=Paper= {{Paper |id=Vol-2018/paper-08 |storemode=property |title=Modeling of Regional Limits to the Ferrous Scrap Prices Growth in Russia Based on the Auction Pricing |pdfUrl=https://ceur-ws.org/Vol-2018/paper-08.pdf |volume=Vol-2018 |authors=Tatiana Ivanova,Violetta Trofimova,Mariia Karelina }} ==Modeling of Regional Limits to the Ferrous Scrap Prices Growth in Russia Based on the Auction Pricing== https://ceur-ws.org/Vol-2018/paper-08.pdf
             Modeling of Regional Limits
    to the Ferrous Scrap Prices Growth in Russia
            Based on the Auction Pricing?

Tatiana Ivanova1[0000−0002−5600−1841] , Violetta Trofimova[0000−0002−4167−4007] ,
                  and Mariia Karelina[0000−0001−7477−3194]

        Nosov Magnitogorsk State Technical University, Magnitogorsk, Russia
                                1
                                  jun275@mail.ru



        Abstract. One of the instruments of price policy at metallurgical plants
        in procurement of ferrous scrap is a differentiated approach in setting
        prices for scrap depending on the region of the country. For these pur-
        poses, the mathematical “Auction procurements” model based on the
        auction principle pricing was developed in order to assess the range
        of regional scrap prices of scrap stockists taking into account compe-
        tition between scrap consumers. Construction of such a model will allow
        taking into account territorial imbalances of scrap offer and demand in
        the regions, costs of scrap transportation from supplier to consumer for
        price formation. The model allows estimating limits of growth of regional
        prices and inter-regional flows of scrap. The article presents the formal
        structure of the model, the algorithm of its implementation and the re-
        sults of calculations. The proposed mathematical model implements a
        differentiated approach to formation of the regional scrap prices range,
        simulating a competitive activity for scrap collection markets of metal-
        lurgical enterprises taking into account market trends.

        Keywords: computer modeling of limits price growth, decision making,
        ferrous scrap


1     Introduction

One of the instruments of price policy at metallurgical plants in procurement of
ferrous scrap is a differentiated approach in setting prices for scrap depending
on the region of the country [14]. When forming a pricing quotation for a region,
decision-makers have to operate with a range of prices to get an idea of the price
tolerance range and price point values as final results of the evaluation.
    Point estimates of the scrap value do not show the boundaries of the price
range as a decision-making area. In this connection, it is interesting to estimate
boundaries of the price change interval. The market price of the scrap is formed as
a result of negotiations between scrap producers and consumers so the price range
may be considered as the area of intersection of interests of the seller and the
?
    This work was supported by the Magnitogorsk Iron and Steel Works OJSC.
buyer. The lower limit will correspond to the minimum price, at which the seller
agrees to sell his goods, and the upper limit – to the maximum price, at which
the buyer agrees to buy the goods. It is obvious that the transaction will take
place if the price is within the range. Having information about the boundaries
of the most likely price, the buyer and the seller have the instrument to justify
their decisions and ensure more accurate price positioning corresponding to their
expectations [6].
    In view of the above, the aims of this research include analyzing the purchase
prices for ferrous scrap and developing a regional scrap procurement model for
Russian metallurgical companies.
    As part of the research, the following objectives were achieved:
 – a theoretical analysis of recent developments in mathware designed for cal-
   culating the purchase price range for ferrous scrap;
 – a method was developed for compiling the range of regional scrap prices and
   for generating the regional scrap procurement model;
 – a mathematical model was developed for procurement auctions that can help
   estimate the top regional price line for scrap based on consumer competition;
 – a logical structure was developed for input and output data for modelling;
 – a software package was developed.


2   Review of existing methods for price range
    determination
Among the most frequently used practical approaches to estimation of the price
ranges, we can distinguish economical, statistical one based on the current prices
level and technocratic approaches.
    With the economic approach, the lower limit of the price is estimated by
the seller as the price covering costs and allowing you to get a reasonable profit
for this sector of the economy, and the upper limit would correspond to the
minimum expected profit of the buyer. However, on the scrap metal market,
which is a consumer market, this approach fails to work. Purchase prices in a
region ranging from minimum to maximum are formed based on the purchase
prices of metallurgical enterprises and are set on the customer’s discretion [6].
    The statistical approach determines price limits as the confidence interval
of the mathematical expectation with unknown dispersion. The interval width
characterizes the degree of possible proximity of the sample estimate of the mean
scrap price in the region to an unknown value of the average of the universe
parent population and is explained not by market conditions but by the random
nature of the prices. It will depend on the prices in the region and the sample
size, i.e., a wide interval may be obtained both for regions where the number of
consumers purchasing scrap is small under low price dispersion, and for regions
with large dispersion of mill prices because of a relatively large volume of the
sample [1].
    Within the framework of the approach based on the current price level, the
price range is composed of the price sample values of comparable operations
between the lower and the upper quartile of such range [15]. The values of the
lower and upper quartiles are respectively minimum and maximum values of
the price range. Commercial offers of companies are used as initial data for
calculations; for purchasing scrap metal, these are regional prices for certain
types of scrap set out by steelworks.
    As a part of the technocratic approach, estimate of the price range is based on
a mathematical model of a process or an object. Mathematical models represent
schematic reflection of the influence impact of various factors on the price level.
In [5, 7], the problem of modeling regional prices and inter-regional deliveries on
the scrap market of the United States is considered. The prices for two grades
of the ferrous scrap are calculated (low-residual scrap, a circulating scrap in
the production activity of metallurgical enterprises and high-residual scrap, a
depreciation scrap, its source is out of use steel products collected from local
inhabitants) in each region of the US (that is, regional distribution of prices is
considered). Distribution of the scrap for a particular user is determined on the
basis of a logistic choice model based on the prices of scrap suppliers. This model
takes into account the regional distribution of demand and offer of the scrap.
In addition, the inter-regional flows of scrap metal and the sensitivity of the
equilibrium values of prices to changes on the scrap market are assessed (taking
into account appearance or exit from the market of major consumers, etc). The
model proposed in that paper includes a number of assumptions that may not
work on scrap markets of other countries: the assumed market model is perfect
competition; a logistic choice model for the spatial distribution of scrap is used
based on the idea of heterogeneity in the behavior of market agents [2, 3, 11, 12];
other assumptions include the model for determining ratio in consumption of
scrap of the first and the second type; assumption on proportionality between
the population of the region and volume of offer of the second scrap type in the
region and the quadratic form of dependency of the scope of offer on the price of
scrap. Moreover, a weak point of the model is the need for appropriate choice of
the parameters (B, a) for each time period. Another drawback is that the model
does not take into account seasonal variations in the scope of demand and offer
of the scrap metal. Issues of the spatial pricing equilibrium are subject of many
studies beginning with Hotelling’s model [8]. The existence of equilibrium in
formal spatial models was studied by Aspremont, Gabszewicz, Thisse [4], Palma
et al. [2, 3, 11, 12], Sheppard, Haining, Plummer [13] and others.
   To construct the interval estimation of scrap prices on the Russian market,
the current price level and technocratic approaches can be used. In the approach
based on the current price level, the price range will reflect the current situation
on the scrap market. The use of mathematical models allows getting an alter-
native estimate of the price range taking into account factors inherent in the
mechanism of the model. That is, the use of mathematical models allows ex-
cluding the impact of the irrational behavior of the players on the scrap market
and allows obtaining justification of high or low prices of the scrap by regions.
   The paper deals with the construction of interval estimation of price on the
basis of a mathematical model. When forming the price range, the estimation
of the lower boundary of the scrap price is suggested from the “export parity”
principle for scrap producers on the basis of equality of prices on domestic and
foreign markets. The price in the “export parity” mechanism is calculated as the
minimum level of scrap prices, to which scrap stockists and sellers are oriented.
The upper limit should reflect maximum price level, which a buyer (scrap con-
sumer) could offer. In practice, when forming price quotations, scrap consumers
are guided by the competition level existing in the region of scrap purchase. If
the demand level is below or equal to the level of offer, prices are generally set
at the lower limit. If demand exceeds offer, prices are growing as a result of
competition between scrap consumers. The extent, to which a particular scrap
consumer may increase prices, is modeled on an individual basis based on taking
into account the average purchase price of scrap for a metallurgical plant, cost
of delivery from the scrap stockist to the plant, terms of delivery proposed by
scrap producers in other regions and demand level of the metallurgical plant.
The authors developed a mathematical model of “Auction procurements” sim-
ulating the process of price competition of metallurgical enterprises for scrap
volumes in the regions taking into account the factors described above. This
approach has not been covered yet in published works of Russian and foreign
researchers [9, 10].


3   Research Methodology

The mechanism of formation of maximum price level for scrap stockists simu-
lates the process of competition for volumes of scrap between consumers and
is based on scrap demand and offer ratio departing from the “export parity”
prices for producers and taking into account delivery costs to consumers. The
model includes a mechanism of interaction of prices of neighboring producers. In
the course of iterative calculations, prices of scrap producers increase with some
incremental step depending on the selected simulation parameters. The growth
of price for a scrap producer will stop when the demand for its stock will be
exhibited by a single user only. The criterion for stopping the iterative modeling
process is the achievement of equilibrium in the market, i.e., the situation when
for the majority of scrap producers the price growth stops. The price range for
purchase of scrap by regions of the RF is determined as a range between the
lower price level (the price calculated from the “export parity” principle), and
the upper price level, the price of the “export parity” plus an allowance calcu-
lated by the “Auction procurements” model. The model also designs an optimal
regional structure of scrap procurement for each scrap consumer at each price
level from the point of view of his individual interests in the form of a list of
scrap procures offering the most favorable purchase prices of scrap taking into
account delivery costs.
    Description of “Auction procurements” model and the modeling process.
Initial data: n is the number of scrap producers; m is the number of consumers;
V proc is the volume of the scrap at the stock of the scrap producer, t; V dem is the
demand of the scrap consumer, t; freight rates between procurers and consumers;
freight rates between procurers; cEP
                                  i  is the starting prices of producers, calculated
by the “export parity” principle according to the formula:

                    cEP
                     i  = max {CPk − Ti,k } ,        i = 1, . . . , n,             (1)
                           1≤k≤5

where Ti,k are freight rates between the i-th producer and k-th “export hub”; i is
the number of the scrap producer; n is the total number of scrap procures; k is
the number of the “export hub”; CPk is the reduced price for the 3A type scrap
for the k-th port (“export hub”) in rubles, which is calculated by the following
rule:
             CPk = (PPk − Tax − CCk ) · R + PTS, k = 1, . . . , 5,            (2)
where PPk is the price in the port of shipment k (without freight); Tax is the
tax to be paid to the RF budget; CCk is the cost of cargo handling services; R
is dollar exchange rate, RUB; PTS is the scrap type-specific allowance.
    Step 1. The iterative process of calculating scrap demand coefficients for each
producer.
 1. For each particular consumer of scrap, the optimal purchase plan is deter-
    mined taking into account only its interests, i.e. the problem of minimizing
    the purchasing cost of scrap for this consumer is solved. In the calculations,
    the price of scrap per ton for a consumer is defined as the producer’s price
    for scrap plus freight rate from procurer to consumer. For the first step, the
    producer’s price of scrap is used, which is calculated as the “export parity”
    cEP
     i   value and initial volumes of procurers’ stock. For next steps, the adjusted
    price calculated at the previous iteration ci (Step 2) and adjusted volumes
    of procurers’ stocks (cl. 4 of step 1) are used.
 2. Total demand for scrap of each of n producers, Videm from the part of m
    consumers on the basis of optimal procurement plans found in cl. 1 of step
    1 is calculated.
                      V dem
 3. The factor ki = iproc , is calculated, where i = 1, . . . , n, Videm is total scrap
                      Vi
    demand for the scrap for the i-th producer; Viproc is the volume of scrap
    stocks of the i-th producer.
 4. Check of conditions for stopping the iterative process coefficients calculation.
    In case of equality of the total volume of stocks and scrap demand, the
    absence of coefficients less than 1 is verified indicating complete satisfaction
    of scrap consumer’s needs. If the condition is fulfilled, then go to step 2,
    otherwise for producers with coefficients above 1 initial volumes are divided
    by ki , for other procurers, initial volumes do not change and we go to cl. 1
    of step 1.
   Step 2. Adjustment of scrap producer’ prices
 1. Checking condition for stopping the iterative process of scrap producer’
    prices recalculation: coefficients are equal to unity for all producers. If this
    condition is satisfied, then the iterative process is stopped and price model-
    ing is completed. If the condition is not fulfilled, the producers’ prices are
   recalculated according to cl. 2–3 of step 2 and the transition to step 1 is
   performed.
2. Change in price ∆i for the i-th producer is calculated depending on de-
   mand/offer ratio for the procurer and its ni neighboring producers, nearest
   to him (j = 1, . . . , ni ), within the radius R by an iterative formula (3).

                        1−sign(kj −1)
             
               j−1
             ∆i + (−1)
             
                             2       · dij ,             if (kj − 1) · ∆ij−1 < 0;
                    1−sign(kj −1)
     ∆ji =     (−1)       2
                                    · max(dij ; |∆j−1 |), if (kj − 1) · ∆ij−1 ≥ 0;
                                                 i
              j−1
             
               ∆i ,                                       if kj = 1
                                                                      j = 1, . . . , ni , (3)

   ∆i = ∆ni i is the total change in the price of scrap for the i-th producer taking
   into account the influence of demand and offer of neighboring producers,
   ∆0i = 0;
   ∆ji is an intermediate value for calculation of the price change ∆i ;
   dij is the price change of the i-th producer under the influence of demand/offer
   ratio at the j-th procurer, which is estimated in accordance with (4):
             
                                            tar2
                                               ij
                                      −
                                              R 2
                                           ( 2.5 ) , if k > 1;
                                        2
               delta · (k    − 1)  · e
             
             
             
                          j                             j
                                            tar2
             
                                              ij
                                       −
      dij =                                   R 2                 j = 1, . . . , ni , (4)
             
              delta · ( k1j − 1) · e 2( 2.5 ) , if 0.1 < kj < 1;
             
                                   2
                                 tarij
             
                            −         2
                               2( R )
             
              delta · 5 · e      2.5    ,           if kj < 0.1,

   where delta is the price change increment step, RUB; tarij is the tariff dis-
   tance between the i-th and j-th producer; R is the radius (tariff distance),
   within which the influence of the demand/offer ratio on the neighboring
   procurers is taken into account, ni is the number of neighboring producers
   within a radius R of the i-th producer.
3. Recalculation of producer’ scrap prices taking into account price change ∆i ,
   provided that the price cannot fall below the price value of the “export
   parity” according to the rule:
                           (
                             cold
                              i   + ∆i , if cold
                                              i   + ∆i > cEP
                                                          i ;
                      ci =    old
                                                                             (5)
                             ci ,         if ci + ∆i ≤ cEP
                                              old
                                                          i ,


   where cold
          i   is the price calculated at the previous iteration.
    Parameters of the model delta and R are tuned taking into account the
following recommendations:
 – delta is the extra charge per unit change of the coefficient: the lower is
   this step value, the more accurate is the simulation result, but the total
   computation time of the algorithm increases;
 – R is the radius of influence of the scrap producer’s price on the prices of his
   neighbors: a larger radius involves more neighboring producers in the price
   change process and could destabilize the process of finding an equilibrium
   price.
   In practice, solving large-scale problems with hundreds of scrap producers
   and dozens of scrap consumers made vital the questions of ensuring con-
   vergence of the algorithm and reducing the computation time. To this end,
   a number of assumptions were introduced into the model leading to errors
   occurrence:
 – at the step 1, cl. 4, when checking conditions for stopping the iterative process
   of calculation of coefficients, the condition of the absence of the coefficients
   less than unity is replaced by the check for number of producers with this
   coefficient equal to zero; their number should be less than 3% of the total
   number of producers. The closer to zero is this parameter, the more precise
   are the calculations, however, the calculation time increases. Relaxing this
   condition leads to occurrence of “doubled” consumption volumes in the sys-
   tem at each iteration step, i.e. volumes of the same scrap, which are taken
   into account for several scrap consumers simultaneously; at the step 2, cl. 1
   a fixed number of iterations and a posteriori selection of the optimal iter-
   ation number at the moment of stabilization of prices is performed. In the
   condition for stopping the iterative process of producers’ prices recalculation
   instead of checking the equality of coefficients to unity for all producers, the
   algorithm stops upon reaching a predetermined number of iterations, and
   then the iteration is selected, according to which, scrap prices of all produc-
   ers are determined. Iteration selection criterion is as follows: the number of
   scrap producers with coefficients equal to unity must be greater than 75%
   of the total number of producers and the increase in the number of stations
   with coefficient equal to unity in one step should be maximal. Such criterion
   of iteration number selection allows us to find the moment of stopping the it-
   erative process for price determination, when in the course of the process the
   price stabilization is reached, i.e., prices do not change significantly anymore
   and the local minimum of total costs for the purchase of scrap in Russia as a
   whole is reached. To ensure that an iteration number meeting the specified
   requirements will be found, the algorithm provides a possibility of reducing
   the percentage of stations with the coefficient equal to unity below 75% of
   unit coefficients.

    Under these assumptions, the overall price calculation error is the sum of
errors at previous iterations.
    To detalize the mathematical formulation of the problem, let us list the
sources of the original data and factors with a significant influence on the simu-
lation results, in this case, on the scrap conveyance plan. In the study only the
volumes of scrap carried by railroad transport are considered since the sole car-
rier of goods by rail in Russia is Russian Railways JSC, and it maintains a com-
plete database on volumes of scrap metal shipment, points of departure/delivery,
preparation and organizations – consignors/consignees, etc. By the estimate of
IA “Metal-Courier”, in 2015 the railway transport transported about 77% of the
total amount of scrap collected in the RF. Scopes of delivery by water and road
transport are not taken into account, as there is no single all-Russian database
on these shipping operations. R/w stations are considered as both consumers
and producers of scrap. The number of scrap producers (n) is taken to be equal
to the number of departure stations per the database of Russian Railways JSC,
the number of scrap consumers (m) is equal to the number of scrap reception
stations. Using the database of r/w transportation of scrap for the selected pe-
riod for each station of departure and destination, aggregated volumes of scrap
are determined, which are taken as volumes of stocks (Viproc ) and volumes of
demand (Videm ), respectively. The problem was solved only for the part of the
scrap flows, which is supplied by the producers who are not subsidiaries of the
metallurgical plants (independent suppliers), since it is assumed that volumes of
scrap transported by subsidiaries cannot be reallocated.
    The following initial data was used: data on railroad transportation of ferrous
scrap in the RF provided by Russian Railways JSC (departure station and des-
tination station, the organization – consignor and organization – consignee, the
amount of cargo, kind of cargo, date of dispatch); handbooks of railway tariffs
10-01 between r/w stations of the RF, statistical data on prices of scrap metal of
3A type in the “export hubs” (seaports: St. Petersburg, Novorossiysk, Rostov-
on-Don, Vladivostok and the border crossing on the border with Belarus); the
cost of services in the “export hub” for handling scrap metal; dollar exchange
rate; data on subsidiaries of metallurgical plants carrying out scrap collection;
quotations of purchase prices for scrap of 3A type for a number of particular
metallurgical enterprises in Russia’s regions.
    On the basis of the calculation results in terms of r/w stations, we calculated
the weighted average cost indices by regions of the RF and formed the reports
for major metallurgical plants.
    Software was developed for algorithm implementation and for pre-processing
of initial data and report generation. Microsoft Office Excel 2007 with the Visual
Basic for Application programming language was used as a development tool.
The software is a MS Office Excel add-in programme (*.xlam). The source data
is stored in Oracle Database 10g on a server. The programme communicates
with the database via ADO (with Oracle OLEDB Provider). This technology is
designed for both local databases and File/Server and Client/Server databases.
Oracle SQL Developer 4.1.1 was applied for SQL queries and PL/SQL units.


4   The results of calculations

The results of price modeling for scrap of 3A type, based on the “Auction pro-
curements” model are illustrated by the example of calculations for May 2015
for the RF as a whole and for MMK OJSC.
    Figure 1 shows the distribution of average weighted purchasing prices by re-
gions of the RF for the billing month: prices calculated by the “export parity”
principle, actual prices and the maximum scrap price level per “Auction pro-
curements” model. The width of the interval between the price by the “export
parity” and “Auction procurements” model characterizes the possible level of
warm-up in prices in the collision of interests of buyers. Therefore, the maxi-
mum width of the interval is observed in Chelyabinsk, Sverdlovsk, Kurgan and
other regions where scrap demand exceeds offer significantly.




Fig. 1. Weighted average prices for scrap without delivery in the regions of the Russian
Federation by the “export parity” principle, prices by the “Auction procurements”
model, May 2015


    Figure 2 shows the distribution of weighted average prices for scrap including
delivery from regions of the RF to MMK OJSC by “export parity” actual and
the “Auction procurements” model prices for May 2015.
    When comparing the actual and model prices, the most interesting are the
cases of exceedance of the actual price beyond the upper limit of the price interval
calculated by the “Auction procurements” model; here one can say that the
enterprise price is overrated with respect to simulated possible price increase
under conditions of scrap consumers competing for the regional scrap market. In
May 2015 for MMK OJSC actual prices with delivery go beyond the boundaries
of the interval only for the Omsk region.
    Prices by the “Auction procurements” model correspond to a particular re-
gional scrap purchase pattern. Figure 3 presents charts for actual and model
procurement plans for MMK OJSC without taking into account the volumes
supplied by subsidiary enterprises. The scrap purchase plan by the “Auction
procurements” model shows the regional structure, which could be formed for
MMK OJSC, if metallurgical enterprises adhered to the strategy of the fierce
price struggle competing for scrap collection markets. As can be seen from the
Figure showing the model price levels, MMK OJSC has the scrap purchase struc-
ture, which is maximally localized near the enterprise, i.e. the company has
Fig. 2. Weighted average delivered prices of scrap in the regions by “export parity”,
in fact and by the “auction procurements” model, May 2015


maximum reserve for raising purchase price in home regions as compared with
competitors at the expense of savings in delivery.




Fig. 3. Charts of actual and model procurement plans for MMK OJSC without taking
into account volumes supplied by subsidiary enterprises, tons, May 2015




5   Conclusions
The proposed mathematical model implements a differentiated approach to for-
mation of a regional scrap prices range simulating a competitive activity for scrap
collection markets of metallurgical enterprises and taking into account market
trends.
    Prices yielded by the “Auction procurements” model can be used in man-
agement as potentially the highest price levels which can be reached under con-
ditions of competitive struggle between scrap consumers in a situation where
negotiations are excluded.


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