colony algorithm with neighborhood operator on traveling salesman problem. Neural Comput Appl 23(1):9–21. doi:10.1007/s00521-011-0794-0
Glover F, Laguna M (1997) General purpose heuristics for integer programming—part I. J Heuristics 2(4):343–358. doi:10.1007/BF00132504
Glover F, Laguna M (1997) General purpose heuristics for integer programming—part II. J Heuristics 3(2):161–179. doi:10.1023/A:1009631530787
Ibaraki T, Ohashi T, Mine H (1974) A heuristic algorithm for mixed-integer programming problems. In: Balinski ML (ed) Approaches to integer programming, vol 2. Mathematical programming studies. Springer, Berlin, pp 115–136. doi:10.1007/BFb0120691
Luo Y-C, Guignard M, Chen C-H (2001) A hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization. J Intell Manuf 12(5–6):509–519. doi:10.1023/A:1012256521687
Sgurev V, Vassilev V, Vladimirov P (1985) An algorithm of external feasible integer directions for integer programming problems. In: Coelho JD, Tavares LV (eds) Or models on microcomputers. North-Holland Publishing Company, Amsterdam, pp 137–146
Rahman RA, Chooi-Leng A, Ramli R (2010) Investigating feed mix problem approaches: an overview and potential solution. World Acad Sci Eng Technol 47:424–432
Silver EA (2004) An overview of heuristic solution methods. J Oper Res Soc 55(9):936–956
Eberhart R, Kennedy J (1995) New optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science (MHS’95), Nagoya, pp 39–43
Fvd Berg, Engelbrecht AP, Engelbrecht AP (2000) Cooperative learning in neural networks using particle swarm optimizers. S Afr Comput J 26:84–90
Salman A, Ahmad I, Al-Madani S (2002) Particle swarm optimization for task assignment problem. Microprocess Microsyst 26(8):363–371. doi:10.1016/S0141-9331(02)00053-4
Allahverdi A, Al-Anzi FS (2006) A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application. Comput Oper Res 33(4):1056–1080. doi:10.1016/j.cor.2004.09.002
Eberhart R, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: Porto VW, Saravanan N, Waagen D, Eiben AE (eds) Evolutionary programming VII, vol 1447. Lecture notes in computer science, vol 1447. Springer, Berlin Heidelberg, pp 611–616. doi:10.1007/BFb0040812
Naka S, Genji T, Yura T, Fukuyama Y (2003) A hybrid particle swarm optimization for distribution state estimation. IEEE Trans Power Syst 18(1):60–68. doi:10.1109/TPWRS.2002.807051
Yoshida H, Kawata K, Fukuyama Y, Nakanishi Y (1999) A particle swarm optimization for reactive power and voltage control considering voltage stability. In: Proceedings of the international conference on intelligent system application to power system (ISAP’99), Rio de Janeiro, pp 117–121
Sevkli M, Guner AR (2006) A continuous particle swarm optimization algorithm for uncapacitated facility location problem. In: Paper presented at the proceedings of the 5th international conference on ant colony optimization and swarm intelligence, Brussels
Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: 1997 IEEE international conference on systems, man, and cybernetics, 1997. Computational cybernetics and simulation, vol. 4105, 12–15 Oct 1997, pp 4104–4108. doi:10.1109/ICSMC.1997.637339
Yin P-Y (2004) A discrete particle swarm algorithm for optimal polygonal approximation of digital curves. J Vis Commun Image Represent 15(2):241–260. doi:10.1016/j.jvcir.2003.12.001
Liao C-J, Chao-Tang T, Luarn P (2007) A discrete version of particle swarm optimization for flowshop scheduling problems. Comput Oper Res 34(10):3099–3111. doi:10.1016/j.cor.2005.11.017
Pan Q-K, Fatih Tasgetiren M, Liang Y-C (2008) A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Comput Oper Res 35(9):2807–2839. doi:10.1016/j.cor.2006.12.030
Gürdoğan N (1981) Üretim planlamasında doğrusal programlama ve demir çelik endüstrisinde bir uygulama, vol 473. Ankara Üniversitesi Siyasal Bilgiler Fakültesi Yayınları
Coşkun B, İnal F, İnal Ş (2014) Ration programs. http://www.selcuk.edu.tr/dosyalar/files/014/RASYON.rar. Accessed 17 Jan 2016
Coşkun B, İnal F, Şeker E (2000) Yemler ve Teknolojisi. Veterinary Medicine Faculty Publication Unit, Selçuk University Konya
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Şahman, M.A., Altun, A.A. & Dündar, A.O. A new MILP model proposal in feed formulation and using a hybrid-linear binary PSO (H-LBP) approach for alternative solutions. Neural Comput & Applic 29, 537–552 (2018). https://doi.org/10.1007/s00521-016-2467-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-016-2467-5