optimization of production planning using … · optimization of production planning using...

ijcrb.webs.com

INTERDISCIPLINARY JOURNAL OF CONTEMPORARY RESEARCH IN BUSINESS

COPY RIGHT © 2012 Institute of Interdisciplinary Business Research

845

SEPTEMBER 2012

VOL 4, NO 5

OPTIMIZATION OF PRODUCTION PLANNING USING MATHEMATICAL MODEL

(CASE STUDY :BEHNOUSH IRAN COMPANY

Yaser Ghorbanzad Master of Industrial Management(OR), Department of Management and Economy, Science and Research Branch, Islamic Azad

University, Tehran, Iran

Abbas Toloie Eshlaghy Industrial Management Dept., Islamic Azad University, Science and Research Branch, Tehran, Iran

Mohammadali Afshar Kazemi Industrial Management Dept., Islamic Azad University, Science and Research Branch, Tehran, Iran

Abstract

The present survey has been conducted to optimize production planning in production systems

based on product using a mathematical model in a beverage manufacturing company for

modeling by means of ideal planning techniques.

Objective of this survey is to study the current status of manner of production and planning in the

factory under study and the existing problems in production process. Therefore dependent

variables in production planning have been defined. Accordingly effective production ideals on

production planning are identified given to managers' viewpoints and mathematical model of

planning is designed in the above factory using ideal planning technique. Given to the capability

of Lingo software in solving mathematical problems this software was used to solve the designed

mathematical model.

Keywords: Production planning, ideal planning, mathematical modeling, Lingo software

1- Introduction

Today modern challenges are dominant in industrial organizations and companies parallel to

previous issues. Exhaustibility and constraint of raw materials, human resources, production

capacity, place, time and capital are among the previous issues. Nowadays manufacturing

companies are faced with important apprehensions which have increased necessity of using

scientific methods in encountering with the related issues following commercial phenomena like

competition in the market.

Dynamism of the commercial and industrial environment and multiplicity of effective factors on

performance of organizations encounter organizational decision-makers with various purposes

that gratifying satisfaction levels of them becomes important. "Operation research" is one of the

scientific tools that has high capability in gratifying the above needs as a scientific branch.

Techniques of this branch of management science have a significant impact on playing decision-

making role given to the high capability in formulating organizational issues and considering

limitations and needs of managers of the organization. Also, it is a powerful tool in

measurement, directing and controlling of organizational indigenous and exogenous factors for

management (Bransson, 1993).

It has been tried in this survey to formulate and model this activity scientifically using the

knowledge of operation research and studying planning production process of the above factory.

ijcrb.webs.com



846

SEPTEMBER 2012

VOL 4, NO 5

2- Research literature

The vast majority of the works reviewed opt for the linear programming-based modeling

approach, particularly mixed integer linear programming models Conversely, nonlinear

programming is only used in two references (Benjamin, 1989; Lababidi et al., 2004). Six

references refer to the multi-objective programming-based modeling approach, of which three

use either multi-objective linear or integer linear multi-objective programming, while the other

three opt for nonlinear modeling. The inclusion of uncertainty in the various models is achieved

by fuzzy programming with stochastic programming. Both kinds of mathematical programming

appear as either a complementary modeling approach or the main approach as in Sakawa et al.

(2001), Demirli and Yimer (2006) and Aliev et al. (2007) for fuzzy programming, or as in Sabri

and Beamon (2000) and Goetschalckx et al. (2002) for stochastic programming. Likewise,

heuristic solution algorithms and metaheuristics are used as complementary techniques to solve

mathematical programming models, mainly integer linear programming. gramming and, to a

lesser extent, nonlinear, multi objective or fuzzy programming. The use of simulation tools to

complement the mathematical models is considered in the hybrid modeling approach referred to

in four references (Lee and Kim, 2000, 2002; Lee et al., 2002; Lim et al., 2006). Next, the details

of each modeling approach used by the different works reviewed are provided. Martin et al.

(1993) presented a linear programming model for planning production, distribution and

inventory operations in the glass sector industry. Chen and Wang (1997) proposed a linear

programming model to solve integrated supply, production and distribution planning in a supply

chain of the steel sector. Ryu et al. (2004) suggested a bi-level modeling approach comprising

two linear programming models, one for production planning and one for distribution planning.

These models subsequently consider demand uncertainty, resources and capacities when they are

reformulated by multi-parametric linear programming. Kanyalkar and Adil (2005) proposed a

linear programming model for aggregated and detailed production and dynamic distribution

planning in a multiproduct and multiplant supply chain. Oh and Karimi (2006) put forward a

linear programming model that integrates production and distribution planning for a

multinational firm in the chemical sector in a multi-plant, multi-period and multi-product

environment. This model also works with tax and financial data, such as taxes related with the

firm’s business activity or amortiza tions. Jung et al. (2008) compared linear programming

models for centralized and decentralized production and transport planning environments.

2-1 Advantages of production planning

Applying appropriate method of production planning will create advantages as below for the

organization. Enhancement of productivity and better using of possibilities such as raw materials,

machineries, human force and etc

Reduction of inventory level of raw materials and parts, incomplete products and

final product in the warehouse that is leaded to decrease costs.

Increasing of human force efficiency due to coordination and decreasing of

pressures due to lack of prediction in activities

On-time accomplishment of commitments to customers and enhancing their

satisfaction Reduction of stops and increasing efficiency of machineries

ijcrb.webs.com



847

SEPTEMBER 2012

VOL 4, NO 5

Realization of long-term purposes of production in the form of production planning

Reduction of losses arising from missed sales

Reduction of dependence of production system on the individual and prohibition of

doing works by taste

Creating balance among productive stations and workshops and optimal application

of production capacities (Korajewski & Ritzman, 2001).

2-2 Techniques of production planning

Usually techniques of production planning could be divided into two major classes in terms of

finding the best possible response or optimal solution:

A) Techniques that give optimal response

B) Techniques that don't necessarily give optimal response

C) Linear programming and its applications

D) Many of the management decisions intend to make using resources of the organization

effective. These resources typically include machineries, labor force, money, space of the

warehouse and raw materials which are used to produce goods and services. Linear

programming is a mathematical technique with extensive application that has been

designed to help managers in programming and decision-making about resource

allocation.

E) In quantitative analysis field modeling and solving a problem mathematically is called

programming. Also, computer programming has played a significant role in advancement

and using linear programming (Mehregan, 1996).

3- Designing mathematical model of production planning in production systems based on

the product

3-1 Main hypotheses to design the model

The following hypotheses are regarded as fundamental assumptions in the proposed model given

to conditions of the above company:

1- There are four production lines in Iran Behnoush Company that each one can produce a

family of products. It is noteworthy that production or not production of each product

doesn't affect production or not production of other products.

2- Demand level of each product that is determined by the business unit and by obtaining

orders of customers is specified for the programming unit.

3- Price of each product is determined given to the contract between the company and

customers.

4- Length of the period for production planning of the company is monthly due to high

variety of products, variability of customers' demand and cold or hot temperature (by

assuming that coldness and hotness of air temperature during months of a year is

specified).

5- Number of workers (available human force) will be stable during the programming

period. It is notable that number of available human force will be reviewed at the

beginning of each month and given to demand prediction.

6- Given to day and night production of the company there will be no problem regarding

preparing incomplete products. In other words, prerequisites of ordered products will

always be provided.

7- Production capacity of each product is specified given to the allocated human force to it.

ijcrb.webs.com



848

SEPTEMBER 2012

VOL 4, NO 5

8- Wastage is not involved in designing the mathematical model because of its low level

that is created during production process.

9- Cost of every product is determined due to the used materials in it, side costs such as

electricity, wind, personnel expenses of non-productive forces at the regular time of

production and overtime.

3-2 Major elements of the proprietary model

First, variables, specifications and the applied parameters in the survey are represented by

studying production process. Then systemic limitations which affect production capacity and

modeling manner of the issue in the production process will be identified. Where a part of

process or operational station has no impact on production capacity or the model and doesn't

create any limitation for the model practically it is omitted from the model.

3-2-1 Characteristics (specifications) of production

Given to variety of the effective factors on production level of each product and the allocated

force to each production line it is first essential to be familiar with characteristics

(specifications).

Insert Table 1

4-2-2 Decision variables

In systemic viewpoint the major portion of outputs of the mathematical model is its decision

variables. Decision variables of production planning mathematical model in this survey are

defined based on the following characteristics:

Insert Table 2

4-2-3 Parameters of the mathematical model (fixed amounts of model)

Each mathematical model needs specified amounts that have a direct impact on final results of its

solution as the model input. Technical coefficients of limitations, amounts at the right side of

ideals and coefficients of the variables used in the target function are elements of inputs in the

mathematical model. Fixed amounts that must be determined from documents and analysis of the

collected data before solving the model include the below amounts:

Insert Table 3

4-3 Systemic limitations

As we know systemic limitations constitute one part of ideal programming model. These

limitations are restraints which limit having access to purposes. Among such limitations that are

considered in this survey we can refer to limitation of the needed raw materials to produce

nonalcoholic beer and limitation of production capacity of production lines. Parameters related to

these limitations were obtained through studying internal information of the company and the

transmitted information from various units such as industrial accounting, warehouses, production

saloons, marketing, sales and production planning.

ijcrb.webs.com



849

SEPTEMBER 2012

VOL 4, NO 5

4-3-1 Limitation of providing the required raw materials

Preparing of raw materials is one of the most important difficulties that manufacturing

companies and factories are faced. This issue becomes more complicated when such materials

are of imported type. Given that Iran Behnoush Company imports a considerable volume of its

raw materials limitation of raw materials must be regarded among essential limitations in

designing the mathematical model for production planning of this company.

Management of the company determines amount of the consumption raw materials from type m

to be purchased at the beginning of each year given that volume of consumption raw materials in

the previous years is specified. Due to the point that percentage amount of combination of raw

materials in one liter of nonalcoholic beer and annual purchasing amount of materials (Rm) are

specified limitation of raw materials is defined as below:

≤

m=1, 2, …, 5 , i= 1, 2,…, 4 , j=1, 2, …, 5 , t= 1, 2, …, 12

Where:

i= characteristic of nonalcoholic beer based on packaging type of the produced nonalcoholic beer

(1- bottle, 2-can, 3-rotational, 4-pet)

j= characteristic of nonalcoholic beer based on capacity (1- 280 cc, 2- 330 cc, 3- 500 cc, 4- 1000

cc, 5- 1500 cc)

t= characteristic of months of production planning (1- April, 2- May, 3- June, …, 12- March)

m= characteristic of the applied raw materials in producing nonalcoholic beer (1- malt, 2- hop, 3-

HFCS, 4- citric acid, 5- ascorbic (vitamin c))

= amount of raw materials of type m that is used to produce nonalcoholic beer with capacity

j

= production amount of nonalcoholic beer with packaging i and liter j in time period t

= amount of raw materials of type m that is available in one year.

4-3-2 Production capacity limitation of production lines

Iran Behnoush Company has four production lines that are named based on packaging type of

nonalcoholic beer of these lines including: 1-bottle, 2- can, 3- rotational, 4- pet. Every production

line has limited productive capacity. As we know each line has a nominal production capacity

and a real production capacity that real production capacity is considered in this model so that

the model becomes closer to reality.

Meanwhile, it is noted that amount of real production capacity of production lines don't have

considerable difference in monthly time periods with each other.

Thus, limitation of real production capacity of production lines in one month is as below:

≤

i=1, 2,…,4 , j=1, 2, …, 5, t=1, 2, …, 12

ijcrb.webs.com



850

SEPTEMBER 2012

VOL 4, NO 5

Where


(1-bottle, 2- can, 3- rotational, 4- pet)


cc, 5- 1500 cc)



Ci= amount of real production capacity of production line i during the year

It must be noted that real production capacity of production lines during each time period

(monthly) doesn't have perceptible difference with each other. Therefore, real production

capacity of each production line is considered similar during various time periods. Real

production capacity of each production line is as below.

4-4-4 Managerial purposes

As we know ideal is a certain position (or quantity) in time and place that the decision maker

intends to access it. Amounts related to these ideals are obtained through counseling with experts

and the clear-sighted and about some issues like market share it is exploited from comprehensive

programs of the company. Ideal level of managerial purposes in the present survey has been

designed in the model given to studying of compiled programs and the represented policies in

programs as well as interviewing with managers of Iran Behnoush Company.

4-4-4-1 The ideal to increase return on sales

One of the most important purposes that management of Iran Behnoush Company considers in

determining the programs is to reach maximum return on sales during the planning period.

Increasing of selling amount of products will be leaded to more profit and increased liquidity

potential as well as maintenance of the market share in management view. Since all products will

have profit for the company through their selling ideal of maximum return on sales is the product

of sum of productions in profit of each unit of products and is stated as below:

+ 1+- 1

-) =

i=1, 2,…,4 , j=1, 2, …, 5, t=1, 2, …, 12

Where


(1-bottle, 2- can, 3- rotational, 4- pet)


cc, 5- 1500 cc)


= profit of each unit of nonalcoholic beer with packaging i and liter j


1+= positive deviation from ideal of maximum return on sales

1-= negative deviation from ideal of maximum return on sales

= maximum expected return on sales

ijcrb.webs.com



851

SEPTEMBER 2012

VOL 4, NO 5

4-4-4-2 Ideal of decreasing the loss due to missed sale of products

Given to the policy of Iran Behnoush Company's management the loss arising from missed sale

must be decreased as much as possible to maintain the market share and obtain more customer

satisfaction. Therefore, management of the company intends to minimize the difference between

production level of products of the company and demand level of the market. Lower production

level with regard to demand level of customers is leaded to lose a portion of market demand and

this is resulted in the loss of missed sale. Ideal of decreasing the loss due to missed sale of

products is the product of profit of each nonalcoholic beer unit by amount of unprovided demand

of each unit of products. It is stated as the following:

+ ( 2+- 2

-) =

i=1, 2,…,4 , j=1, 2, …, 5, t=1, 2, …, 12

Where

i= characteristic of nonalcoholic beer based on packaging type of the produced nonalcoholic

beer (1-bottle, 2- can, 3- rotational, 4- pet)


cc, 5- 1500 cc)


= profit of each unit of nonalcoholic beer with packaging i and liter j

= amount of unprovided demand (missed sale) of nonalcoholic beer with packaging i and liter

j in time period t

2+= positive deviation from ideal of amount of unprovided demand (missed sale) of products

2-= negative deviation from ideal of amount of unprovided demand (missed sale) of products

G2= maximum amount of the intended cost due to missed sale of products

4-4-4-3 Ideal of decreasing storage time of products

When amount of products is more than demand level of customers the company is forced to store

them. Therefore, this brings about imposing of additional storage cost which is an unfavorable

cost for the company. Management of the company is determined to decrease storage of products

as much as possible:

+ ( 3+- 3

- ) =

i=1, 2,…,4 , j=1, 2, …, 5, t=1, 2, …, 12

Where

i= characteristic of nonalcoholic beer based on packaging type of the produced nonalcoholic

beer (1-bottle, 2- can, 3- rotational, 4- pet)

ijcrb.webs.com



852

SEPTEMBER 2012

VOL 4, NO 5


cc, 5- 1500 cc)


= storage cost of each unit of nonalcoholic beer with packaging i and liter j

= number of nonalcoholic beer with packaging i and liter j stored in time period t.

3+= positive deviation from ideal of decreasing storage time of products

3-= negative deviation from ideal of decreasing storage time of products

G3= maximum amount of the intended cost due to storage of products

5-4-3 Objective function

Now objective function of the mathematical model is designed based on principles of ideal

planning technique by considering the above political limitations and managerial ideals.

We know that objective function in ideal planning is the strength of this technique because of the

possibility to lay several ideals beside each other in objective function of this technique.

Structure of the objective function is according to minimization of inappropriate deviations of

ideals.

Given to the intended ideals of Iran Behnoush Company's management unfavorable ideal

deviations are determined as below:

Insert Table 4 Cardinal method is used to design objective function as importance of minimization of each

unfavorable deviation is identical for company managers. The considerable point of this

technique regarding the necessity that elements of objective function should have an identical

scale (unfavorable deviations) is based on a software that it is not needed to use this issue in the

present survey because all ideals are of one type (money type).

Therefore, objective function of the mathematical model under study is proposed as below:

Minimize Z= 1- + 2

++ 3

+

Subject To:

+ 1-- 1

+) =

+ ( 2-- 2

+) =

+ ( 3-- 3

+ ) =

≤

ijcrb.webs.com



853

SEPTEMBER 2012

VOL 4, NO 5

≤

i= 1, 2, …, 8

j=1, 2, …, 4

t=1, 2, …, 12

m=1, 2, …, 5

All Variable ≥0

5- Conclusion

Finally a model was represented for production planning in Iran Behnoush Company after

conducting various studies, studying the existing conditions and limitations, interviewing with

managers and experts and defining the variables. The represented model could be effective on

income increase, decreasing overtime cost and cost of lost sales in addition to conducting weekly

production planning. Obtained results and claims of the company's managers and the proposed

mathematical model could be effective on saving time besides providing the management's

needs.

Given that several purposes were considered by management of Iran Behnoush Company such as

increased income, decreased overtime and decreased cost of loss in production (lost sales) it

could be argued that sum of these different and almost opposite purposes is only possible

through ideal planning. This is confirmed by observing the results and verifying their accuracy

by users and managers of this company.

Confirmation of the general director of Iran Behnoush Company is provided below about

usefulness of the proposed model given to obtained results regarding the model implementation.

ijcrb.webs.com



854

SEPTEMBER 2012

VOL 4, NO 5

References Aouni, B, and Kettani, O, (2001), "Goal Programming Model: A Glorious History and A Promsing Future ",

European Journal of Operational Research, Vol 133, PP 225-231.

Bredstrom, D., Ronnqvist, M., 2002.Integrated production planning and route scheduling in pulp mill industry. In:

Proceedings of the 35th Annual Hawaii International Conference on System Sciences, 2002. HICSS.

Benjamin, J., 1989. An analysis of inventory and transportation cost in a constrained network. Transportation

Science 23, 177–183.

Chen, C.L., Wang, B.W., Lee, W.C., 2003. Multiobjective optimization for a multienterprise supply chain network.

Industrial and Engineering Chemistry Research 42, 1879–1889

Jung, H., Jeong, B., Lee, C.G., 2008. An order quantity negotiation model for distributor-driven supply chains.

International Journal of Production Economics 111, 147–158.

Korajewski, L.J and Ritzman, L.P, (2001), "Operation Management", Sixth Edition, New Jersy : Prentice Hall, PP

78-120.

Kanyalkar, A.P., Adil, G.K., 2005. An integrated aggregate and detailed planning in a multi-site production

environment using linear programming. International Journal of Production Research 43, 4431–4454.

Lee, Y.H., Kim, S.H., 2000. Optimal production–distribution planning in supply chain management using a hybrid

simulation-analytic approach. Proceedings of the 2000 Winter Simulation Conference 1 and 2, 1252–1259.

Lee, Y.H., Kim, S.H., 2002. Production–distribution planning in supply chain considering capacity constraints.

Computers and Industrial Engineering 43, 169–190.

Lee, Y.H., Kim, S.H., Moon, C., 2002. Production–distribution planning in supply chain using a hybrid approach.

Production Planning and Control 13, 35–46.

Martin, C.H., Dent, D.C., Eckhart, J.C., 1993. Integrated production, distribution, and inventory planning at Libbey–

Owens–Ford. Interfaces 23, 78–86.

Oh, H.C., Karimi, I.A., 2006. Global multiproduct production–distribution planning with duty drawbacks. AICHE

Journal 52, 595–610.

Ryu, J.H., Dua, V., Pistikopoulos, E.N., 2004. A bilevel programming framework for enterprise-wide process

networks under uncertainty. Computers and Chemical Engineering 28, 1121–1129.

Sabri, E.H., Beamon, B.M., 2000. A multi-objective approach to simultaneous strategic and operational planning in

supply chain design. Omega-International Journal of Management Science 28, 581–598.

Sakawa, M., Nishizaki, I., Uemura, Y., 2001. Fuzzy programming and profit and cost allocation for a production and

transportation problem. European Journal of Operational Research 131, 1–15.

ijcrb.webs.com



855

SEPTEMBER 2012

VOL 4, NO 5

Annexure

Table 1- Specifications of decision variables of mathematical model

Table 2- Decision variables of the mathematical model

Table 3- Parameters of the mathematical model

Variable Description

qijt Production amount of nonalcoholic beer with packaging i and liter j in period t

d1+ Positive deviation from ideal of maximum return on sales

d1- Negative deviation from ideal of maximum return on sales

d2+ Positive deviation from ideal of products' missed sale (unprovided demand)

d2- Negative deviation from ideal of products' missed sale (unprovided demand)

d3+ Positive deviation from ideal of decreasing the amount of time to store productions

d3- Negative deviation from ideal of decreasing the amount of time to store productions

Variable Description

Sijt Amount of unprovided demand (missed sale) of nonalcoholic beer by packaging i and

liter j in period t

Nijt Number of nonalcoholic beer with packaging i and liter j stored in period t

Bij Profit of each unit of nonalcoholic beer with packaging i and liter j

Fij Warehouse cost of each unit of nonalcoholic beer with packaging i and liter j

Emj Amount of raw materials of kind m that are used to produce nonalcoholic beer with

capacity j

Rm Amount of raw materials of kind m that are available in one year

Ci Amount of capacity of real production of production line i during the year

G1 Maximum level of the expected return on sales

G2 Maximum level of the intended cost due to missed sale of products

G3 Maximum level of the intended cost due to the stored products

Specification Description Range

i Characteristic of nonalcoholic beer based on kind of the product's packaging (1-

bottle, 2- can, 3- rotational, 4- pet)

i=1, 2, 3, 4

j Characteristic of nonalcoholic beer based on capacity (1- 280 cc, 2- 330 cc, 3-

500 cc, 4- 1000 cc, 5- 1500 cc)

j=1,2,…,5

t Characteristic of months of production planning (1- April, 2- May, 3- June, …,

12- March)

t= 1, 2, …, 12

m Characteristic of the usable raw material in producing nonalcoholic beer (1-

malt, 2- hop, 3- HFCS, 4- citric acid, 5- ascorbic (vitamin C)

m= 1, 2, .., 5

ijcrb.webs.com



856

SEPTEMBER 2012

VOL 4, NO 5

Table 4- Information related to unfavorable deviations in objective function Variable of

unfavorable

deviation

unfavorable deviation Ideal

1- Negative deviation Ideal of increasing return on sales

2+ Positive deviation Ideal of decreasing amount of loss due to missed sale of products

3+ Positive deviation Ideal of decreasing storage time of products

optimization of production planning using … · optimization of production planning using...

Documents