A review of discrete-time optimization models for tactical production planning

TL;DR: In this paper, the authors present a review of optimization models for tactical production planning and identify streams and future research directions in this field based on the different classification criteria proposed by the authors.

Abstract: This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively...

Summary

1 Introduction

• Production planning is related to managing the productive resources required to perform transformation from raw materials to final products to satisfy customers in the most efficient way (Pochet, 2001) .
• These authors also contemplate the inclusion of setup times, multi-level product structures and overtime.
• Moreover, the authors extend these classification criteria by adding the following categories: problem type, modeling approach, solution method, development tool, application, benefits and limitations (Mula et al., 2010a) .

3.1 Problem type

• The MPS establishes an optimal production plan which meets customers' orders, and provides release dates and amounts of final products to manufacture by minimizing production, holding and set up costs.
• Given the increase of integration and coordination among suppliers, manufacturers and distributors, multi-site production planning or SCP has become a very important issue in recent decades.
• Besides, the distinction of different planning levels based on the time period and the amount of detail in the plans is known as HPP, which decomposes the global production planning problem into a number of subproblems that correspond to different levels of a hierarchy of plans.
• Of the reviewed works, 142 of them address MPS problems, followed by a group of 47 references which deal with SCP and 39 references which consider MRP problems.

3.2 Number of products and number of levels

• The complexity of not only the production planning problem, but also its modeling, may be influenced by the number of items manufactured in the production system.
• Among the papers analyzed, 71 references address production planning for a single product, while the remaining 172 correspond to multi-item models.
• Another important characteristic that can affect the complexity of production planning problems is products structure and its number of levels.
• The former corresponds to production systems where only final products are manufactured according to the demand obtained directly from customer orders or market forecasts.

3.3 Time period

• In terms of the time period terminology, multi-item production planning problems fall into the big or small bucket problems categories (Karimi et al., 2003) .
• In small bucket models, only one type of item can be manufactured, or at most one item can be set up per period, while the time period is long enough to produce multiple items in big bucket models.
• Table 4 presents the time period and the product structure details of the references addressing multi-product planning problems.
• With regard to small bucket models, only Stadtler (2011) deals with multi-level planning problems, while those references which present both small bucket and big bucket models (Transchel et al., 2011; Van Vyve and Wolsey, 2006) only consider mono-level product structures.

3.4 Nature of demand

• Demand acts as a typical parameter of production planning models and its nature can affect their complexity.
• If demand levels are known exactly, demand is called deterministic.
• In production planning models, uncertainty is modeled by using probability distributions, fuzzy sets, stochastic approaches based on stochastic values, or several scenarios and robust approaches.
• On the other hand, 207 references consider deterministic demand and 37 uncertain demand levels.

3.5 Capacities or resource constraints

• Capacity constraints may increase the complexity of the production planning models and their resolution, but enable more realistic models.
• The authors identify the constraints related to inventory limitations (48 references), supply of parts and raw materials from suppliers (24 references), productive resources such as machines and workforce (194 references) and transportation resources (21 references).
• A model may have only production capacity constraints, while another might also include limitations related to inventory capacity constraints and/or supply from suppliers.
• Table 6 shows the different combinations associated with each capacity constraint class.
• Most of the analyzed papers (143 references) present only capacity constraints related to productive resources.

3.6.a Demand

• In order to obtain production planning models that come closer to reality, in addition to considering price-dependent demand levels, several extensions related to demand are identified.
• The ability to meet demand through product substitution, the existence of time windows, the option of backlogs to meet demand in following periods, and modeling lost sales if demand cannot be met during the corresponding period or during the subsequent one.
• Table 7 presents the different extensions related to demand considered in this work.
• There is a group of 12 papers that considers product substitutions with several approaches.
• Moreover, one of the reviewed papers (Wolsey, 2006) presents models with production and time windows separately.

Lost sales 30

• Substitution 14 Price-dependent levels 10 Time windows 7 3.6.b Setups Generally, setup activities are included in production planning models by considering the setup costs and/or setup times which model the production changeovers between different products.
• Moreover according to Karimi et al. (2003) , three other setup types of complex setups can be contemplated: setup carry-overs; sequence-dependent setups; family setups.
• The inclusion of setup carry-overs reduces the setup times needed as compared to standard production planning models, which use a setup for each product produced per period.
• Table 8 provides details of the number of references dealing with the considered setup extensions.
• Moreover, Menezes et al. (2011) incorporate sequence-dependent and period-overlapping setup times.

3.6.c Production times

• In order to adjust the capacity usage level of productive resources, production planning models include overtime, subcontracting and undertime decisions.
• If during a period production capacity is less than customer demand, the decision maker may choose to produce in overtime or to outsource part of the production to meet demand without backlogs.
• Of the reviewed works, 35 references consider overtime decisions, 19 include the possibility of subcontracting production, and only 4 references (Fandel and Stammen-Hegene, 2006; Lusa et al., 2009; Mula et al., 2008; Peidro et al., 2010) contemplate modeling idle time.
• Besides, all the references that consider outsourcing decisions model them in terms of the amounts of products to manufacture by subcontractors.
• Table 9 shows the different combinations associated with extensions on production times.

3.6.d Multiple and parallel machines

• According to Quadt and Kuhn (2007) , standard production planning models can represent the existence of parallel machines by augmenting the production variables and the capacity parameters by an additional index indicating the individual machines.
• Finally, 2 references (Jozefowska and Zimniak, 2008; Mateus et al., 2010) deal with production planning problems with parallel unrelated machines (with no particular relationship between the processing times in the different machines).
• Finally, 2 references present conjoined supply chains formed by several suppliers, one manufacturer and several customers (Zolghadri et al., 2008) , and by several plants, a distribution center and several customers (Romero and Vermeulen, 2009) .
• Table 12 details the number of references dealing with the considered remanufacturing extensions.
• The quality of the returned products to be remanufactured is an important aspect to consider when organizing and planning remanufacturing activities.

3.7 Modeling approach

• Since the 1950s, mathematical programming formulations have been proposed for a wide range of production-related problems to address problems of aggregate production planning, lot sizing and detailed short-term production scheduling, among others (Missbauer and Uzsoy, 2011) .
• In general terms, in order to solve multi-objective problems using a standard MILP solver, multi-objective programs are converted into an equivalent MILP model with goal programming or fuzzy programming approaches and their variants.
• Qu and Williams (2008) use a commercial NLP solver with default settings to solve their proposed nonlinear model, whereas Fandel and Stammen-Hegene (2006) present neither a solution procedure nor results.

3.8 Solution approach

• According to Buschkühl et al. (2010) , the approaches to solve different types of production planning or capacitated lot-sizing models can be classified into five groups: mathematical programming-based (MP-based) approaches, Lagrangian heuristics; decomposition and aggregation heuristics; metaheuristics; problem-specific and greedy heuristics.
• Based on the idea that most variables are nonbasic and assume a value of zero in the optimal solution, in theory it is necessary to consider only one subset of variables when solving the problem.
• Column generation can be hybridized with the branch-andbound algorithm to generate a solution method called branch-and-price.
• Metaheuristics have emerged as a result of the extensive application of these heuristic-type algorithms to many optimization problems.

3.9 Development tool

• Sixty-three references do not provide any implementation or development details.
• The second most frequently used tool considered in the reviewed papers is the C programming language and its variants, such as C++ or Visual C, which appears in 49 references.
• Besides, AMPL and GAMS are used mainly with CPLEX solver, and are presented in 11 and 9 references, respectively, while Xpress-MOSEL is presented as the main development tool in Akartunali and Miller (2009) , Akbalik and Pochet (2009) and Transchel et al. (2011) .

3.10 Application

• The proposed models can be validated by using data from real-world production systems or by carrying out numerical experiments based on artificially generated instances.
• Of the 250 papers analyzed, 71 were validated by practical applications in real-world environments and 160 by numerical experiments, 18 of which were inspired in real practices from several industrial sectors.
• Moreover, 14 references do not present any application result.
• Tables 17 and 18 present the industrial areas in which each reference was validated with a practical application or with a numerical experiment inspired in real environments, respectively.
• These tables show the variety of industries in which the reviewed models were validated; sawmills, wood and furniture, automobile and semiconductor and electronic devices industries in the case of practical applications, and processed food, beverages and dairy and pulp and paper industries with regard to numerical experiments, are highlighted.

3.11 Limitations

• Some of the limitations pointed out by the authors of the proposals are related to the solution method used, the considered production systems, demand issues, capacities, the non consideration of uncertain parameters, product properties, applications in non real-world environments, supply chain issues and costs.
• A hundred and two references present limitations related to solution methods.

3.12 Benefits

• Table 20 summarizes the main benefits pointed out by the reviewed references reported by their authors.
• The vast majority (187 references) obtain good solutions in terms of either the CPU time needed or optimality, or they present solution procedures that outperform previous methods in the literature.
• Flexibility in lead times (Bjork and Carlsson, 2007) , routing and processes (Ahkioon et al., 2009) , transport capacity (Hwang et al., 2010) , related to uncertainty or different scenarios (Erromdhani et al., 2012; Leung and Chan, 2009; Schütz and Tomasgard, 2011) and to modeling new constraints (Helber and Sahling, 2010) are an important advantage in dynamic production environments.
• Moreover, the capability of extending their proposed models is emphasized by Li and Meissner (2011) and Stadtler (2011) .

4 Discussion

• After reviewing the selected papers on tactical production planning, this section provides some relevant streams and limitations in the literature on tactical production planning.
• Among them, extensions related to demand and setup properties are those more included in the reviewed models.
• In general, industrial practitioners look for tools whose general purpose is to solve production problems easily without having to learn new modeling or programming languages.

5 Conclusions

• This work surveys 250 articles related to tactical planning in relevant operations research and management journals.
• To study the analyzed works, a classification based on the analysis of the following aspects is proposed: problem type, aim, number of products, time period, nature of demand, capacities constraints, extensions, modeling approach, solution approach, development tool, application, limitations and benefits.
• Like Mula et al. (2010a) , one can confirm the need for optimization models and tools for the production and procurement transport planning processes which contemplate different forms of long-and short-distance transport (railway, air, full truck load, grouping, milk round, routes, etc.) and different characteristics (legal or environmental restrictions).the authors.
• Analytical models based on these conceptual models are a forthcoming work; (2) growing customer requests and increasing competition make demand management an important part of the success and applicability of tactical production planning models.

Figures

Table 8. Extensions on setups

Table 19. Main limitations of the reviewed works

Table 2. Problem type of the reviewed works

Table 3. Number of products and number of levels in the product structure

Table 7. Extensions on demand

Table 13. Extensions on quality

Table 12. Extensions on remanufacturing activities

Table 17. Practical applications

Table 20. Main benefits of the reviewed works

Table 11. Multi-site configurations

Table 4. Time period and number of levels in the product structure

Table 5. Nature of demand and the uncertainty approaches considered

Table 10. Multiple and parallel machines extensions

Table 9. Combinations of extensions on production times

Table 18. Numerical experiments inspired in real environments

Table 1. Distribution of references according to journals

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http://hdl.handle.net/10251/53703
Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time
optimization models for tactical production planning. International Journal of Production
Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721
http://doi.org/10.1080/00207543.2014.899721
Taylor & Francis: STM, Behavioural Science and Public Health Titles
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Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721

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A review of discrete-time optimization models for tactical production planning
Manuel Díaz-Madroñero, Josefa Mula
∗
, David Peidro
Research Centre on Production Management and Engineering (CIGIP)
Universitat Politècnica de València, Spain
Abstract
This paper presents a review of optimization models for tactical production planning. The
objective of this research is to identify streams and future research directions in this field based
on the different classification criteria proposed. The major findings indicate that: (1) the most
popular production planning area is master production scheduling with a big-bucket time-type
period; (2) most of the considered limited resources correspond to productive resources and, to a
lesser extent, to inventory capacities; (3) the consideration of backlogs, setup times, parallel
machines, overtime capacities and network-type multi-site configuration stand out in terms of
extensions; (4) the most widely used modeling approach is linear/integer/mixed integer linear
programming solved with exact algorithms, such as branch-and-bound, in commercial MIP
solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools
among solvers, programming languages and modeling languages, respectively; (6) most works
perform numerical experiments with random created instances, while a small number of works
were validated by real-world data from industrial firms, of which the most popular are sawmills,
wood and furniture, automobile and semiconductors and electronic devices.
Keywords: Production planning; lot sizing; mathematical programming; optimization; tactical
planning; discrete-time models.
1 Introduction
Production planning is related to managing the productive resources required to perform
transformation from raw materials to final products to satisfy customers in the most efficient
way (Pochet, 2001). The production planning problem can be decomposed according to the time
horizons considered. Several authors, such as Anthony (1965), Salomon et al. (1991),
McDonald and Karimi (1997), Min and Zhou (2002) and Gupta and Maranas (1999, 2003),
among others, classify production planning problems into strategic, tactical and operational
problems. Strategic planning models affect design and configuration over a time between 5 and
10 years.
Tactical planning models attempt to adopt the most optimum use of the available
resources by determining materials flow, inventory levels, capacity utilization, the amounts to
produce and maintenance activities, with a planning horizon from one or several months to 2
years. Tactical planning assumes that the system design and configuration is given. Operational
planning models are related to the detailed scheduling definition, sequencing, lot sizes,
assigning
loads and vehicle routes, etc. Operational models use time periods which last between
one and two weeks.
*
Corresponding author: Josefa Mula, Escuela Politécnica Superior de Alcoy, Plaza Ferrándiz y Carbonell,
2, 03801, Alcoy (Alicante), SPAIN. Tel.: + 34966528423. Fax: + 34966528585. E-mail address:
fcodiama@cigip.upv.es, fmula@cigip.upv.es, dapeipa@cigip.upv.es
.

Although the scientific literature based on the tactical production planning concept is vast, the
main motivation of this paper is to collect, classify and overview scientific articles from the last
years. Other similar reviews do not address this time window, but other previous reviews on lot-
sizing models (Brahimi et al., 2006b; Buschkühl et al., 2010; Comelli et al., 2008; Karimi et al.,
2003; Quadt and Kuhn, 2008), production planning models under uncertainty (Aloulou et al.
2013; Dolgui & Prodhon 2007; Dolgui et al. 2013; Grosfeld-Nir and Gerchak 2004; Koh et al.
2002; Mula et al. 2006, Yang et al. 2007), supply chain planning models under uncertainty (Ko
et al. 2010; Peidro et al., 2009) and mathematical programming models for supply chain
production and transport planning (Mula et al., 2010a) do.
Papers were selected based to be included in this survey on the following main criteria: (i)
mathematical programming models or quantitative approaches; (ii) tactical problems; (iii)
discrete-time models. We briefly describe each paper, but we do not describe or formulate the
models considered in detail. This work intends to provide the reader with a starting point to
investigate the literature on optimization models for tactical production planning problems. The
main contributions of this paper are to (i) review the literature; (ii) classify the literature based
on the problem type, aim, number of products, time period, nature of demand, capacities
constraints, extensions, modeling approach, solution approach, development tool, application,
limitations and benefits; (iii) identify current trends and future research directions.
The remainder of the paper consists of four other sections. The next section introduces the
review methodology. Section 3 describes the classification criteria of the reviewed papers.
Section 4 presents the limitations and discussion of the present study. Finally, the last section
provides the conclusions and directions for future research.
2 References collection methodology
The search for published production planning articles was performed using the Web of
Knowledge platform from January 2006. The following search criteria were applied to the topic
field of this web search engine: lot sizing, production planning, tactical planning, master
planning, operations planning, supply chain planning, material requirement planning,
manufacturing resource planning, aggregate planning, hierarchical production planning,
procurement planning, replenishment planning. From the references obtained, and after
performing a reviewing process of the abstracts, approximately 600 references were selected.
An additional filter, based on the journal in which each reference is published, was applied to
this group. Barman et al.'s (2001) ranking was considered, which is a collection of
internationally recognized production and operations research and management journals, and it
was previously applied in the works of Chaudhry and Luo (2005) and Wong and Lai (2011).
Barman et al.'s (2001) ranking was also completed with those journals rated at the 3rd and 4th
levels from the ABS Academic Journal Quality Guide in the Operations, Technology and
Management, and Operations Research and Management Science subjects. It is important to
highlight that we are focused on tactical planning optimization models, thus a new group of 342
references was formed, from which those articles which focus only on strategic planning
approaches (e.g., supply chain design, plant location, among others), operational decision level
applications (e.g., production scheduling), non quantitative approaches, continuous-time or non
discrete models and non optimization models were excluded. Having completed this process,
250 references were reviewed (Table 1).
As shown in Table 1, one group of three journals represented 56.40% of the references included
in this work, these being: International Journal of Production Research (50 references),
European Journal of Operational Research (47 references) and International Journal of
Production Economics (44 references). They were followed by Computers & Operations
Research (24 references) and Computers & Industrial Engineering (15 references), which

together account for the 15.60% of the reviewed papers. The remaining 15 journals published
28.00% of the total considered references.
Table 1. Distribution of references according to journals
ABS
ranking
Bartman et al’s
(2001) ranking
Journal References % of total
X
X
International Journal of Production Research
50
20.00%
X
X
European Journal of Operational Research
47
18.80%
X
X
International Journal of Production Economics
44
17.60%
X
Computers & Operations Research
24
9.60%
X
Computers & Industrial Engineering
15
6.00%
X
X
Journal of the Operational Research Society
11
4.40%
X
Production Planning & Control
11
4.40%
X
X
Operations Research
10
4.00%
X
Mathematical Programming
7
2.80%
X
IIE Transactions
6
2.40%
X
OR Spectrum
6
2.40%
X
X
Naval Research Logistics
5
2.00%
X
Journal of Scheduling
4
1.60%
Journal of Intelligent Manufacturing
2
0.80%
X
X
Production and Operations Management
2
0.80%
X
Interfaces
2
0.80%
X
X
Management Science
1
0.40%
Supply Chain Management - An International Journal
1
0.40%
X
IEEE Transactions on Engineering Management
1
0.40%
X
Mathematics of Operations Research
1
0.40%
TOTAL
250
100.00%
3 Classification criteria
Karimi et al. (2003) present a review of models and algorithms for capacitated lot sizing
problems. According to these authors, modeling and complexity of lot sizing decisions depend
on the following characteristics: planning horizon and time period, number of levels in the
product structure, number of products, nature of demand, capacity or resource constraints, setup
structure and inventory shortages. Quadt and Kuhn (2007) survey capacitated lot sizing
problems by taking into account different extensions, such as backorders, setup carry-overs,
sequence-dependent setups and parallel machines. These authors also contemplate the inclusion
of setup times, multi-level product structures and overtime. Accordingly, we propose a new
classification scheme with two broader categories which we call setup and demand extensions
and additional extensions. In relation to setup extensions, we consider setup times and complex
setup issues such as setup carry-overs, sequence-dependent setups and family setups. On the
other hand, demand extensions include backlogged demand, lost sales, price-dependent demand,
product substitution and time windows. Additional extensions relating to production times
(overtime, undertime, subcontracting time), parallel machines and multisite, remanufacturing
and quality are also contemplated. Moreover, we extend these classification criteria by adding
the following categories: problem type, modeling approach, solution method, development tool,
application, benefits and limitations (Mula et al., 2010a).
All the classification criteria are described as follows:
1. Problem type. This is the production planning area addressed by each article.
2. Number of products and number of levels. It refers to the number of manufactured
products considered in each model and their product structures; e.g., single-item or
multi-item and single-level or multi-level, respectively.

Frequently asked questions

Q1. What have the authors contributed in "A review of discrete-time optimization models for tactical production planning" ?

This paper presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. 

Q2. What are the future works mentioned in the paper "A review of discrete-time optimization models for tactical production planning" ?

To study the analyzed works, a classification based on the analysis of the following aspects is proposed: problem type, aim, number of products, time period, nature of demand, capacities constraints, extensions, modeling approach, solution approach, development tool, application, limitations and benefits. After conducting this review, the authors indicate some gaps in the literature with some proposed future research lines: ( 1 ) it is important to underline that they found no work that examines multi-level tactical production problems by considering not only the existence of near and offshore suppliers of parts and components, but also the impact that procurement transport may involve on accomplishing production plans. In this sense, like Mula et al. ( 2010a ), the authors can confirm the need for optimization models and tools for the production and procurement transport planning processes which contemplate different forms of long- and short-distance transport ( railway, air, full truck load, grouping, milk round, routes, etc. ) and different characteristics ( legal or environmental restrictions ). Thus, consideration of demand-driven tools and mass customization practices can be an important extension to bear in mind ; ( 3 ) applying tactical planning models in real-world production environments in which uncertain conditions can also be considered ; ( 4 ) real-world industrial problems often have several conflicting objectives. 

Q3. What are some of the used approaches to model uncertainty in production planning problems?

Stochastic programming (SP), fuzzy programming (FP), robust optimization (RO) and stochastic dynamic programming (SDP) are some of the most used approaches to model uncertainty in production planning problems (Sahinidis, 2004). 

Q4. What are the popular decomposition and aggregation approaches to solve production planning problems?

time-based and resource-based are the most popular decomposition and aggregation approaches to solve production planning problems. 

Q5. What is the main reason for the inclusion of setup times in production planning models?

The inclusion of setup times involves reducing the production capacity available per period and increases the models’ complexity because they are usually modeled by introducing zero-one variables. 

Q6. What type of heuristics are proposed by Sahling et al.?

Another class of MP-based heuristics called fix-and-optimize heuristics is proposed by Sahling et al. (2009) and Helber and Sahling (2010). 

Q7. What are the common solutions proposed in the analyzed papers?

Mathematical programming-based solution procedures and specific solution methods such as heuristic algorithms are proposed in most of the analyzed papers, and in a lesser extent metaheuristics. 

Q8. What are the main reasons for the increase in the use of heuristics?

the impossibility of discovering the exact solutions corresponding to optimization problems and the need to respond to the practical situations considered in many real-world cases have led to an increased use of heuristic-type algorithms, which have proven to be valuable tools that provide solutions where exact algorithms do not (Verdegay et al., 2008). 

Q9. How can the production planning model represent the existence of parallel machines?

3.6.d Multiple and parallel machinesAccording to Quadt and Kuhn (2007), standard production planning models can represent the existence of parallel machines by augmenting the production variables and the capacity parameters by an additional index indicating the individual machines. 

Q10. How many papers address mono-level production planning problems?

among the 169 papers presenting big bucket models, 99 address mono-level production planning problems, while the 70 remaining ones consider multi-level production systems. 

Q11. How many references address multi-level product planning?

Of the 177 references addressing production planning for multiple items, 106 references correspond to final products and 71 references consider multi-level product structures. 

Q12. What are the main types of remanufacturing activities?

These include the collection of used products, dismantlement or disassembly of returned products, incorporation of remanufacturing activities into the overall production planning (Guide and Van Wassenhove, 2002), and the recycling or disposal of unused products. 

Q13. What are the main benefits of the extended lot sizing models?

these papers focus mainly on developing efficient algorithms for typical lot-sizing extensions, such as inclusion of backlogs, setup times, sequence-dependent setups, etc. 

Q14. What is the main aspect to consider when planning remanufacturing activities?

The quality of the returned products to be remanufactured is an important aspect to consider when organizing and planning remanufacturing activities. 

Q15. What are the main reasons for the classification of production planning problems?

Several authors, such as Anthony (1965), Salomon et al. (1991), McDonald and Karimi (1997), Min and Zhou (2002) and Gupta and Maranas (1999, 2003), among others, classify production planning problems into strategic, tactical and operational problems.