A Comparative Analysis of Disaggregation Types in Hierarchical
Production Planning
NAZLI GOKER, MEHTAP DURSUN
Industrial Engineering Department, Decision Analysis Application and Research Center
Galatasaray University
Cıragan Cad. No:36 Ortakoy, Besiktas, Istanbul
TURKEY
Abstract: - Supply chain management has become an important component of global economy through
competitive environment among businesses. Production planning is a significant major element of value chains,
and considered in two different models namely monolithic and hierarchical. Hierarchical approach divides the
problems into several stages according to product type and product family, and provides problem solving much
more easily. This study introduces a comparative analysis for disaggregation types of two research papers which
utilize hierarchical production planning models in supply chain processes.
Key-Words: - Hierarchical production planning, comparative analysis, disaggregation types, supply chain
Received: March 21, 2021. Revised: March 16, 2022. Accepted: April 12, 2022. Published: May 9, 2022.
1 Introduction
Nowadays, supply chain management becomes more
and more important day by day as a result of rapid
competition and there is a need for cost reduction in
supply chain operations that include logistics
activities. Supply chain departments of firms have
become major elements instead of support elements
in the global economy. Supply chain management
has become a significant element in the global
economy as a result of competition among the
businesses. Supply chain is seen as the area to
minimize the cost [1]. In the global economy, the
supply chain operations become major elements in
the firms instead of support elements. With the
increased competition, it can be said that firms want
to establish more sustainable and successful
relationships wih their suppliers. However, supply
chain operations have exposed to different kinds of
risks in nowadays as a result of globalization [2].
Production planning problems are generally
constructed in two different ways namely monolithic
and hierarchical. The monolithic approach solved a
mixed integer linear programming model for all the
items, while the hierarchical approach, illustrated in
Figure 1, divides the problem into several stages
corresponding to product type and product family.
Since the detailed problems can be solved much more
easily, the hierarchical models may satisfy managers'
requirements for a quick solution than a monolithic
approach [3].
The aim of this study is to provide a comparative
analysis for disaggregation types of two research
papers which use hierarchical production planning
models in supply chain processes.
The rest of the paper is organized as follows.
Section 2 reviews the literature on hierarchical
production planning applications in supply chain.
Section 3 provides the notes on Xue et al. [3] and
Gansterer [4], respectively. Concluding remarks and
future research directions are delineated in Section 4.
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2 Literature Review on Hierarchical
Production Planning Applications in
Supply Chain
Over the last decade, scholars contributed to the
hierarchical production planning applications on
supply chain. Selot et al. [6] developed a hierarchical
multiobjective programming model for a supply
chain of a gas production system in Malaysia. You
and Grossmann [7] developed a hierarchical
production plan for different decision making stages
namely strategic and operational, and illustrated the
application with two numerical examples of
polystyrene supply chains. Caramanis et al. [8]
developed a hierarchical production planning model
by disaggregating the time as weekly and hourly, and
applied it for a supply chain performance. Gharbi et
al. [9] proposed a methodology which enables
obtaining an optimal and reactive tactical plan of
supply chain in uncertain environment. The method
was centered upon two stage decisional framework.
The first stage carries out an aggregate planning by
minimizing the production costs while the second
stage makes the planning of the aggregate level and
takes into consideration the constraints ignored at the
aggregate level.
Sawik [10] suggested a monolithic and a
hierarchical approach for scheduling material
manufacturing, material supply and product
assembly in a customer driven supply chain, and
provided a comparative analysis between these two
models. Boulaksil et al. [11] proposed an iterative
two-stage hierarchical production planning model for
capacity planning of an outsourced supply chain.
First, they solved the aggregate problem that is
integer programming model. Second, they conducted
a simulation study in which a mathematical
programming was solved in order to evaluate system
performance. Xue et al. [3] introduced an aggregate
production planning model, and family
disaggregation and scheduling models in hierarchical
production planning by taking into account setup
times. Optimal production plan for each product type
and product family in each period is obtained by
proposed approach. The model was applied to a mold
manufacturing factory.
Li et al. [12] proposed a novel hierarchical belief-
rule-based inference methodology for an aggregate
production planning under uncertain environment of
demand. They carried out a case study in a paint
factory. Wang and Huang [13] introduced a two-level
programming model for indicating an accurate
decision for recycle volume, time of the end-of-life
Figure 1. Hierarchical production planning structure [5]
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product and recovery procedures. Fahimnia et al. [14]
compared the results of a mixed-integer nonlinear
production planning model and a hierarchical
production model in order to investigate the benefits
of cost reduction obtained from a supply chain via
global integration of production and distribution
decisions. Case study was conducted in an
automotive company.
Manzini et al. [15] proposed a top-down approach
that combines the strategic planning, the tactical
planning, and the operational planning of distribution
networks. The influence of the strategic and tactical
decisions on the performance of the operational
planning was assessed by employing a hierarchical
planning approach in logistics sector. Jin et al. [16]
investigated if the different patterns of data
aggregation affect the measures of the supply chain,
and made the use of hierarchical linear programming
model for testing the influences of the data
aggregation on various measures. The model was
applied in a company performing in the retail sector.
O'Reilly et al. [17] discussed the role of hierarchical
production planning, and aimed at implement
hierarchical production strategies to the food
manufacturer companies.
Vargas et al. [18] introduced a business-to-
business model which addresses the issue of dealing
with unexpected events in hierarchical production
planning, and how the B2B framework is
incorporated into programming model. The case
study was conducted in a Spanish ceramic tile
factory. Acar and Atadeniz [19] evaluated the effect
of integrated production planning for the value chain
of a global lubricant manufacturer company. They
considered cost and performance indicators in an
uncertain environment of demand, and proposed a
mixed integer programming model for the
hierarchical framework of the problem. Finally, they
utilized ANOVA in order to identify the relationships
among experimental factors.
Gansterer [4] introduced a hierarchical production
planning framework by solving a linear programming
model which identifies the influence of aggregate
planning in make-to-order environment. Case study
was conducted by obtaining real data from a supplier
firm performed in automotive industry.
Bakhshizadeh et al. [20] proposed a hierarchical
programming model that is more efficient for value
chains in which some elements are more effective
and powerful than the others. Moreover, decision
makers in the aggregate level indicated their
objectives and decisions, and asked the detailed level
of the organization to optimize the objectives
separately. The application was employed in a car
company in order to test the robustness of the
proposed approach. Paiva et al. [21] developed a
hierarchical optimization model for the sugar-alcohol
energy sector with robust optimization analysis to
provide managerial insights. Munduteguy [22]
explored how a foreman deals with work flexibility
by constructing a hierarchical production planning
framework. Albornoz et al. [23] used hierarchical
production planning for zone delineation and crop
planning under uncertainty. Xue and Offodile [24]
integrated a non-linear mixed integer programming
model and hierarchical production planning approach
for optimizing dynamic manufacturing systems in a
metal mold manufacturing plant. Gahm et al. [25]
applied a machine learning method for the
anticipation of complex nesting solutions in
hierarchical production planning in metal processing
sector.
The table format of the literature survey with
regard to the research area of the reviewed papers is
provided in Table 1.
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Table 1. Literature survey with regard to the research area
Author(s)
Year
Research Area
Selot et al.
2008
Gas production
You and Grossmann
2008
Polystyrene supply chain
Caramanis et al.
2009
Supply chain performance
Gharbi et al.
2009
Raw material supply
Sawik
2009
Material supply
Boulaksil et al.
2009
Outsourced supply chain
Xue et al.
2011
Mold manufacturing
Steinruecke and Jahr
2012
Logistics sector
Li et al.
2013
Paint industry
Wang and Huang
2013
Recycling
Fahimnia et al.
2013
Automotive sector
Manzini et al.
2014
Logistics industry
Jin et al.
2015
Retail sector
O'Reilly et al.
2015
Food manufacturing
Vargas et al.
2015
Ceramic tile industry
Acar and Atadeniz
2015
Lubricant manufacturing
Gansterer
2015
Automotive sector
Bakhshizadeh et al.
2016
Automotive sector
Paiva et al.
2020
Energy sector
Munduteguy
2020
Logistics sector
Albornoz et al.
2020
Agriculture industry
Xue and Offodile
2020
Mold manufacturing
Gahm et al.
2022
Metal processing industry
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3 Comparative Analysis Between Two
Hierarchical Production Planning
Approaches
In this section of the study, a comparative analysis
between Xue et al. [4] and Gansterer [5] is provided
in order to better understand the difference between
aggregate planning models and disaggregation types
in hierarchical production planning.
3.1 A Note on Xue, Offodile, Zhou, and Troutt’s
Hierarchical Production Planning Approach
Xue et al. [3] developed an integrated model for
aggregate production planning and family
disaggregation planning. The model identifies the
optimal production plan for each product type and
product family in each period of production, and
obtains a big amount of cost savings. The model is
applied to a mold manufacturing factory. At the type
level, the aggregate production planning model
taking into consideration mid-term decisions is
formulated as follows:
(1)
subject to
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
where M and T represent the index of type and index
of period, respectively. refers to the unit
production cost (materials + overhead), refers
to the processing time for type m in period t. ,
, signify unit inventory carrying,
subcontracting and backordering costs for type m in
period t. and represent regular time and
overtime costs per man-hour for for type m in period
t. and refer to the cost of hiring one man-hour
and laying off one man-hour in period t. refers to
the net demand for type m in period t. A signifies the
capacity allowance percentage (used for allowing
machine breakdowns, earlier due dates, etc.).
represents permitted percentage of overtime to
available regular time. refers to maximum
subcontracting capacity costs for type m in period t.
signifies maximum backordering quantity
permitted for type m in period t. represents the
space occupied by each unit inventory of type m.
refers to the total available space for inventory
storage. and signify production and inventory
level of for type m in period t. and represent
subcontracting and backordering quantity of type m
in period t. and refer to man-hours of regular
time hired and laid off in period t. and
signify regular time and overtime hours consumed by
type type m in period t. and represent
available regular time and overtime hours in period t.
In the model formulated above, the objective
function aims to minimize the total costs in the
planning horizon. Production balance equations are
given in Constraints (2). Capacity bounds are
provided by Constraints (3). Constraints (4) are total
capacity consumed by each type of period.
Constraints (5) guarantee that the total overtime in
one period will not exceed available overtime.
Subcontracting capacity limits are given in
Constraints (6) and backordering limits are provided
in Constraints (7). Labor force balance equations and
inventory storage space bounds are given in
Constraints (9).
Second, the authors develop a family
disaggregation model which aims to minimize setup
costs via objective function, and the constraints
ensure that the total quantity assigned to all families
are equal to the type quantity determined by
aggregate plan in the current period. The
disaggregation model is provided below:
(11)
subject to
(12)
(13)
where represents the index of the family, j(m) refers
to the set of families pertaining to type m, signifies
setup cost of family i, and represents lower
bound and upper bound of the lot size of family i in
period t, and represents the lot size of family i in
period t.
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3.1 A Note on Gansterer's Aggregate Planning
Approach
Gansterer [4] provided a hierarchical production
planning framework in which aggregate production
plan is developed as a linear programming model and
solved to obtain the optimal solution. The
mathematical programming model is as
(14)
subject to
(15)
(16)
(17)
where P, T and J represent the set of product families,
the set of time periods and the set of machine groups,
respectively. refers to production amount of
product family p in period t. signifies inventory
level of product family p in period t. represents
backorders for product family p in period t. refers
to the capacity consumption factor, signifies
inventory cost factor, represents cost factor for
backorders. and refer to forecasted demand
and available capacity.
The objective function is to minimize inventory
and backordering costs. Constraints (15) guarantee
that capacities are not exceeded. Production balance
equations are given in Constraints (16). Constraints
(17) provide non-negativity of decision variables.
The model is constructed by using aggregate data
with regard to time periods, capacities and product
groups. Production amounts are computed for
product families instead of products. The aggregate
production plan is utilized for balancing production
quantities of product families on a monthly basis.
Subsequently, the aggregate plan is converted to
MPS and then MRP where it is disaggregated in order
to obtain production quantities for end products
rather than product families.
4 Concluding Remarks
This work presents a comparative analysis for
disaggregation types of two research papers which
utilize hierarchical production planning models in
supply chain processes. For that reason, a literature
review on hierarchical production planning
application in supply chain is provided.
Subsequently, some interpretations for Xue et al. [3]
and Gansterer [4] are given and the differences in
terms of disaggregation types of these two
approaches are observed. Future research will focus
on real case applications by solving these models to
optimality utilizing real data.
Acknowledgement
This work has been financially supported by
Galatasaray University Research Fund FBA-2021-
1050.
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