Fixed production cost (fpc) planning step holds
the estimated fixed production cost on plant (plt)
basis as given in Equation 5. This fixed cost
component reflects the production cost drivers
that are not affected by the production volume but
correlated with installed capacity such as
amortization and direct labor cost calculated
according to the production routing.
Sample planning user interfaces for sales,
transportation and production planning steps are
given in Appendix. Additionally, capacity constraints
are other determinants handled at data management
phase:
Plant-based capacity planning step includes plant
utilization rate, total capacity, and product type
(bag or bulk) capacity figures on plant (plt) basis.
These capacity figures per plant are revaluated on-
the-fly by the utilization rate input.
At product-based capacity planning step, capacity
figures are specifically planned at product
(dp
i
.prd) and plant (plt) details. These product
relevant capacity figures per plant are calculated
on-the-fly by the utilization rate planned at
previous plant-based capacity planning step.
3.2.2 Optimization
Optimization phase consists of three steps namely
network optimization data pre-processing,
optimization and valuation as shown in Figure 2.
In network optimization data pre-processing,
three different input data, which are objective
function coefficients (coef
dpi,pltj
) for all demand
point:plant combinations, demand satisfaction and
capacity constraints, are all generated by using
customization, master and planning data for the
underlying version.
In the case of contribution margin maximization
objective function preference for the underlying
version, objective function coefficient (coef
dpi,pltj
in
Equations 3-4) implies the sum of gross sales
(Equation 2), transportation cost (Equation 3) and
variable production cost (Equation 4) for each
demand point(dp):plant(plt) combination. In the case
of net profit maximization objective function
preference, fixed production cost is also considered at
objective function calculation as given in Equation 5.
Underlying objective function coefficient calculation
steps are given at Equations 2-5:
DP = STP × PRD
(1)
gr_sl
dpi
= vol
dpi
× prc
dpi
(2)
coef
dpi,pltj
= gr_sl
dpi
−
vol
dpi
× trs
dpi.stp,dpi.prd_typ,pltj
(3)
coef
dpi,pltj
= coef
dpi,pltj
−
vol
dpi
× vpc
dpi.prd,pltj
(4)
coef
dpi,pltj
= coef
dpi,pltj
−
vol
dpi
× fpc
pltj
(5)
Demand satisfaction constraint holds the planned
sales volumes of the demand points that are set as
simulated at simulated/preset indicator. In other
words, preset demand points are omitted at demand
satisfaction constraint. This constraint line item also
holds additional information such as ship-to-party,
product and product type features of the underlying
demand point. As a restriction, total volume of
demand point must be replenished by a single plant.
Since underlying sales volume cannot be distributed
over multiple plants, Network Optimization solutions
evolves towards an integer programming (IP)
characterized mathematical model.
Capacity constraints reflect the rationale of scarce
production source of production facilities. These
constraints can be designated at four distinct detail
levels: plant, product type (bag/bulk) and plant,
product segment and plant, and lastly product and
plant via the capacity planning steps introduced in
Section 3.2.1. Additionally, sales volumes of preset
typed demand points are subtracted from the
corresponding capacity figures before network
optimization run.
At optimization step, linear programming
algorithm is applied to achieve profit maximization
and solve the underlying assignment problem. This
algorithm retrieves all simulated type demand
point:plant combinations as candidate solutions and
takes production capacity and demand satisfaction
constraints into account. After data pre-processing
step, the input data calculated at SAP BW system
layer for the underlying version is transferred to
optimization logic layer as shown in Figure 2.
Respectively, optimization step aims to maximize
total objective function value, i.e. contribution margin
or net profit. In this aspect, assignment of a demand
point dp
i
to a plant plt
j
implies the demand
satisfaction for dp
i
and a local increase at objective
function value worth of the unit margin value realized
by dp
i
:plt
j
assignment calculated at Network
Optimization data pre-processing step. On the
contrary, a portion of capacity figures related to
demand point dp
i
and plant plt
j
is diminished due to
this demand satisfaction.
Technically, we positioned an integer
programming characterized mathematical model to
satisfy each demand point with exactly one plant in
an optimality fashion such that, it maximizes total
contribution margin or net profit with respect to any
given number of plants and demand points.
ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics