A Buffer Stocks Model for Stabilizing Price in Duopoly-Like Market.

(1)

________________________________________

† : _{Corresponding author}

IV-9

A Buffer Stocks Model for Stabilizing Price

in Duopoly-Like Market

Wahyudi Sutopo †

Ph. D Student of Industrial Engineering & Management, Bandung Institute of Technology Jalan Ganesa 10, Bandung 40132, INDONESIA

Department of Industrial Engineering, Sebelas Maret University Jalan Ir. Sutami No. 36A, Surakarta 57136, INDONESIA

E-mail: wahyudisutopo@students.itb.ac.id and wahyudisutopo@yahoo.com Senator Nur Bahagia1), Andi Cakravastia2), and TMA. Ari Samadhi3)

Department of Industrial Engineering, Bandung Institute of Technology Jalan Ganesa 10, Bandung 40132, INDONESIA

Email: senator@mail.ti.itb.ac.id1), andi@mail.ti.itb.ac.id2), samadhi@mail.ti.itb.ac.id3)

Abstract. This paper presents the staple-food distribution problem in agro-industry. There is a great difference

of staple-food supplies in the harvest-season and in the planting-season meanwhile the demand is relatively constant. This situation will trigger price-volatility and shortage of staple-food, and it causes opportunity-losses for the stakeholders (producer, consumer, wholesaler/trader, and the government). For stabilizing the price, the government has several stabilization policies; one of them is market-intervention policy by using buffer-stocks schemes. The market-intervention policy should be utilized for improving producer’s profit, for cutting consumer’s expenditure, and for sustaining wholesaler’s margin-profit by implementing price-support and price-stabilization. In duopoly-like market, we assume that there are only two market-players in the distribution system. The objective of this research is to determine the instruments for operating Market-Intervention Program which consist of the quantity, time, and price of the buffer-stocks schemes. The problem was solved using 3 approaches. First, a comparative cost/benefit analysis between free-market and intervention-market can be used to formulate the objective function of each stakeholders. Second, the integration of optimization model and econometrics model were use to develop the decision-variables subject to the expectation of stakeholders, the buffer-stocks requirement, and the dynamics price equilibrium properties. Third, model market with Inventory was applied for solving the market-price equilibrium. The result could be used to analyze such the staple-food distribution system, incorporating the configuration of duo-producers, duo market-buyers, and duo-consumers.

Keywords: buffer-stocks, duopoly-like market, market-intervention program, model market with inventory,

and staple-food distribution system.

1. INTRODUCTION

Supply Chain Management (SCM) is the integration of key business processes from end user through original suppliers that provides products, services, and information that add value for customers and other stakeholders

(Lambert and Cooper, 2000). The main objective of SCM is to achieve suitable economic results together with the

desired consumer satisfaction levels (Guilléna, et al., 2005). The SCM problem may be considered at different levels depending on the planning horizon and the detail of the analysis: strategic, tactical and operational (Chopra and Meindl, 2004). In this work, the SC design problem is addressed, thus strategic decisions are considered especially a buffer stocks model for stabilizing price.

We discuss the SC network problem of staple food distribution system in agro-industry. There is a great difference of staple-food supplies, such as sugar, in the harvest-season and in the planting-season meanwhile the demand is relatively constant (Reiner and Trcka, 2004; ISO, 2005). This situation will trigger price-volatility and lead food-security problems, especially related to scarcity and price-hikes for households (Smith, 1997; Brennan, 2003). Sutopo et al. (2009) analyzed the opportunity-losses and market risks for the stakeholders at Free-Market. The producer is forced to sell staple-food at lowest price during the harvest season. The consumer has to deal with the scarcity of staple-food and price hikes during the planting season. The wholesaler/trader is forced to spend a larger procurement cost and they lack goods.

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IV-10 Market intervention program should be conducted to

reduce opportunity-losses and market risks for both producer and Wholesaler; and to maintain food-security for the households. In order to maintain expectation of stakeholders, the government can apply the buffer stocks schemes to maintain the market-price on certain price-band (William and Wright, 2005). Therefore, the government has several price stabilization policies; one of them is market-intervention program by using buffer stocks schemes (Athanasioa et al., 2008). The market-intervention policy be able to utilized for improving producer’s profit, for cutting consumer’s expenditure, and for sustaining wholesaler’s margin-profit by implementing price-support and price-stabilization (Sutopo et al., 2009).

This research is started with concerning a variety of buffer stocks models from previous researches. The previous models are classified according to relevant features, such as the performance criteria, the trigger of uncertainty, number of model's stakeholder, buffer stocks policy, and models type. A lot of investigations have been made to model for stabilizing price by market-intervention policy (Table 1).

In previous researches, the buffer stocks models had been developed separately based on optimization methods and econometrics methods. Optimization methods have

been used to determine the level of availability with buffer stocks schemes consisting of time and amount of buffer stocks. Econometrics methods have been used to determine the equilibrium price by using the selling price and the amount of buffer stocks.

Tersine (1992) and Graves (1999) have developed buffer stocks models based on inventory system approach. The models addressed to reduce uncertainty of supply side only and to determine buffer stocks schemes consisting of time and amount of procurement.

Harker (1986), Guder (1988), Chavas et al. (1998), Coulson et al. (2001), Véricourt et al. (2002), Rossi-Hansberg (2005) and Pompermayer et al. (2007) have developed buffer stocks models based on location-allocation approach. The models addressed to reduce uncertainty of supply side and to determine buffer stocks schemes consisting of amount and price of procurement.

Labys (1980), Nguyen (1980), Edwards and Hallwood (1980), Newbwry & Stiglitz (1982), Underwood & Davis (1997), Jha & Srinivasan (1999), Brennan (2003) and Athanasioa et al. (2008) developed buffer stocks models based on supply-demand approach. The models addressed to reduce uncertainty of demand side and to determine buffer stocks schemes consisting of amount and price of procurement.

Table 1: Mapping of previous researches

Author (s), Models type:

(Published) (Descriptive

Price) Optimal)

TC TB Q P 1S 2S 3S Q P T L D O

Labys (1980).      

Nguyen (1980)      

Edwards & Hallwood (1980)      

Newbwry & Stiglitz (1982)      

Harker (1986)     

Guder (1988)     

Tersine (1992)      

Chavas et al (1998)      

Jha & Srinivasan (1999)      

Graves (1999)      

Coulson et al. (2001)      

Véricourt et al. (2002)     

Brennan (2003)      

Rossi-Hansberg (2005)     

Pompermayer et al. (2007)      

Athanasioa et al. (2008)      

Sutopo et al. (2008)       

Proposed Model (2009)    *   * 

Performace Uncertainty Number of Buffer Stocks policy

Benefit) Stakeholder Time, Location)

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IV-11 The previous models cannot reduce excessive

fluctuations of supplier side that consist of amount, price and time simultaneously. Sutopo et al. (2008) have been developed a buffer stocks model for stabilizing price under 2 stakeholders with the decision variables that consist of quantity and price. Furthermore, Sutopo et al. (2009) develop a buffer stocks model for 3 stakeholders with the decision variables that consist of quantity, price, and time but the model limited for each entity has only one player. In this paper, we develop a buffer stocks model for stabilizing price in Duopoly-Like Market through extend model of Sutopo et al. (2009).

2. PROBLEM SETTINGS AND DESCRIPTION

The relevant system illustrated the relationship among structural and functional aspects is shown in Figure 1. We assume those three components of supply-chain entities (duo-producers, duo-Wholesaler, and duo-consumers) and a regulator (government). The functional aspects consist of the producer-Wholesaler-customer relationship based on the free market mechanisms; and the producer-government-customer relationship based on the intervention of market mechanism.

In free-market (FM), the theory of supply and demand states that price itself is determined by supply and demand forces. At the harvest season, producer sells staple-food to the Wholesaler, and the Wholesaler sells them to the consumer. The market-price (producer-wholesaler and wholesaler-consumer) sets off equilibrium process. At the planting season, Wholesaler sells staple-food to the consumer. The market-price (wholesaler-consumer) sets off equilibrium process. Firms with excess inventories cut prices to try to undersell their competitor.

Figure 1: Overview of system relevant.

In interventioned-market (IM), the market-price is determined by supply-demand forces and buffer stocks schemes forces. At the harvest season, government intervenes the market with the price-support program (support) when the market-price falls. Price support

program is conducted through the procurement program from domestic-market. Government purchases the staple-food in boom periods so that the market-price goes up. At the planting season, the government intervenes the market when the market-price soars with the price-stabilization program.The price-stabilization program is conducted through the market-operation from staple-food owned by government. The government releases the staple-food in bush periods so that the market-price goes down.

We assumed the market situation through 4 periods as shown at Table 2. The planning horizon is differentiated through 4 periods as follows: (i) the early of harvest season (period t0-t1); (ii) the end of harvest season (period t1-t2);

(iii) the beginning of planting season (period t2-t3), and (iv)

and the end of plantting season (period t3-t4). It is assumed

that commodity cannot be replaced by substitution products but it is consumed continuously in a year.

Table 2: Resume of market assumstions

Period t0-t1 t1-t2 t2-t3 t3-t4

Production normal booming none none Consumption stable stable stable stable Availability sufficient surplus sufficient shortage Price-FM normal/

lower

lowest price

normal/ higher

highest price Intervention support support stabilization stabilization

The objective of development proposed-model is to determine instruments of Market-intervention program for giving maximal benefit to the producers and the consumers, and also for giving minimal loss/expenditure to the wholesalers and the government. Total benefit or total losses of market-intervention program can be calculated pursuant to total difference between total revenue and total cost at Free Market with Intervention Market for each stakeholders.

3. MATHEMATICAL FORMULATION

We assume that prior to the staple food distribution and all relevant data (costs, supply-availability-demand and other factors) were collected using e.g. historical data and appropriate forecasting methods. Historical data have been drawn from the Central Board of Statistics (BPS) and Trade Data Center, Ministry of Trade, Republic of Indonesia. Before presenting a mathematical formulation for the price stabilization problem described in Section 2, we first introduce the notation that will be used throughout the paper. All costs for parameters and decision variables are measured in Indonesia Domestic Rupiah (IDR).

Sets and index

P

p



: set of producers,

W

w



: set of wholesalers,

C

(4)

IV-12 Parameters

c

: production cost for staple food per unit from producers (IDR/Kgs) ,

c

: distribution cost for staple food per unit from wholesalers (IDR/Kgs) ,

c

: operation cost for staple food per unit from government (IDR/Kgs) ,

c

: holding cost for buffer stocks per unit (IDR/Kgs) ,

c

: import cost for buffer stocks per unit IDR/Kgs) ,

s pt

q

: production of staple food from producer

p

in time period

t

(tons),

d ct

q

: demand of staple food from consumer

c

in time period

t

(tons),

a wt

q

: maximum availability of staple food from wholesaler

w

in time period

t

(tons),

g t

q

: amount of staple-food from government in the beginning period

t

(tons),

p pwt

p

: purchasing-price between producer

p

and wholesaler

w

in time period

t

at FM (IDR/Kgs),

p pwt

p

* : purchasing-price between producer

p

and wholesaler

w

in time period

t

at IM (IDR/Kgs),

s wct

p

: selling price between wholesaler

w

and

consumer

c

in time period

t

at FM (IDR/Kgs),

s wct

p

* : selling price between wholesaler

w

and consumer

c

in time period

t

at IM (IDR/Kgs),

irr

: percentage of internal rate of return,

nrr

: percentage of normal rate of return, and

srr

: percentage of speculative rate of return. Decisions variables

Min

P

: minimum price-limit for government to purchase staple food per unit from producer

p

(IDR/Kgs),

Max

P

: maximum price-limit for government to sell buffer stocks per unit for

consumer

c

(IDR/Kgs),

OP pt

Q

: amount of staple-food that is purchased by government from producer

p

in time period

t

(tons),

OI t

Q

: amount of staple-food that is imported by government in time period

t

(tons),

OR ct

Q

: amount of buffer stocks that is released to consumer

c

in time period

t

(tons),

OG t

Q

: amount of buffer stocks that is stored by government in time period

t

(tons).

3.1. Multi-objectives of stakeholders

A goal programming approach based on recourse model with two stages is proposed in this work to incorporate the expectation of stakeholders. The first-stage variables corespond to those decisions the need to be made,

prior to the realisation as parameters of each stakeholders and market-equilibrium. The second-stage decisions are made subject to restrictions imposed by second-stage problem.

First-stage, let consider the simple one-staple-food market model. It is only governed by production, demand, maximum availability of wholesaler, and its market-price in time period

t

. _{Based on partial market equilibrium theory} (a linear model), we translated the simple one-staple-food market model with the following:

c ct d

a

bp

q





(1)

p pt s

c

dp

q







(2)

a wt a

e

gp

q







(3)

Where (

a

,

c

,

e

) are constants; (

b

,

d

,

g

) are point price elasticity; then (

a

,

c

,

e

) and (

b

,

d

,

g

) should be mutually independent parameters.

Producers and consumers will get advantages when market intervention done, the other way wholesalers and government will get disadvantages due to market-price intervention. For that reasons, proposed-model accounts for the maximisation of the expected value of the benefit for producers and consumers. All at once, proposed-model is aimed for minimisation of opportunity-losses and market risks for wholesalers and government. The methematical formulation of each stakeholders is next described. i). producers side

Total benefit is obtained from total revenue less total production cost. Both in FM and IM, total production cost is obtain ed as production cost per unit multiplied by

production from producer

p

in time period

t

. Furthermore in FM, total revenue is calculated from

multiplication of production from producer

p

at purchasing-price. Total revenue in IM is expected from the amount of staple-food bought by the government multiplied by the minimum price-limit and the amount of staple-food sold to wholesalers at purchasing-price. The total benefit for producers can be expressed as:





    

   

 

1 2

1 * 2

1 2

) )

( (

FM Revenue IM

Revenue

p w t

s pt p pwt OP pt s pt p pwt p t

OP pt Min

q p Q q p

Q P P

(4)

ii). consumers side

Total benefit is calculated from total difference of consumption cost between IM and FM. In FM, total consumption cost is expected from demand of staple food from consumer

c

in time period

t

multiplied by selling

(5)

IV-13 price. In IM, consumers will spending budget to fulfill total

demand of consumer

c

at selling-price between consumer

c

in time period

t

and consumer

c

during period t1-t2. Since period t3-t4, the consumers bought the amount of

staple-food at the maximum price-limit when market-operation done, and the remain one bought at selling-price. The total benefit for consumers is expressed as:

)} ) ( ( { costIM Total FM cost Total 2 1 2 1 4 3 * 2 1 2 1 2 1 * 4 1 w 4 1 c 4 1 t OR ct Max

w c t

OR ct d ct s wct w c d ct t s wct d ct s wct Q P Q q p q p q p C TB       



     

   (5)

iii). wholesalers side

Total profit of wholesalers will be decrease when market operation done due to market-price intervention. Total profit is calculated from total revenue less total cost (procurement, distribution and inventory cost) between IM and FM. Total revenue for wholesaler is the multiplication of total supply to consumer at the selling-price in FM. Furthermore in IM, total sales is calculated by total consumer’s demand less amount of buffer stocks when market-operation done; than total revenue is obtained as the selling-price multiplied by total sales. Both in FM and IM, total procurement cost is obtained from the amount of staple-food bought from the producer at selling-price; total distribution cost is obtained as the distribution cost per unit of item multiplied by total demand of staple-food from the consumers; and total inventory cost is obtained as a holding cost per unit in stock per unit of time multiplied by total of average inventory in a year. The total cost for wholesalers can be written as:

} ) ( 4 ) ( ) ( ) ( { } 4 { IM profit total -FM profit total 2 1 4 1 2 1 2 1 4 1 2 1 2 1 2 1 * 2 1 2 1 4 1 * 2 1 4 1 2 1 4 1 2 1 2 1 2 1 4 1 w 4 1 c 4 1 t

 

  

 

  

                                 

c t w p

OP pt a wt t h OR ct d ct d p w t

OP pt s pt p pwt w c t

OR ct d ct s wct a wt w t h d t d ct d s pt w p t

s pwt d ct s wct q q c Q q c Q q p Q q p q c q c q p q p W TC (6)

iv). government side

Total intervention cost is obtained as total cost less total revenue. Total cost consists of procurement cost, distribution cost and inventory cost. Total revenue is obtained from multiplication of amount of buffer stocks

that is released to consumer in time period

t

at the maximum price-limit. Total distribution cost is obtained as cost of market operation by the government multiplied by amount of buffer stocks should be released to market. Total inventory cost is obtained as a holding cost per unit in stock per unit of time multiplied by total of average the government’s inventory in a year. Total procurement cost is calculated from amount of staple-food bought by the government from the producer at the minimum price-limit and amount of staple-food bought by the government from import at a purchase cost per unit of the staple-food from import. Total intervention cost for the government is expressed as:

 



 



 

              2 1 4 3 4 1 2 1 4 3 4 3 2 1 2 1 4 IM revenue total -IM cost total c t OR ct Max OG t t h c t OR ct o t OI t i p t OP pt Min Q P Q c Q c Q c Q P G TC (7)

3.2. Objective function

We have developed a buffer stocks schemes for stabilizing price of the staple-food under volatility target (VT) for controlling the expectation of stakeholders. The buffer stocks model whose model has been described before must attain two targets:

- maximise the benefit of producers and consumers, and - minimise the total cost of wholesalers and government. The resulting objective function which includes the two objectives be finally expressed as follows:

) ,Q ,Q (P TC Min ) ,Q ,Q (P Max. TB OI t OR ct Max W,G OG t OP pt Min P,C and , (8) All constraints are classical like the market-price rules, the formulation of stakeholder’s expectation, the requirement of buffer stocks and market clearing of dynamic equilibrium. The model is subject to:

)]

(

)

[(

_wta ₁ s_pt _ctd

pwt

q

d

b

c

a

p













_ (9)

a wt s wct

q

g

b

e

a

p









(

)

(10)

)] ( ) [( 1 * OP pt d ct s pt a wt p

pwt q q q Q

d b

c a

p    

 

   (11)

)] ( ) [( * OP pt a wt s

wct q Q

g b

e a

p  

 





(12)

)

2 ,

1 (

,

)

,

(

* ₂



p

P



VT

t



VT

P Min

pwt (13)

)

1 (

c

irr

(6)

IV-14

)

1

2 d d

pwt

+ c

) x (

irn)-c

((p

VT





₍₁₅₎

) 4 , 3 ( , 4 ) , * (

3 VT t

Max P s wct p VT (16) ) + 1 )( (

3 c_p irr

p pwt p

VT   (17)

) + 1 )( (

4 c_a irs

p pwt p

VT   (18)



               2 1 4 3 2 1 4 3 2 1 2 1 2 1 2 1 2 1 4 1 1 c t d ct p t OR ct p t OP pt p t s pt w t a wt q Q Q q q (19)

)

2 ,

1 (

,

0

2 1













Q

t

Q

p OP pt OG t (20)

)

4 ,

3 (

,

0

2 1















Q

t

Q

_tOI

c OR ct OG t (21)

)

2 ,

1 (

,

2 1 2 1 2 1 2 1











   

t

q

Q

q

c d ct p OP pt w a wt p s pt (22)

)

4 ,

3 (

,

2 1 2 1 2 1









  

t

q

Q

q

c d ct c OR ct w a wt (23)

T

t

Q

P

Min

,

Max

,

OP_pt

,

_ctOR

,

_tOI

,

_tOG



0 ,



(24) Objective function (8) corresponds to function of multi-objectives in equation (4) until (7), aims to maximize the benefit of both producers and consumers, and to minimize the total lossses or expenditure of wholesalers and government. In free-market, we proposed a market model with inventory to determine the purchasing-price and the selling-price, equations (9) and (10). In intervention-market, we modify a market model with inventory less the amount of staple-food bought by the government, equations (11) and (12). Where  denotes the stock-induced-price adjusment coefficient.

We introduce constraints (13), (14) and (15) to ensure that the price-equilibrium fulfilled the expectation of the producers and the wholesalers at price-support program. The producer’s expectation is protected from distortion of selling-price as impact of excess supply; and the wholesaler’s expectation is protected from purchasing-price that costly as the impact of price-floor regulated by the government. We have to ensure the expectation of the wholesalers and the consumers at price-stabilization program in each period by considering the constrains (16), (17) and (18). The wholesaler’s expectation is protected from fall of selling-price as impact of ceiling-price regulated by the government; and the consumer’s expectation is the availability of staple-food at rational selling-price for consumers. The government has to ensure

the market-intervention program could fulfill the demand in each period, constraint (19).

We have to ensure that the buffer stocks schemes are adequate to hold the market-intervention program in each period by considering the constrains (20) and (21). Finally, we have to ensure the supply of staple-food are adequate the demand in each period and to ensure that all decision variables cannot be negative by considering the constraints (22), (23) and (24).

4. SOLUTION METHODS AND ANALYSIS

The optimal solution can be obtained by solving the pre-emptive of the multi-objectives programming above. The methodology to solve the proposed problem is depicted in Figure 2.

Figure 2: Solution methods.

In order to illustrate the capabilities of the proposed-model, a numerical example has been studied. The problem consists of hypothetic-parameters for reflecting data of Indonesian sugar market. Let a = 32.0, b = 0.17, c = 167.0, d = 4.8, e = 0.1, g = 0.45,  = 0.1, ch = 2.0, cd = 2.0, cO = 4.0,

cp = 34.0, ci = 40.0, irr = 5.0, nrr = 10.0, srr = 25.0, in

appropriate units. Thus, the supply-demand parameters are shown in Table 3.

Table 3: Hypothetic-parameters

Period t0-t1 t1-t2 t2-t3 t3-t4 Total d

q

, c=1 26 25 24 25 100 d

q

, c=2 26 25 24 25 100 s

q

, p=1 34 56 - - 90

s pt

q

, p=2 34 56 - - 90

a wt

q

, w=1 24 - - - -

a wt

q

, w=2 24 - - - -

Determining the optimal configuration of duo-producers, duo market-buyers, and duo-consumers are difficult problem since a lot of factors and objectives must be taken into account when designing configuration. Therefore, we must seek the solution methods for the

First-stage, set initial targets and parameters: - forecast parameters from

historical data, - set initial targets of

volatility target, - obtain market price by

using Model Market with Inventory

Second-stage, solve the proposed model: - formulate mathematical

statements of objectives function,

- formulate all constraints of model solution, - input model equation

(7)

IV-15 problems above. First, we simplify the problems by

generating similar parameters of set of producers, wholesalers, and customers. This simplification is needed to spread out complexity. Furthermore, we processed on determining the 6 DVs by using parameters in Table 3. We processed on determining the decision variables by using GP-ILP software. Computational results are shown in Table 4.

Table 4: A computational of decision variables

Period t0-t1 t1-t2 t2-t3 t3-t4 Min

P

35.7 35.7 - -

Max

P

- - 45.61 45.61

OP pt

Q

21.6 21.6 - -

OI t

Q

- - 21.6 21.6

OR ct

Q

- - 21.6 21.6

OG t

Q

0 21.6 21.6 21.6

The proposed-model has estimated improving the selling-price producers-wholesalers and degrading the selling-price wholesalers-consumers. The mechanism of improving/degrading is explained by a market model with inventory. A comparative analysis of price-equilibrium between FM and IM is depicted in Table 5.

Table 5: Price-equilibrium analysis

t0-t1 t1-t2 t2-t3 t3-t4 t0-t1 p

pwt

p

40.04 36.54 33.54 - - p

pwt

p

* 40.04 36.74 35.80 - - s

wct

p

51.77 48.27 45.47 47.87 50.37 s

wct

p

* 51.77 48.47 47.53 45.61 48.11

The government conducts price support program through the procurement program from domestic-market at period t2, so that the market-price goes up. At the planting

season [t3-t4], the government conducts market-operation

through release buffer-stock, so that the market-price goes down. For a set of hypothetic-parameters given, it can be noted that each of total benefit for the producers and the consumers are 131.19 and 98.32 in appropriate units. Furthermore, total cost for the wholesalers and the government are 1344.05 and 733.97 in appropriate units.

5. CONCLUSION AND FUTURE WORK

We have presented a methodology to solve a problem of the staple-food distribution system, incorporating the configuration of duo-producers, duo market-buyers, and duo-consumers. The proposed-model has a significant effect to enhance the benefit for both the producers and the consumers under the minimum cost/losses for wholesalers and government. The revenue of

price stabilization is intended to induce an equivalent reduction in the fluctuations of total market revenue. Moreover, the producers get bigger benefit than the consumers do, and the wholesalers get bigger cost/losses than the government does. The proposed-model is developed based on the integration of optimization model (multi-objectives programming) and econometrics model (a price-equilibrium model with inventory).

The proposed model can be extended in several ways. There are many other factors as offering distribution system for the staple food that are affected on price stabilization policy. The future researches can identify the better government intervention policy for instant by using government-Wholesaler for guarantying sustainability of business and by considering optimal market share for government-Wholesaler.

ACKNOWLEDGMENT

This paper is an initial model of the project-research for stabilizing price of staple-food in Indonesia-Market. The previous results were presented at 20th National Conference of Australian Society for Operations Research (ASOR) and the 5th International Intelligent Logistics System (IILS) Conferences, September 27th-30th 2009, Gold Coast, AUSTRALIA. The authors have benefited from the comments and suggestions of the participants at the conference. Finally, the authors want to grateful the DGHE in HIBAH BERSAING Research Program 2009 (DIPA ITB, PN-1-13-2009) for the support to this research.

REFERENCES

Athanasioua, G., Karafyllisb, I., and Kotsiosa, S. (2008), Price stabilization using buffer stocks, Journal of Economic Dynamics and Control, 32, pp. 1212-1235.

Brennan, D. (2003), Price dynamics in the Bangladesh rice market: implications for public intervention, Agricultural Economics, 29, pp. 15–25.

Chopra, S. and Meindl, P. (2004), Supply Chain Management : Strategy, Planning, and Operations, 2nd Edition. Prentice Hall, New Jersey, USA.

Chavas, J.P., Cox, T. L., and Jesse, E. (1998), Spatial allocation and the shadow pricing of product characteristics, Agricultural Economics,18 (1), pp. 1-19.

Coulson, N.E., Laing, D. and Wang, P. (2001), Spatial Mismatch in Search Equilibrium. Journal of Labor Economics, 19 (4), pp. 949-972.

Edwards, R. and Hallwood, C.P. (1980), The Determination of Optimum Buffer Stock Intervention Rules. The Quarterly Journal of Economics, 0033-5533/80/0094, pp. 151-166.

(8)

IV-16 Graves, C.S. (1999), A Single-Item Inventory Model

for a Non Stasionary Demand Process. Manufacturing & Service Operation Management, 1(1), pp. 50-61.

Guder, F. (1988). An Iterative LP Algorithm for Quadratic Spatial Equilibria. The Journal of the Operational Research Society, 39(12), pp. 1147 -1154.

Guilléna, G., Melea, F.D., Bagajewiczb, M.J., Espuñaa, A., And Puigjanera, L. (2005), Multiobjective Supply Chain Design Under Uncertainty, Chemical Engineering Science, 60, pp. 1535 – 1553.

Harker, P. T. (1986). Alternative Models of Spatial Competition. Operations Research, 34(3), pp. 410-425

International Sugar Organization/ISO (2005), An International Survey of Sugar Crop Yields and Prices Paid for Sugar Cane and Beet. MECAS, Vol. 05.

Jha, S. and Srinivasan, P.V. (2001), Food inventory policies under liberalized trade, International Journal Production Economics, 71, pp. 21-29.

Labys, W.C. (1980), Survey of Latest Development-Commodity Price Stabilization models: A review and Appraisal, Journal of Policy Modeling, 2 (1), pp. 121-126. Lambert, D. M. and Cooper, C. M. (2000), Issues in Supply Chain Management, Industrial Marketing Management, 29, pp. 65–83.

Nguyen, D. T. (1980), Partial Price Stabilization and Export Earning Instability, Oxford Economic Papers, 32 (2), pp. 340-352.

Newbery, M.G. D., and Stiglitz, E. J. (1982), Optimal Commodity Stock-Piling Rules. Oxford Economic Papers, New Series. 34 (3), pp. 403-427.

Pompermayer, F.M, Florian, M., Leal, J.E. and Soares, A.C. (2007), A Spatial Price Equilibrium Model In The Oligopolistic Market for Oil Derivatives: An Application To The Brazilian Scenario, Pesquisa Operacional, 27(3), versão impressa, pp. 517-534.

Reiner, G. and Trcka, M. (2004), Customized Supply Chain Design: Problems And Alternatives For A Production Company In The Food Industry: A Simulation Based Analysis, International Journal Production Economics, 89, pp. 217–229.

Rossi-Hansberg, E. (2005). Spatial Theory of Trade. The American Economic Review, 95(5), pp. 1464-1491.

Smith, L. (1997), Price Stabilization, Liberalization, and Food Security Conflicts and Resolution?, Food Policy, (22), pp. 379-392.

Sutopo, W., Nur Bahagia, S., Cakravastia, A. and Arisamadhi, TMA. (2008), A Buffer Stocks Model to Stabilizing Price of Commodity under Limited Time of Supply and Continuous Consumption, Proceedings of APIEMS, pp. 321-329.

Sutopo, W., Nur Bahagia, S., Cakravastia, A. and Arisamadhi, TMA. (2009). A Buffer Stocks Model For Stabilizing Price With Considering The Expectation

Stakeholders In The Staple-Food Distribution System, Proceedings 20th ASOR and the 5th IILS Conferences, p.p.

101.1 – 101.10.

Tersine, R.J. (1994), Principle of Inventory Materials Management, Fourth Edition, Prentice-Hall International, Inc., New Jersey, USA.

Véricourt, F., Karaesmen, F. and Dallery, Y. (2002). Optimal Stock Allocation for a Capacitated Supply System. Management Science, 48(11), pp. 1.486-1.501.

Williams, J.C. and Wright, B.D. (2005), Storage and

Commodity Markets, Cambridge University Press,

Cambridge, UK.

AUTHOR BIOGRAPHIES

Wahyudi Sutopo is a lecturer in Department of Industrial Engineering, Faculty of Engineering, Sebelas Maret University. He obtained his Bachelor’s degree in Industrial Engineering from Bandung Institute of Technology in 1999 and Master’s degree in Management Science from University of Indonesia in 2004. He is candidate of Ph.D from Bandung Institute of Technology and his dissertation is at supply chain management area. His study is funded by BPPS (The Postgraduate Scholarship Program) from Directorate General of Higher Education (DGHE), Ministry of National Education Republic of Indonesia.

Senator Nur Bahagia is a Professor in the Department of Industrial Engineering, Bandung Institute of Technology. He obtained his Ph.D degree in Logistic System and Production Management from Universite d’Aix-Marseille III, France in 1985. His research interest is at logistic and supply chain development. He has published many papers in several national and international logistic system journals.

Andi Cakravastia is an Assistant Professor in Department of Industrial Engineering, Faculty of Industrial Technology, Bandung Institute of Technology, Indonesia. He received a Doctoral Degree from the Graduate School of Engineering at Hiroshima University, Japan in 2004. His teaching and research interests include supply chain management and applied operations research. He has published many papers in several national and international journals.

TMA Ari Samadhi is an Associate Professor in Department of Industrial Engineering, Faculty of Industrial Technology, Bandung Institute of Technology, Indonesia. He received a Doctoral Degree from University of New South Wales, Australia in 1996. His teaching and research interests is at Manufacturing Engineering. He has published many papers in several national and international journals.

(1)

IV-11

The previous models cannot reduce excessive fluctuations of supplier side that consist of amount, price and time simultaneously. Sutopo et al. (2008) have been developed a buffer stocks model for stabilizing price under 2 stakeholders with the decision variables that consist of quantity and price. Furthermore, Sutopo et al. (2009) develop a buffer stocks model for 3 stakeholders with the decision variables that consist of quantity, price, and time but the model limited for each entity has only one player. In this paper, we develop a buffer stocks model for stabilizing price in Duopoly-Like Market through extend model of Sutopo et al. (2009).

2. PROBLEM SETTINGS AND DESCRIPTION The relevant system illustrated the relationship among structural and functional aspects is shown in Figure 1. We assume those three components of supply-chain entities (duo-producers, duo-Wholesaler, and duo-consumers) and a regulator (government). The functional aspects consist of the producer-Wholesaler-customer relationship based on the free market mechanisms; and the producer-government-customer relationship based on the intervention of market mechanism.

Figure 1: Overview of system relevant.

(iii) the beginning of planting season (period t2-t3), and (iv)

and the end of plantting season (period t3-t4). It is assumed

that commodity cannot be replaced by substitution products but it is consumed continuously in a year.

Table 2: Resume of market assumstions

Period t0-t1 t1-t2 t2-t3 t3-t4 Production normal booming none none

Consumption stable stable stable stable

Availability sufficient surplus sufficient shortage

Price-FM normal/

lower

lowest price

normal/ higher

highest price Intervention support support stabilization stabilization

3. MATHEMATICAL FORMULATION

Sets and index

P

p



: set of producers,

W

w



: set of wholesalers,

C

(2)

IV-12 Parameters

c

: production cost for staple food per unit from producers (IDR/Kgs) ,

c

: distribution cost for staple food per unit from wholesalers (IDR/Kgs) ,

c

: operation cost for staple food per unit from government (IDR/Kgs) ,

c

: holding cost for buffer stocks per unit (IDR/Kgs) ,

c

: import cost for buffer stocks per unit IDR/Kgs) ,

s pt

q

: production of staple food from producer

p

in time period

t

(tons),

d ct

q

: demand of staple food from consumer

c

in time period

t

(tons),

a wt

q

: maximum availability of staple food from wholesaler

w

in time period

t

(tons),

g t

q

: amount of staple-food from government in the beginning period

t

(tons),

p pwt

p

: purchasing-price between producer

p

and wholesaler

w

in time period

t

at FM (IDR/Kgs),

p pwt

p

* : purchasing-price between producer

p

and wholesaler

w

in time period

t

at IM (IDR/Kgs),

s wct

p

: selling price between wholesaler

w

and

consumer

c

in time period

t

at FM (IDR/Kgs),

s wct

p

* : selling price between wholesaler

w

and consumer

c

in time period

t

at IM (IDR/Kgs),

irr

: percentage of internal rate of return,

nrr

: percentage of normal rate of return, and

srr

: percentage of speculative rate of return.

Decisions variables Min

P

: minimum price-limit for government to purchase staple food per unit from producer

p

(IDR/Kgs),

Max

P

: maximum price-limit for government to sell buffer stocks per unit for

consumer

c

(IDR/Kgs),

OP pt

Q

: amount of staple-food that is purchased by government from producer

p

in time period

t

(tons),

OI t

Q

: amount of staple-food that is imported by government in time period

t

(tons),

OR ct

Q

: amount of buffer stocks that is released to consumer

c

in time period

t

(tons),

OG t

Q

: amount of buffer stocks that is stored by government in time period

t

(tons). 3.1. Multi-objectives of stakeholders

prior to the realisation as parameters of each stakeholders and market-equilibrium. The second-stage decisions are made subject to restrictions imposed by second-stage problem.

First-stage, let consider the simple one-staple-food market model. It is only governed by production, demand, maximum availability of wholesaler, and its market-price in time period

t

. _{Based on partial market equilibrium theory} (a linear model), we translated the simple one-staple-food market model with the following:

c ct d

a

bp

q





(1)

p pt s

c

dp

q







(2)

a wt a

e

gp

q







(3)

Where (

a

,

c

,

e

) are constants; (

b

,

d

,

g

) are point price elasticity; then (

a

,

c

,

e

) and (

b

,

d

,

g

) should be mutually independent parameters.

i).producers side

Total benefit is obtained from total revenue less total production cost. Both in FM and IM, total production cost is obtain ed as production cost per unit multiplied by

production from producer

p

in time period

t

. Furthermore in FM, total revenue is calculated from

multiplication of production from producer

p





    

   

 

1 2

1 * 2

1 2

) )

( (

FM Revenue IM

Revenue

p w t

s pt p pwt OP pt s pt p pwt p t

OP pt Min

q p Q q p

Q P P

(4)

ii). consumers side

Total benefit is calculated from total difference of consumption cost between IM and FM. In FM, total consumption cost is expected from demand of staple food from consumer

c

in time period

t

multiplied by selling

(3)

IV-13

price. In IM, consumers will spending budget to fulfill total demand of consumer

c

at selling-price between consumer

c

in time period

t

and consumer

c

during period t1-t2. Since period t3-t4, the consumers bought the amount of

staple-food at the maximum price-limit when market-operation done, and the remain one bought at selling-price. The total benefit for consumers is expressed as:

)} ) ( ( { costIM Total FM cost Total 2 1 2 1 4 3 * 2 1 2 1 2 1 * 4 1 w 4 1 c 4 1 t OR ct Max

w c t

OR ct d ct s wct w c d ct t s wct d ct s wct Q P Q q p q p q p C TB       



     

   (5)

iii). wholesalers side

} ) ( 4 ) ( ) ( ) ( { } 4 { IM profit total -FM profit total 2 1 4 1 2 1 2 1 4 1 2 1 2 1 2 1 * 2 1 2 1 4 1 * 2 1 4 1 2 1 4 1 2 1 2 1 2 1 4 1 w 4 1 c 4 1 t

 

  

 

  

                                 

c t w p

OP pt a wt t h OR ct d ct d p w t

OP pt s pt p pwt w c t

OR ct d ct s wct a wt w t h d t d ct d s pt w p t

s pwt d ct s wct q q c Q q c Q q p Q q p q c q c q p q p W TC (6)

iv). government side

that is released to consumer in time period

t

 



 



 

3.2. Objective function

)]

(

)

[(

_wta ₁ s_pt _ctd p

pwt

q

d

b

c

a

p













_ (9)

a wt s wct

q

g

b

e

a

p









(

)

(10)

)] ( ) [( 1 * OP pt d ct s pt a wt p

pwt q q q Q

d b

c a

p    

 

   (11)

)] ( ) [( * OP pt a wt s

wct q Q

g b

e a

p  

 





(12)

)

2 ,

1 (

,

)

,

(

* ₂



p

P



VT

t



VT

P Min

pwt (13)

)

1 (

c

irr

(4)

IV-14

)

1

2 d d

pwt

+ c

) x (

irn)-c

((p

VT





₍₁₅₎

) 4 , 3 ( , 4 ) , * (

3 VT t

Max P s wct p

VT (16)

) + 1 )( (

3 c_p irr

p pwt p

VT   (17)

) + 1 )( (

4 c_a irs

p pwt p

VT   (18)



 

   

     

 



1 4

3 2

1 2

1 4

1 1

c t d ct

p t OR ct p t

OP pt p t

s pt w t

a wt

Q Q

q q

(19)

)

2 ,

1 (

,

0 











Q

t

Q

p OP pt OG

t (20)

)

4 ,

3 (

,

0 













Q

t

Q

_tOI

c OR ct OG

t (21)

)

2 ,

1 (

,

1 2











 

t

q

Q

q

c d ct p

OP pt w

a wt p

pt (22)

)

4 ,

3 (

,

1 2









 



t

q

Q

q

c d ct c

OR ct w

wt (23)

T

t

Q

P

Min

,

Max

,

OP_pt

,

_ctOR

,

_tOI

,

_tOG



0 ,



the market-intervention program could fulfill the demand in each period, constraint (19).

4. SOLUTION METHODS AND ANALYSIS

The optimal solution can be obtained by solving the pre-emptive of the multi-objectives programming above. The methodology to solve the proposed problem is depicted in Figure 2.

Figure 2: Solution methods.

cp = 34.0, ci = 40.0, irr = 5.0, nrr = 10.0, srr = 25.0, in

appropriate units. Thus, the supply-demand parameters are shown in Table 3.

Table 3: Hypothetic-parameters

Period t0-t1 t1-t2 t2-t3 t3-t4 Total d

q

, c=1 26 25 24 25 100

d ct

q

, c=2 26 25 24 25 100

s pt

q

, p=1 34 56 - - 90

s pt

q

, p=2 34 56 - - 90

a wt

q

, w=1 24 - - - -

a wt

q

, w=2 24 - - - -

First-stage, set initial targets and parameters:

- forecast parameters from historical data,

- set initial targets of volatility target,

- obtain market price by using Model Market with Inventory

Second-stage, solve the proposed model:

- formulate mathematical statements of objectives function,

- formulate all constraints of model solution,

- input model equation into GP-ILP software.

(5)

IV-15

problems above. First, we simplify the problems by generating similar parameters of set of producers, wholesalers, and customers. This simplification is needed to spread out complexity. Furthermore, we processed on determining the 6 DVs by using parameters in Table 3. We processed on determining the decision variables by using GP-ILP software. Computational results are shown in Table 4.

Table 4: A computational of decision variables

Period t0-t1 t1-t2 t2-t3 t3-t4

Min

P

35.7 35.7 - -

Max

P

- - 45.61 45.61

OP pt

Q

21.6 21.6 - -

OI t

Q

- - 21.6 21.6

OR ct

Q

- - 21.6 21.6

OG t

Q

0 21.6 21.6 21.6

Table 5: Price-equilibrium analysis

t0-t1 t1-t2 t2-t3 t3-t4 t0-t1 p

pwt

p

40.04 36.54 33.54 - -

p pwt

p

* 40.04 36.74 35.80 - -

s wct

p

51.77 48.27 45.47 47.87 50.37

s wct

p

* 51.77 48.47 47.53 45.61 48.11

The government conducts price support program through the procurement program from domestic-market at period t2, so that the market-price goes up. At the planting

season [t3-t4], the government conducts market-operation

5. CONCLUSION AND FUTURE WORK

ACKNOWLEDGMENT

REFERENCES

Athanasioua, G., Karafyllisb, I., and Kotsiosa, S. (2008), Price stabilization using buffer stocks, Journal of Economic Dynamics and Control, 32, pp. 1212-1235.

Brennan, D. (2003), Price dynamics in the Bangladesh rice market: implications for public intervention, Agricultural Economics, 29, pp. 15–25.

Chopra, S. and Meindl, P. (2004), Supply Chain Management : Strategy, Planning, and Operations, 2nd Edition. Prentice Hall, New Jersey, USA.

Chavas, J.P., Cox, T. L., and Jesse, E. (1998), Spatial allocation and the shadow pricing of product characteristics,

Agricultural Economics,18 (1), pp. 1-19.

Coulson, N.E., Laing, D. and Wang, P. (2001), Spatial Mismatch in Search Equilibrium. Journal of Labor Economics, 19 (4), pp. 949-972.

Edwards, R. and Hallwood, C.P. (1980), The Determination of Optimum Buffer Stock Intervention Rules.

The Quarterly Journal of Economics, 0033-5533/80/0094, pp. 151-166.

(6)

IV-16

Graves, C.S. (1999), A Single-Item Inventory Model for a Non Stasionary Demand Process. Manufacturing & Service Operation Management, 1(1), pp. 50-61.

Guder, F. (1988). An Iterative LP Algorithm for Quadratic Spatial Equilibria. The Journal of the Operational Research Society, 39(12), pp. 1147 -1154.

Guilléna, G., Melea, F.D., Bagajewiczb, M.J., Espuñaa, A., And Puigjanera, L. (2005), Multiobjective Supply Chain Design Under Uncertainty, Chemical Engineering Science, 60, pp. 1535 – 1553.

Harker, P. T. (1986). Alternative Models of Spatial Competition. Operations Research, 34(3), pp. 410-425

International Sugar Organization/ISO (2005), An International Survey of Sugar Crop Yields and Prices Paid for Sugar Cane and Beet. MECAS, Vol. 05.

Jha, S. and Srinivasan, P.V. (2001), Food inventory policies under liberalized trade, International Journal Production Economics, 71, pp. 21-29.

Supply Chain Management, Industrial Marketing

Management, 29, pp. 65–83.

Nguyen, D. T. (1980), Partial Price Stabilization and Export Earning Instability, Oxford Economic Papers, 32 (2), pp. 340-352.

Newbery, M.G. D., and Stiglitz, E. J. (1982), Optimal Commodity Stock-Piling Rules. Oxford Economic Papers,

New Series. 34 (3), pp. 403-427.

Rossi-Hansberg, E. (2005). Spatial Theory of Trade. The American Economic Review, 95(5), pp. 1464-1491.

Smith, L. (1997), Price Stabilization, Liberalization, and Food Security Conflicts and Resolution?, Food Policy,

(22), pp. 379-392.

APIEMS, pp. 321-329.

Sutopo, W., Nur Bahagia, S., Cakravastia, A. and Arisamadhi, TMA. (2009). A Buffer Stocks Model For Stabilizing Price With Considering The Expectation

Stakeholders In The Staple-Food Distribution System, Proceedings 20th ASOR and the 5th IILS Conferences, p.p.

101.1 – 101.10.

Tersine, R.J. (1994), Principle of Inventory Materials Management, Fourth Edition, Prentice-Hall International, Inc., New Jersey, USA.

Véricourt, F., Karaesmen, F. and Dallery, Y. (2002). Optimal Stock Allocation for a Capacitated Supply System.

Management Science, 48(11), pp. 1.486-1.501.

Williams, J.C. and Wright, B.D. (2005), Storage and Commodity Markets, Cambridge University Press, Cambridge, UK.

AUTHOR BIOGRAPHIES