Modeling in Achieving Knowledge Management Performance Optimally Considering Disruption

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Modeling in Achieving Knowledge Management Performance Optimally Considering Disruption

Sajadin Sembiring¹, Herman Mawengkang², Tulus³, M. Zarlis⁴

1,4 Postgraduate Studies, Department of Computer Science, Faculty of Computer Science and Information Technology, Universitas Sumatera Utara, Medan, Indonesia, 20155

2,3Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Sumatera Utara, Medan, Indonesia, 20155

Abstract. Modern business or non-business firms are urged to increase agility and sustained competitiveness if they wish to operate on the global market and engage in alliances. One key success factor for these firms is the involvement of knowledge management (KM) process. The important point in achieving success is in making good decisions as the problems encountered are not well structured and situations faced are complex. Therefore it is necessary to optimize the KM performance in these firms to achieve sustaining competitiveness objective. Nevertheless, occasionally there may occur disruption in the decision-making process based on KM. This paper proposes an optimization model to describe the KM process with the objective is to minimize the expected cost due to disruption.

Keywords: KM Performance, KM Processes, Decision making, Optimization, Disruption.

1. Introduction

Disruption is one of the main challenges to be faced by organizations in the business world which occurs unexpectedly during the planning horizon. Clayton Christensen [5, 6] has shown, representing changes to the market, that is, some forms of structural change or fragmentation or hyper-growth [1]. Disruption in business is not only driven by new technology - it is also driven by climate change and many other global imbalances that currently challenge business as usual. Cragun and Sweetman (2016) [20] have identified that, there are five factors that triggers for disruption waves which occurred since 1980, namely: Technology (especially IT), Management theory (new methods of managing human resources, leadership, production and business), economic events (the role of the state, central bank, supply-demand fluctuations), global competitiveness, and geopolitics (tensions between regions). Disruption replaces old markets, industry and technology and produces a more efficient and comprehensive novelty, it could be destructive and creative [6].

Over the next 15 years, sustainability according to leading global CEOs - will be as big and disruptive in every sector as digital technology has become more than the last 15 years. Apart from cynicism, it remains true that disruption has become a problem [1]. The business community seems to be beset by challengers in many key market segments including energy, finance, mobility, construction, transportation, manufacturing, and more. Disruption should be taken as a change in industry structure. It is not simply about the arrival of a new competitor or improvements of/deterioration in competitive conditions. It takes place in the context of a changing industry structure. That, in turn, should indicate many more players entering a market, a significant drop in the cost of innovation, a change in the power relations within an industry or a new technology that changes market segmentation.

The Knowledge Management (KM) process depends heavily on the nature and activities of the company, the specificity of the industry, the organizational culture and its knowledge management strategy. A distinctive feature of the KM process is that they relate to certain activities carried out with knowledge, as stated - certain resources. Knowledge is dominant over other resources, which occur simultaneously, are inexhaustible and are ISSN: 2005-4238 IJAST

405

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not linear, relative, ambiguous, dynamic, intangible and difficult to understand, becoming obsolete quickly, can be done in various ways, and utilizing knowledge in full is a difficult task. The specificity of knowledge as a resource is reflected in the characteristics of processes related to their knowledge and management.

At present, to achieve success in a turbulent environment requires intelligent organizations to make wise decisions and to take action based on relevant knowledge, and managed properly [9]. Modern organizations are under intense pressure to increase agility and competitiveness to operate in global markets and engage in alliances. Knowledge management plays a key role in an organization's ability to drive technology development, understand the market context and strategic implications and to gain a competitive advantage from it [12].

The purpose of the KM process is to enable organizations to act intelligently in meeting customer demands and make decisions in uncertain conditions, thereby maximizing profits or minimizing operating costs by placing, selecting, managing, distributing and transferring important information in the company. Therefore problems in the knowledge management process can be categorized into optimization problems. Therefore, it is necessary to optimize KM performance in these companies to achieve the goal of sustainable competitiveness.

However, sometimes disruption can occur in the decision-making process based on KM.

The purpose of this study is to propose an optimization model to minimize expectations costs due to disruption in KM process problems. In term of mathematical modeling, optimization of KM process could be categorized into a two-class model; deterministic models and stochastic models. In the deterministic model, the parameters or data are assumed to be known. This deterministic model will ultimately solve the problem of

"average value" or "worst case". Solutions for such problems as "worst players" or "average values" are often inadequate - a large error margin appears [1]. The model of KM process deterministic problems, although widely studied in the literature, is very lacking and less acceptable. Every time the parameters are uncertain, a stochastic model is used. Usually, uncertainty can be overcome by using the "best guess" of uncertain values.

For the rest, this paper is organized as follows: In Section two, showing the brief review of KM Process and optimization of stochastic programming to justify the relationship of KM process under disruption. Section three describes the optimization models in KM Process to achieve optimally Knowledge Management Performance under disruption. To guide practically, the model implemented at small-medium enterprises as shown in Section four. Section five presents the algorithm as a solution basic approach. Data preparation Computational results presented in section six and seven, respectively. Conclusions and future work, presented in Section eight as the end of this paper.

2. Literature Review

Process Optimization refers to the logic of the process (what is done and why it is done) and its effectiveness (how it is done). This allows organizations to improve the effectiveness of their functions and can flexibly adjust to a changing business environment. The Optimization Process increases the ability of the organization to achieve the goals set in various fields of its operations. If an organization can achieve its goals better and faster than competitors, its competitiveness increases. One method used in the optimization process is benchmarking, which has been a standard operating procedure since the 1980s and has been successfully used by many organizations to improve their performance.[19]

The KM Process can operate under usual conditions or disruptions. A shift from the KM Process usual state to the disruption state is characterized by the inability to continue operations according to the production schedule due to capacity constraints of a Knowledge Management Process component caused by an unplanned event. When the KM Process can run again according to the original production schedule, it is considered to be returned to the KM Process usual state. The particular realization of the future, or more practically a realization of the random variables that define the KM Process environment such as demand, feedstock prices and supply disruptions a scenario. Most of the references of optimization problems which contain uncertain parameter come under the heading of stochastic programming [21]. The appropriate structure for our KM Process problem is a two-stage stochastic program with recourse. In such models, generally, the objective function value is assigned to minimizing expected costs or to maximizing expected benefits (linear or nonlinear), although the function value can also refer to the expected value of the quadratic deviations of certain specific targets or the variance of the second-stage recourse function. There are two kinds of decision variables involved. Those determined at the first stage called here-and-now decision variables, in which the random variables are still unknown; in this paper, they correspond to the production cost and workforce of the first period. Those determined at the second stage, called recourse decision variables, in which the random variables have been realized. These variables represent reactive decisions made to respond to the uncertainty factor

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An interesting literature review of Stochastic programming [1, 6, 10] and robust optimization [13] have made several successful applications in production planning. A multi-stage stochastic programming approach was used for addressing a multi-product production planning model with random demand [11]. Developed a stochastic LP model based on the two-stage deterministic equivalent problem to incorporate demand uncertainty in a multi-period multi-product production planning model by Bakir and Byrune [3]. Huang [7] proposed multi- stage stochastic programming models for production and capacity planning under uncertainty. A two-stage stochastic model for addressing multi-product production planning with uncertain yield proposed by Kazemi et al. [4, 12]. A robust optimization model for stochastic aggregate production planning proposed in [13]. In [14] a robust optimization model was considered to address a multi-site aggregate production planning problem in an uncertain environment. Wu [15] applied the robust optimization approach to the problem with uncertain production loading under the global supply chain management environment. Two robust optimization models with different recourse cost variability measures to address multi-product production planning with uncertain yield have been proposed in [7]. In the case of discrete random variables, the resulting of two-stage recourse models are usually large and complex, and thus must be solved numerically using suitable algorithmic strategies. Most of these algorithms apply decomposition strategies that break the model down by scenario or stage in an iterative scheme, allowing the resolution of smaller models (smaller in comparison to the deterministic equivalent model in its extensive form which gave rise to the original two-stage model).

3. Optimization Model of Knowledge Management Performance

The decision to carry out the KM process must be well studied, and cannot be realized on an ad hoc basis or by unintentional activities. Identifying KM processes is the first important step: implementation, realization and monitoring. In the next step the results of the KM process must be measured (observation scenario). If the results are satisfactory, there is no need to make changes in the process. However, if the process results are not satisfactory, the cause must be identified. When analyzing the causes of unsatisfactory results from the KM process, and their impact on the intra-organizational and external environment must be taken into account (action scenario). In many cases, the lack of success of the KM process is not due to errors made by the organization but caused by changes that occur in the business environment, such as disruptions (uncertainty).

Determining the causes of why unsatisfactory results are a fundamental reason for optimizing KM performance.

The main objective of stochastic programming is a concern for optimal decision-making problems in uncertainty situations. Uncertainty situations are presented by a probability distribution. An interaction of stochastic programming and decision-making processes modelled so that decision-makers have choices which are appropriate based on how uncertainty develops. Based on the modelling perspective, there are many studies in the stochastic program literature relating to exogenous uncertainty problems (Jonsbraten (1998). An optimal decision cannot influence the stochastic processes. Based on these descriptions, the KMP can be represented conceptually with a basic model in such a way to obtain an optimal result. The basic model can be expressed as follows:

Action x (First-Stage)  Observe scenario  Action y (Second-Stage)

Where x is the vector variables in the first stage and y is the vector variables in the second stage. The second- stage problem depends on first-stage decision and scenario realized. The objective function E is total cost performance due to the disruption. The conceptual model could represent an optimal formulation of KM Process that the “action” as a result of the first stage process should be reconsidered due to the uncertainty parameter of “disruption” that occur in the next period of the KM Process. Therefore it is necessary to make recourse to anticipate the occurrence of disruption. If the pattern of the uncertainty disruption has a discrete probability distribution, the optimal model can be expressed mathematically as follows:

1

( )

S s s

s

Min cx p Q x



 

(1) Subject to :

0 Ax b x





(2)

Where

407

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( ) { }

s s s s s

Q x  Min f y D y h   T x

(3)

P^s is the probability of the disruption occurrence. x is the vector of the variable of the first stage in which there is no disruption. Due to the disruption, we will have y vector of variable as the KM Process. S is the scenario needed to describe parameter for disruption. Vector of variable x can be regarded as one of the following results from KM process, such as productivity, profitability, sales growth, or market share. Let for the time being x is considered as productivity. In the first stage, it is assumed that the model to gain maximum productivity is in the linear program, as described in the Eqs. (1) and (2), without the term

1

( )

S

s s

s

p Q x





To accomplish a process it is necessary to have time. So during the process, an uncertain disruption could occur.

Due to the problem in the KM Process contains random parameter ω then the problem has turned out as expressed in Eqs. (1) and (2). This called stochastic programming problem [21].

It is no doubt that nowadays an organization needs to put the sustainable concept in their KM performance to handle competitiveness [22]. There are three main factors should be included, economic, environment, and social welfare. Therefore in a way to get the optimal performance in the production process involved in the KM process, sustainability must be considered. The component of the vector of variable x and y involve these three factors of sustainability. Then we can say that productivity has already made impacts on the profitability, environmental risk and social welfare. With the involvement of sustainability in KM Process problem, the proposed model is no longer linear as in Eqs. (1) and (2), but it has a non-linear form and can contain variable values that are counted. The problem model proposed in this study can be written in the following form.

1

m in ( ) ( ) ( ) 0,

( ) 0, (3)

: ,

.

e

i

x

m nZ

m n

n

f x Q x g x

h x

g R R

h R R

x Z

_











Where

1 2

2

( ) ( , ( ))

( , ( )) m in ( ( ), )

( , ( ), ) 0 (4 ) ( , ( ), ) 0

: :

e

i

y

n n

y

n n

Q x E Q x w

Q x w f y w w

g x y w w h x y w w

g R R

h R R

y Y









  



 is a probability space equipped with -algebra F and a probability measure  are random variables whose probability sizes exist, and f¹, f², g¹, g², h¹, h² are non-linear functions, which are differentiable but not convex.

x represents the first stage variable, while y (w) presents the second stage variable. The set Y is a combination of two subsets of YR and YZ, with ²

n

Y

R

 R

_ _and

Y

_Z

 Z

_ⁿ². So, in the model above, some of the second stage ISSN: 2005-4238 IJAST

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variables (which are indexed by the YZ set) are required to take the count value. The main feature of the two- stage stochastic program model is the "recourse" action. The decision set is divided into two groups. Many decisions must be made before the parameters of the problem are known: this decision is the first stage decision and this decision is taken in the first stage. Other decisions can be made after the uncertainty is revealed. The recourse decision is a function of the actual realization of uncertain parameters and the first stage decision.

Sequences of events characterize the model as a recourse model. Many things need to be considered in the multi-stage model, namely, convexity and continuity. This is mainly due to enumeration requirements. If the count variable is only in the first stage, the nature of the recourse function is the same as in the continuous case.

In the case of continuous nonlinearity if f, h convex and g affine for all , the problem is convex. When the enumeration requirements appear in the second stage, for the linear case recourse functions are generally not convex. Difficulties in dimensions depending on the number of scenarios. The expectations in Equation (4) include multi-dimensional integration. For the problem to be resolved, uncertainty is usually expressed in a discrete distribution that approaches. However, the need for accuracy in modelling increases dimensions in the optimization program. This adds to the limitations of the stochastic program modelling method and the method of completion is still at an early stage. The assumption of a discrete probability space resulting in an objective function can be written as a finite number and the constraints are replicated for each element in . Suppose that

 has a discrete probability distribution at . = 1, .., S with P( = i) = i. Then the problem can be written again in the form:

1

1 1

1 2 1 2

1 2

1 1

1

2

1 1

2 2

min ( ) ( , , ) ( ) 0

( ) 0

( , , ) 0 1, , ( , , ) 0 1, ,

, 1, ,

: :

: : , 1,

e i

S

s s

s

s s s

n

s s

m m

n n

t t

n n n n

f x f x y

g x h x

h x y s S

g x y s S

x Z y Y s S

g R R h R R

g R R h R R s S

 







 

 





  

   

 

  

L L L

L

₍₅₎

Where s states the probability that scenario s occurs. This equivalent deterministic formulation is a problem with large scale nonlinear count programs with variable n1+ n2s and me + mi + tes + tis nonlinear constraints. If all random variables have finite uncertainty support that exists in the dual-stage model, it can be presented by the tree scenario. Because algorithms work with discretization, in this section they are linked between scenario (discrete) and filtration trees, which apply to continuous and discrete random variables.

A scenario tree is a rooted tree in which all leaves with a depth of T. Gusset sets at t depths are expressed by ^t, so the set of gussets is^N ^

U

^t^N ^t^t. The random set of vertices n is expressed by

t

C

n. Each quantity (n, m) has a conditional distribution related to q mn from the transition to n with the knowledge that n is reached. So

1

n nm m C

q







Alternatively, the scenario tree can be described using filtration where--algebra presents information available to decision-makers. Assuming ^r^tit has finite support, --algebra τt =  (^r^t) which is formed by finite ^r^t_and also filtration{ , ,F¹ K F_T}. Because τt is finite it is formed by a finite partition

tj

B of :

1

dengan untuk .

kt

t t t

i j l

i

B B B j l



 

U

   

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1 1 1 1

1

dengan untuk .

kt

t t t

i j l

i

B B B j l

   



 

U

   

Filtration properties result in a relationship between 2 partitions

tj

B and

1 tj

B^

 

:

1

1 1

,1 , 1, , 1 dengan

it

t t t

t i t i k

k J

i i k J k B B



 





     K 

U

Note that when a policy x{ ( ),x_t r t1, , }T

K is taken against filtration{ }F_{t t}^T¹, it means that each xt is measured against the corresponding -algebra τt. This resulted in:

x is -adaptation  x_t( ) konstan r   r B_i^t, ,i t

. The relationship between filtration{ }F_{t t}^T¹_{and the} scenario tree can be made explicit by identifying the components Bⁱ^tof the partition with related gussets from the scenario tree.

4. Case Study: SMEs Fish Industry in North Sumatera Province, Indonesia

Micro, small and medium enterprises (SMEs) have proven to be the main pillars of the Indonesian economy because they can withstand the monetary crisis that has affected Indonesia's national economy to date. MSMEs are very weak business institutions in terms of business management, technology mastery, and access to markets. In this disruption era, SMEs businesses face a very difficult challenge in maintaining the sustainability of their business. The presence of new digital technology-based businesses indirectly also poses a threat to the sustainability of micro, small and medium enterprises. For example, the presence of a digital technology-based start-up business will replace various businesses with old models. To be surviving, SMEs must carry out sustaining innovation and self-disruption in business management processes, use of technology in production and access to markets and financial institutions. One possible form of innovation is the optimization of the knowledge management process so that SME organizations can act intelligently in responding to the challenges of the times in an era of uncertain technological disruption.

The fish processing industry that is the object of this research is located in the eastern coastal region of North Sumatra province, Indonesia. This is one example of SMEs in North Sumatera Province, Indonesia, which traditionally process fish production. There are eight types of fish produced, namely: salted fish, dried fish, BBQ fish, fish bowls, smoked fish, pressed fish, pindangs fish and fish preserved. The SMEs using conventional management strategy. Consequently, they do not have enough information or knowledge regarding market demand and price. In this situation for the current information may be certain, but future events are inevitably uncertain.

These products are marketed manually based on orders from colleagues in the community, in one production period. With the existence of e-commerce technology, this is utilized by the community, so the number of requests for production becomes more and diverse. This situation is a serious challenge for SMEs to provide excellent service that can meet market expectations. The industry run by the SME community must make a production plan for the eight processed fish products in order to be able to meet market demand during each time period t, t = 1, ..., T., In this case, each production period is three month, so there will be four periods in a year. In this matter of production planning, knowledge is needed to decide how many each processed fish product to produce in each period, additional resources to use, and how many additional workers and regular stops in each period. Because demand is uncertain and random for each period, it must also be decided how many each product is to be stored in inventory or to fulfil the fulfilment that is lacking in each period.

Model parameter and decision variables used throughout this paper are defined as follows.

1. Sets

a. T = number of periods b. N = set of products c. M = set of resources d. S = set of scenarios 2. Variables



x

_jt = Quantity of product j N in period t  T (units) ISSN: 2005-4238 IJAST

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J = 1 for dried fish, J = 2 for salted fish, J = 3 for BBQ fish, J = 4 for pindang fish, J = 5 for smoked fish, J = 6 for fish preserved, J = 7 for pressed fish, J = 8 for fish bowl



u

_it : An additional amount of resource i  M to purchase in t  T (units)



k

_t : Number of workers required in period t  T (man-period)



k

_t^ : Number of workers laid-off in period t  T (man-period)



k

_t^ : Number of additional workers in period t  T (man-period)



I

_jt : Quantity of product j  N to be stored in period t  T (units)



B

_jt : Under-fulfillment of product j  N in period t  T (units) 3. Parameters

 , , , , , ,  are all costs (IDR, Indonesian currency, Rupiah)



D

_jt : Demand for product j  N in period t  T (units)



U

_jt : Upper bound on

u

_jt



r

_ij : Amount of resource i  M needed to produce one unit of product j  N



f

_it : Amount of resource i  M available at time t  T (units)



a

_j : Number of workers needed to produce one unit of product j  N 4. The Stochastic Programming Model

Minimize

   

  



     



      

        

         

jt jt it it t t t t

t T j N i M t T t T t T

s s s s

t t s jt jt s jt jt

t T s S j N t T s S j N t T

x u k k

k p I p B

⁽⁶⁾

Subject to:



,



_ji _jt



_it



_it

   

j N

r x f u i M t T

(7)

   ,  

it it

u U i M t T

(8)





_j _jt



_t

 

j N

a x k t T

(9)

1 ^ ^

2,...





  

t t t t

k k k k t T

(10)

. 1_

, ,



^s



^s



^s



^s

     

jt j t jt jt jt

x B I B D j N t T s S

(11)

, , , , , ,

^s ^s

0 , , ,

jt it t t t jt jt

x u k k k I B

^ ^

   j N   i M   t T   s S

(12) The objective function for all these decisions is formulated in expression (6). The number of resources i  M required to produce the product j  N expressed in constraints on expression (7) must at least have the same number of resources available at time t  T along with the additional resources needed.

However, additional resources need to have an upper limit expressed in expression (8). The number of workers needed to produce one unit of product j  N, expressed in constraint expressions (9), meanwhile expressions in constraints (10) to ensure that workers available in each period are equal to the number of workers from the previous period plus each change in number level of workers during the current period.

Changes in the number of workers are possible because there are additional workers or excessive layoffs.

Expression (11) is a limit to determine the number of products to be stored in inventory or to be purchased from outside to meet market demand shortages. The model formulated in expression (6) through to (12) is deterministic equivalent form and the random form, in this case, has been represented by scenario and the objective function of these random terms have been solved with premultiplied by the corresponding ISSN: 2005-4238 IJAST

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probabilities ps . The method for transforming a stochastic programming model to its deterministic equivalent model was addressed in Irvan and Mawengkang [24].

5. The algorithm

The procedure for searching a suboptimal but integer-feasible solution from an optimal continuous solution can be described by expression follows;

Let

x  [ ] x  f , 0   f 1

[x] is the integer component of non-integer variable x and f is the fractional component.

Step 1. Get row i* the smallest integer infeasibility, such that



_i_*

 min{ ,1 f

_i

 f

_i

}

Step 2. Calculate

v

^T_i*

 e B

_i^T_* ^¹ this is a pricing operation Step 3. Calculate



_ij

 v

_i*^T

a

_j With j corresponds to

min

_j ^j

ij

d



 

 

 

 

 

I. For non-basic j at lower bound (LB)

If



_ij

 0

and



_i_*

 f

_i calculate

(1

_i^*

)

ij





  



If



_ij

 0

and



_i_*

  1 f

_i calculate

(1

_i^*

)

ij





  

If



_ij

 0

and



_i_*

  1 f

_i calculate ⁱ^*

ij



  



If



_ij

 0

and



_i_*

 f

_i calculate ⁱ^*

ij



  

II. For non-basic j at upper bound (UB)

If



_ij

 0

and



_i_*

  1 f

_i calculate

(1

_i^*

)

ij





  



If



_ij

 0

and



_i_*

 f

_i calculate

(1

_i^*

)

ij





  

If



_ij

 0

and



_i_*

  1 f

_i calculate ⁱ^*

ij



  

If



_ij

 0

and



_i_*

 f

_i calculate ⁱ^*

ij



  



Otherwise, go to next non-integer non-basic or super basic j (if available).

Eventually the column j* is to be increased form LB or decreased from UB. If none go to next i*.

Step 4. Calculate



_j_*

 B

^¹



_j_* i.e. solve

B 

_j_*

 

_j_*

for 

_j_*

.

step 5. Ratio test; there would be three possibilities for the basic variables in order to stay feasible due to the releasing of non-basic j* from its bounds.

If j* lower bound

Let ^'

*

'

' * 0

*

min

ⁱ

ij

B i

i i ij

x l A

^  ^



  

 

  

 

 

'

*

'

' * 0

*

min

ⁱ

ij

i B

i i ij

u x B

^  ^



  

 

       

Vol. 28, No. 9, (2019), pp. 405-417

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C  

the maximum movement of j* depends on:

 * min( , , )  A B C

If j* upper bound

Let ^'

*

'

' * 0

*

' min

ⁱ

ij

B i

i i ij

x l A

^  ^



  

 

  

 

 

'

*

'

' * 0

*

' min

ⁱ

ij

i B

i i ij

u x B

^  ^



  

 

        '

C  

The maximum movement of j* depends on:

 * min( ', ', ')  A B C

step 6. Exchanging basis for the three possibilities 1. If A or A’



x

Bi' becomes non-basic at lower bound

l

_i_'



x

_j_* becomes basic (replaces

'

Bi

x

)



x

_i_* stays basic (non-integer) 2. If B or B’



x

Bi' becomes non-basic at upper bound

u

_i_'



x

'

Bi

x

)



x

_i_* stays basic (non-integer) 3. If C or C’



x

_i_*)



x

_i_* becomes super basic at integer-valued Repeat from step 1.

6. Data Preparation

The planning production horizon covers for every three months, i.e. T = {1, 2, 3, 4}. After surveying the location, there is the market situation for all the 8 fish processed products could come out three possible situations i.e., good, fair and poor, with associated probabilities of 0.30, 0.50 and 0.20 respectively. The data used in this Production planning problem are described in Table 1 through to Table 10 as follows:

Table 1. The production cost for each fish processed product in each period

Resources

Period

1 2 3 4

Machine1 45600 45800 45800 45900

Machine2 34300 34600 34600 34700

Machine3 32200 32300 32300 32500

413

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Table 2: Additional Resources Cost (IDR/ton)

Product Period

1 2 3 4

1 2300 2300 2350 2400

2 780 800 800 850

3 6700 6700 6750 6800

4 8500 8550 8600 8600

5 15100 15100 15200 15200

6 3500 3550 3600 3600

7 1600 1600 1750 1800

8 8000 8200 8250 8300

Table 3 : Costs for the workforce (IDR Million/man-period)

Cost Notation Period

1 2 3 4

 ²²⁰⁰⁰ ²²⁵⁰⁰ ²²⁵⁰⁰ ²³⁰⁰⁰

 24000 24000 25500 26000

 25000 25000 25600 27000

Table 4: Sources needed for each Product (ton)

Resources J

1 2 3 4 5 6 7 8

Machine1 6 5 6 8 7 6 5 9

Machine2 4 4 5 6 6 5 5 8

Machine3 5 3 5 6 6 5 5 7

Table 5: Capacity of Resource available

Period Machine 1 Machine 2 Machine 3

1 20000 18000 21000

2 20000 18000 20000

3 20000 19000 21000

4 19000 17000 20000

Table 6: Upper Bound for additional Resources

Period Machine 1 Machine 2 Machine 3

1 300 300 200

2 300 300 200

3 250 300 200

4 200 250 250

Table 7: Workforce Needed to Produce Each Product

Product Work force(man/ton)

1 6

2 12

3 24

4 24

5 24

6 20

7 15

8 8

404

Vol. 28, No. 9, (2019), pp. 405-417

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Table 8: Inventory Holding Cost (IDR Million/ton)

Product Period

1 2 3 4

1 2700 2700 2700 5000

2 2500 2500 2500 4000

3 2400 2400 2400 2600

4 3000 3000 3000 5000

5 2400 2400 2400 2700

6 2000 2000 2000 2300

7 3000 3000 3000 4000

8 2500 2500 2500 2500

Table 4 and 5 shows the capacity of resource needed and available for each machine. The upper bound for additional resources is given in Table 6. The data for the workforce needed to produce each fish product is shown in Table 7. The cost of holding products in inventory can be found in Table 8.

The cost if the management has to purchase from outside the product to meet the demand as shown in Table 9 follows:

Table 9: Costs to Purchase from Outside (IDR Million/ton)

Product Cost

1 6700

2 4800

3 10000

4 16200

5 27800

6 11000

7 15500

8 2500

Uncertainty occurs in the demand of each fish processed product in each period. The realization for the demand in every situation and in each period is shown in Table 10 follows:

Table 10. Data for Market Demand (ton)

Product, j Situation, s Period, t

1 2 3 4

1

Good 20000 20000 20500 20500

Fair 18000 18000 18000 19000

Poor 15000 15000 15000 16000

2

Good 115000 115000 115000 116000

Fair 112000 112000 112500 113000

Poor 90000 90000 90000 90000

3

Good 4000 4000 4500 4500

Fair 3600 3600 3600 4000

Poor 3000 3000 3100 3100

4

Good 5000 5000 5000 5500

Fair 4500 4500 4500 4600

Poor 4000 4000 4000 4100

5

Good 3500 3500 4000 4000

Fair 3000 3000 3500 3500

Poor 2000 2000 2200 2200

6 Good 4000 4000 4000 4200

Fair 3600 3600 3600 3700

Vol. 28, No. 9, (2019), pp. 405-417

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Poor 3000 3000 3000 3100 7

Good 5100 5100 5200 5300

Fair 4500 4500 4500 4600

Poor 4000 4000 4100 4100

8

Good 5000 5000 5100 5100

Fair 4500 4500 4600 4600

Poor 4200 4200 4200 4200

7. Computational Results

Based on computational results, the knowledge base found to answer the question about the quantity of each fish processed product to be produced in each period and additional resource to be used and the number of regular additional and laying-off workers in each period are presented in Table 11 and Table 13 respectively.

Table 11. The number of each product to be produced (ton)

Product Period

1 2 3 4

1 25000 25000 25000 30000

2 90000 90000 90000 95000

3 20000 20000 20000 30000

4 20000 20000 20000 30000

5 20000 20000 20000 30000

6 20000 20000 20000 30000

7 20000 20000 20000 30000

8 20000 20000 20000 30000

Table 12. Additional Resources to be used (ton)

Resources Period

1 2 3 4

Machine 1 12.20 12.20 12.20 16.95

Machine 2 9.80 9.80 9.70 13.80

Machine 3 8.65 8.75 8.65 12.55

The number of regular additional and laying-off workers in each period can be found in Table 13 as follows:

Table 13. Workforce plan

Policy Period

1 2 3 4

Reg. workforce 38 35 35 47

Add. workforce 35 0 0 12

Lay off 0 0 0 0

8. Conclusion and Future work

In this paper, we present a model to achieve Knowledge Management Performance optimally in the task to find knowledge for decision support in the decision-making process. The knowledge about the quantity of each product to be produced, additional resources needed, and the plan for a workforce with stochastic demand is very important for solving the planning problem faced by the management of the fish processed industry at the coastal area of Sumatra Province. The model includes the computation of the quantity of product to be produced, resources needed and worker which are very useful for the industry in the order they will be able to schedule some local people.

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