Advances in Economics, Business and Management Research, volume 38 Trends of Technologies and Innovations in Economic and Social Studies (TTIESS 2017) Optimization model of production and product sales within profit maximization Maria F. Tyapkina Elena A. Ilina Department of Finance and Analysis Department of Finance and Analysis Irkutsk State Agrarian University named after Irkutsk State Agrarian University named after A.A. Ezhevsky A.A. Ezhevsky Irkutsk, Russian Federation Irkutsk, Russian Federation [email protected] [email protected] Dmitry I. Ilyashevich Department of Finance and Analysis Irkutsk State Agrarian University named after A.A. Ezhevsky Irkutsk, Russian Federation [email protected] Abstract—Demand for some food differs from day to day. For companies do the research of demand for manufactured example, a sharp increase in demand for poultry meat on products. weekends and holidays is notable. In such conditions, companies need to answer the following question: how many products and Thus, the demand for various types of poultry products what kind of products shall be produced and sold to meet the (whole carcass, cuts, minced meat, ends of cuts) differs from demand of buyers under limited resources and, at the same time, day to day. For example, on weekends and holidays there is a to obtain the maximum profit. To answer this question, a model significant increase in demand for poultry meat. In this regard, for optimizing production and products selling within profit the authors believe that the output should depend on the maximization was developed. The main advantages of the consumption habits. proposed model is the creation of a production structure that will provide the maximum profit, while several types of products, sale To increase the efficiency of production and sale of poultry price, limited resources are taken into account. The proposed meat, as well as to improve the supply of poultry products to model was tested on the materials of the operating company. The the population, an economic and mathematical model was model included 14 types of finished products, their sale price, the developed to optimize the production and sale of poultry meat. rate of consumption of raw materials, restrictions on the The task of this model is to determine such structure of available raw materials, technical and labor resources. As a production and sale of poultry meat which will provide result of the application of the model, the structure of production maximum economic benefit, taking into account the and the maximum forecast profit with minimum and maximum availability of production resources and turnover. As a demand were obtained. Practical application of the model is criterion of optimality, the authors used the maximum profit realized using the Microsoft Office application package (Excel). level in the model, since this indicator objectively characterizes the efficiency of production and marketing Keywords—optimization model, profit maximization, poultry activities of the company and is also the main objective of the meat production. business entity activity. I. INTRODUCTION II. BRIEF LITERATURE REVIEW In market conditions, supply often exceeds demand, which The development of optimization models for maximizing adversely affects producers, as it leads to overstocking of the profits was done by such scientists as Y. Jiang, J. Shang, Y. warehouse. If a company is engaged in the production of short Liu, J. May, M. Moghaddam, S.Y. Nof, M. Natter, A.-M. shelf life products, overproduction and additional costs for Ozimec, J.-Y. Kim, A.V. Prokopyeva, A.S. Nechaev, K. maintaining finished products can lead to a loss due to natural Puranam, M. Katehakis, R.W.Seifert, J.-S.Tancrez, I. Biçer, damage to products. M. Tyapkina, E. Ilina and E. Domanova. To provide the population with quality food, as well as to Optimization modeling of agricultural production is increase the efficiency of their own production, agricultural reflected in the works of S. Robinson, H. van Meijl, D. Willenbockel, H. Valin, S. Fujimori, T. Masui, R. Sands, M. Copyright © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). 246 Advances in Economics, Business and Management Research, volume 38 Wise, K. Calvin, P. Havlik, D. Mason d'Croz, A. Tabeau, A. as Rj. For the production and processing of poultry meat, it is Kavallari, C. Schmitz, J.P. Dietrich, M. von Lampe, S. required as followed: resource R1 - the volume of primary raw Shrestha, T. Hennessy, M. Abdalla, D.Forristal, M.B. Jones, materials in the amount of b1 kg; R2 - manpower in the amount Ya. M. Ivano, V. R. Elohin, T. N. Medvedeva. of b2 people; R3 - equipment in the amount of b3 machines. The resource unit cost is dj, RUB. Therefore, the cost of However, the problems of modeling the optimization of production (C ) is calculated as follows: production and sales of products in order to maximize the i profit of a particular enterprise have not been adequately studied. 3 4 C = ∑ d ∑ a x (4) i j ij i j = 1 i = 1 III. MATERIALS AND METHODS The optimization model for the production and sale of where d - the resource unit, RUB; a - R resource poultry meat takes into account various processing options: j ij j consumption rate for the i option product, x - the amount of the whole carcass, cuts (thigh, drumstick, breast, round cut, i the i option product output. wing, fillet, ends of cuts); giblet (gizzard, liver, heart, heads, paws); minced meat. Let us take yv as an amount of a v The production of xi products is demand-based, which is product where v=1, 2. …, 14. determined in the amount of Si kg (i = 1, 2, 3, 4); therefore, S is the total demand for finished products, kg. In this case, carcasses of different weight categories are used for the production of different types of products. Thus, the mathematical model of production and sale plan Carcasses of the first and second weight categories can be optimization of poultry meat is as follows: used to produce all four considered options for poultry products depending on market demand, non-categorized 14 3 4 = − ⇒ carcasses are used to produce minced meat and ends of cuts ∑ pf y ∑ d ∑ a x max (5) = v v = j = ij i products. v 1 j 1 i 1 The authors introduced aiq factor for each weight category limited by: which reflects the ratio of the whole carcass of a q weight 1) Market demand - based products output, kg: category in the i production option, i.e. q = 1, 2, 3 – weight 4 ≤ categories of the poultry; i = 1, 2, 3, 4 – poultry processing ∑ i Sx i i=1 option. For the q weight category, the following condition is fulfilled: 2) The product sales volume not less than the specified 4 4 volume, kg: ∑ x ≤ M , where М – volume of products sold, ∑ a = 1 . (1) = i = iq i 1 i 1 kg; Then, the quantity of finished products (yv), represented by 3) Actual expenditure of raw materials, manpower and separate parts of the poultry carcass (breast, thigh, drumstick, equipment: fillet, wing, etc.), is determined by the following equation: ≤++ bxaxaxa (kg); 4 1313212111 = yv ∑ aiv xi (2) ≤++ bxaxaxa (people); i=1 2323222121 ≤++ bxaxaxa (units). where aiv – ratio of the v part of the carcass in the i 3333232131 production option, x – amount of the produced products in the i 4) Total whole carcass production, kg: y = x i production option, kg. 1 1 5) The amount of finished products which are separate Revenues are defined as the difference between the sale parts of the poultry carcass (breast, thigh, drumstick, fillet, revenues of produced goods and the cost of production. Sale = 4 revenues of products (Tv) are calculated by the following wing, etc.), kg: v ∑ v xay ii formula: i=1 6) Implementation of conditions for each weight 4 = category: ∑ aiq 1 14 i=1 T = ∑ p y (3) v = v v 7) The condition that the variables are not negative: v 1 ≥ ayx iqvi 0,, where pv – sale price of the v type of the finished goods, The described production and sale optimization model of rub. poultry meat within profit maximization is applied with The cost of production depends on the rate of resources Microsoft Office package (Excel). consumption and their cost. Let us denote the used resources 247 Advances in Economics, Business and Management Research, volume 38 IV. RESULTS AND DISCUSSION TABLE I. FACTORS AFFECTING THE DEMAND FOR POULTRY MEAT IN IRKUTSK REGION FOR 2002-2016 In the described model of production optimization and Growth sales of products, one of the limitations is the magnitude of Year Parameters 2002 2013 2014 2015 2016 ratio, demand for products. In this regard, an analysis of demand in times the poultry meat market was conducted using the example of Price for 1 the Irkutsk region. For a more complete analysis of demand, it ton of poultry 24121 62483 67562 69430 81790 3.4 meat, RUB is necessary to consider the dynamics of meat consumption Production of including poultry meat in the region as compared to that in poultry meat, Russia (fig. 1). thousand tons 12.8 33.9 37.1 37.4 40.8 3.2 (slaughter weight) Price for 1 ton of cattle 21731 76361 92551 86290 97096 4.5 meat, RUB Price for 1 ton of pork 41951 168220 183263 192398 177967 4.2 meat, RUB Average per capita monetary 3609 16017 17720 19276 21763.3 6 income, rubles / month. Over the analyzed period, the pork meat price growth rate (4.2 times) is observed over the growth rate of poultry meat Fig. 1. Consumption of meat, meat products and poultry by prices (3.4 times), which, in the authors’ opinion, should lead the population of Russia and Irkutsk region for 2002-2016 to an increase in demand for poultry meat.