文章基本信息

标题：Solving an optimization problem of a profit calculation taking into account fixed costs in Excel
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作者：Lyudmyla Malyarets ; Olesia Iastremska
期刊名称：Problems and Perspectives in Management
印刷版ISSN：1727-7051
电子版ISSN：1810-5467
出版年度：2015
卷号：13
期号：3
页码：104-111
语种：English
出版社：LLC "CPC "Business Perspectives"
摘要：Objective information for making a management decision is formed on the basis of the results of solving optimization problems of costs calculation.A contradiction in an analytical support of a decision making continues to exist,the content of which is a calculation of variable costs mostly in optimization models in the objective function only,but the category of fixed costs is ignored.Most at calculating production profit and each product sales zj only variable costs,which are dependent on the production volume,are usually considered:zj = (cj – qj) xj ,where cj are selling prices,qj are a product production costs;variable costs qj xj are proportional to production volumes ɯj .If fixed costs pj are considered in addition to variable costs and they don’t depend on the production volume,then following formula will be got to calculate the profit zj = (cj – qj) xj + pj .But at ɯj = 0 (when this type of a product is not produced) it should be zj = 0,and not zj = pj ,as it follows from the above-stated formula.Thus,this formula is not quite correct and should be replaced by the more complex one:zj = (cj – qj) xj – pj vj ,where vj are binary indicator variables that equal to unity (vj = 1) if this type of a product is produced and zero (vj = 0) otherwise.An existence of indicator variables means that the profit function is nonlinear.The procedure of solving an optimization problem using Excel spreadsheet is demonstrated in the article.The advantage of the proposed procedure is the ability to solve the problem with parameters that allow you to find the limits of possible variations of the resources (and prices) for the purpose of increasing profits.
关键词：Objective information for making a management decision is formed on the basis of the results of solving optimization problems of costs calculation.A contradiction in an analytical support of a decision making continues to exist,the content of which is a calculation of variable costs mostly in optimization models in the objective function only,but the category of fixed costs is ignored.Most at calculating production profit and each product sales zj only variable costs,which are dependent on the production volume,are usually considered:zj = (cj – qj) xj ,where cj are selling prices,qj are a product production costs;variable costs qj xj are proportional to production volumes ɯj .If fixed costs pj are considered in addition to variable costs and they don’t depend on the production volume,then following formula will be got to calculate the profit zj = (cj – qj) xj + pj .But at ɯj = 0 (when this type of a product is not produced) it should be zj = 0,and not zj = pj ,as it follows from the above-stated formula.Thus,this formula is not quite correct and should be replaced by the more complex one:zj = (cj – qj) xj – pj vj ,where vj are binary indicator variables that equal to unity (vj = 1) if this type of a product is produced and zero (vj = 0) otherwise.An existence of indicator variables means that the profit function is nonlinear.The procedure of solving an optimization problem using Excel spreadsheet is demonstrated in the article.The advantage of the proposed procedure is the ability to solve the problem with parameters that allow you to find the limits of possible variations of the resources (and prices) for the purpose of increasing profits.