Additional aspects of the application of ABC analysis

ABC analysis is a common variation of the Pareto law adjusted for the economy needs to perform rational allocation of resources among the subsets of a specific population (an object of multiple nature) that significantly differ in levels of relevant features. The author refers to papers that describe no less than half a dozen methods for dividing the population into three segments - A, B and C, however, they do not provide any general guidelines for selection of specific methods for objects of any types. The author believes that the search for the best method for general as well as specific cases has no prospects. Using the results of frequency analysis of a multiple object can ensure positive outcome only when it is connected with maximizing a multiple object's efficiency through the optimum allocation of limited resources, which are herein collectively referred to as technology. Warehouse cargo traffic with unequal frequencies of the available inventory (id est, stock items (SI)) was selected as a typical representative of such an object. With this in mind, the objective set is to assign stock items to particular segments of the traffic. Addressing this objective implies division of SI into technologically homogeneous segments (zones). Let us call this approach "technological zone" method (TZ). Let SI traffic frequency vector be ranked in descending order - Q = (q^, ,.,q ₂,.., q _n), n - the number of SI in the traffic, q _i - the frequency of the ith SI. There is a set of technologies Т,-,/ = 1, m to maintain traffic. Each of them is characterized by a vector of values of conditional performance indicator "maintenance" of a traffic item in case of applying Ту to the ith SI - (pij, p ₂j, .., Pnj)- The totality of such indicators comprises the matrix | P _i;-1. In a similar manner, we introduce a matrix | 11 of unit costs of the jth technology resource per unit of ith SI and the matrix of volume restrictions on the use of technology - Let us introduce the variable x _tj - a property of jth technology assigned to the ith SI that assumes zero value if the technology is not applied to maintain the ith SI or positive value if otherwise. The following model is proposed to determine the optimum allocation of technologies among SI: The objective function Ф= YH=iYIj =iXij *qi * p _tj >max, (1) restrictions, taking into account technological resources available ЕГ i]4i^ij for all j = 1, m, (2) restrictions of mandatory "maintenance" of all SI YIJLi Xij q _t = q _t for all i = 1, n . (3) non-negative restrictions of the unknown variables Xij >0 for all i = 1, n and j = 1, m (4) The resulting decision matrix ||x;j|| defines the division of the object into "technological zones". Quasi-diagonal matrix ||x;j|| is the most favorable decision option. It corresponds to the establishment of optimum structure complex of technologies that maintain the traffic. The intermittent nature of j-zones reduces the efficiency of the corresponding production subsystems, hence such decision option leads to the problem of consolidation, which deserves thorough examination in a separate publication. Development of simplified complexes of locally unified techniques (according to the simplest scenario, proportion schemes) for Q-series partitioning into segments can appear promising due to the relative complexity of the TZ-method when applied in logistics.

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