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18th European Symposium on Computer Aided Process Engineering ESCAPE 18Bertrand Braunschweig and Xavier Joulia (Editors)

2008 Elsevier B.V./Ltd. All rights reserved.

Enterprise-wide Optimization under Tight SupplyContracts and Purchase Agreements

Flavio Manenti and Davide Manca

CMIC Department, Politecnico di Milano, P.zza Leonardo da Vinci, 32

20133 MILANO ITALY davide.manca@polimi.it

Abstract

The manuscript presents and discusses the supply chain optimization of an industrial

enterprise characterized by a decentralized (multi-site) production structure. The studyconcerns the enterprise-wide optimization (comprising production sites, interconnection

pipelines and a distribution network) and solves the multifaceted problem of monthly

production planning subject to legal limitations imposed on the mathematical model bysupply contracts and purchasing agreements, in addition to classical constraints. Take-or-pay clauses and trade agreements, as well as specific services defined by binding

contracts, signed with the National Electric Energy Supplier (NEES), are modeled andimplemented as (in)equality constraints.

Keywords: Enterprise-wide optimization; Supply contracts; Trade agreements; Sales

and purchase clauses; MILP.

1. Introduction

The increasing market competition is pressing enterprises to consider carefully product

prices, raw material costs, and economic market fluctuations, while satisfying theconsumers demand as well as improving the net profit margin of the company [1, 2].

These multifaceted constraints are pushing the enterprises towards real-time market-driven processes and just-in-time production, which are essential goals for industrial

activities characterized by large working capitals. This is the case of gas and oil plantsand oil refineries that require considerable storage volumes for raw materials,

intermediates, and end-products [3-6]. Also, those processes that involve smaller butexpensive inventories, such as cryogenic tanks and subcooled or gas-liquefied storages,

deal with the global supply chain objectives [7]. Moreover, some particular localmarkets involve either enterprises or production sites that are constrained by supply

contracts and/or commercial agreements [8]. Usually, these economical and politicalconstraints comprise complex limitations, both non-smooth and nonlinear, and specific

economic penalties for each disregarded clause. Uncertainties must be taken into

account and modeled in the decision-making process of the enterprise operationalplanning, where a moving horizon structure can be implemented to manage them [9-

12]. This uncertainties concern both the costumers demand fluctuations and process

shutdowns for either programmed or unexpected maintenances. Consequently, bothmulti-site operability and process flexibility appear strongly limited. Trying to

transform the unexpected demand peaks and other market fluctuations into operativemargins is even more difficult. In this perspective, the supply chain approach can be

regarded as a useful tool, also in the unusual field of preliminary/feasibility studies ofsingle- and multi-site enterprises to improve the overall conceptual design. The

associated mixed-integer linear programming (MILP) problem is based on a

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2 F. Manenti and D. Manca

mathematical model discussed in a previous work [12] and consists of a medium-scalemodel of about one thousand decisional variables either integer or Boolean and about

ten thousands real variables.Paragraph 2 discusses common business strategies that lead enterprises to sign tradeagreements. The detailed MILP model of some binding clauses of supply contracts as

well as sale and purchase agreements is presented in Paragraph 3. Finally, preliminaryresults are discussed in Paragraph 4.

2. Strategic contracts and agreements

Large-scale enterprises are used to reach trade agreements for supplies, subcontracts,

sales, and purchases, to ensure a sufficient amount of raw materials, a lower price of

power energy, and a safe profit margin for incoming years. In this case, the enterprisecan sell a future production capacity, or in other terms, a certain amount of end-products

not yet produced, by offering a discount on the original price. The same approach isfrequently adopted to sign trade agreements with raw material suppliers and the

National Electric Energy Supplier (NEES). Actually, it is well known that the electricalenergy demand has an oscillating behavior and the national power supply trend is the

convolution of short-, medium-, and long-frequency fluctuations, strictly related tocommon sources reported in Table 1.

Table 1: Uncertainty frequency, period, and fluctuation source.

Frequency Period Fluctuation source

Very short Minutes Noise concerning market volatilityShort Daily High electric energy demand during the day and low night-

time demandMedium Weekly Low energy consumption during week-ends and holidays

Medium-long Yearly Seasonal (winter/summer) fluctuations in the national energy

demand

As an example, the mean value in 12 hours of the Italian power supply demand variesbetween 41 GW day-time and 28 GW night-time. The seasonal gap for the daily

national-demand-peak is in the order of 10 GW (data of September 2007. Source:TERNA S.p.A., www.terna.it). In this context, the NEES may sometimes need to

interrupt power supply to some industrial and energy-intensive clients, if the end-userdemand presents any instantaneous market peaks. This is due to the real-time demand

prediction methodology adopted by NEES. Actually, NEES continuously monitors thenational power demand and formulates both short- and long-term estimations related to

the future national demand. The predicted trajectories are re-estimated every 15minutes. Again, this can be the situation of most European countries across midday in

summer. Therefore, some primary industries can offer a particular service that gives the

NEES the opportunity to temporarily suspend the power supply. This service is calledBreaking-Off clause (see Paragraph 3 for more details). Other supply contracts, not

considered here for space reasons, concern supply and/or production limitations: e.g. a

maximum constraint about the monthly energy consumption or, occasionally, aminimum guaranteed production. On the other hand, to make the optimization problem

even more constrained and stiff, the manufacturing industry that has to fulfill therequest of the final customer (see also Figure 1), is in the habit of signing ad hoc

purchase agreements together with the upstream energy-intensive enterprises, whichsupply chemicals and primary products.

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Enterprise-wide Optimization under Tight Supply Contracts & Purchase Agreements 3

National ElectricEnergy Supplier

Primary Industry(Energy-intensive)

ManufacturingProcesses

SUPPLY

CONTRACTS

PURCHASE

AGREEMENTS

Final Users(Market Demand)

USERS

SATISFACTION

Figure 1: Qualitative scheme for the horizontal hierarchy in the energy-intensive enterprise-wideoptimization constrained by binding contracts.

At the same time, primary industries want to ensure that the demand from final factories

is enough to absorb the large portion of the future production planning. In thisperspective, several contracts fix economic penalties for lacking supplies, whereas some

commercial strategies define a monthly or yearly minimum supply quantity of primary

products that is defined a priori and must be paid even if future demand will be lower.In this second case, a sales price discount is usually granted. These sales and purchasing

agreements are called Take or Pay contracts.

3. MILP modeling of binding clauses

3.1. The Breaking-Off option

The Breaking-Off clause is a service that some primary industries offer to the NEES.

In fact, the NEES asks the opportunity to temporarily interrupt the power supply at anytime with either a short warning or without any advise. In exchange to the power supply

Breaking-Off offered by the primary industries, NEES recognizes a relatively largediscount in the monthly energetic bill of the single production site (in the order of 100-

500 k). Actually, the discount is granted only if particular conditions are respected: forinstance, by guaranteeing a minimum monthly consumption of electric energy, called

Breaking-Off Threshold. The system is even more complex since every production

site signs a customized supply contract with NEES, by involving costs and conditionsthat significantly influence the enterprise-wide production planning and the end-productdistribution. In the following equations, BreakingOffis the Boolean variable describing

the possibility to achieve the price cut in the overall electric energy cost. The energyconsumption on the discretized time horizon (NP) is evaluated as follows:

( )1

_ _ _NP

t

t

ee BreakingOff ee ProcessUnits ee Utilities=

= + (1)

where tis the single sampling time and prefix ee_means electric energy consumption.

Therefore, as defined by contract, the electrical consumption does account for neitherthe programmed and failure maintenance periods h_maint(equation 2), nor for possible

Breaking-Off shut-downs. BreakingOff_eff is the effective monthly powerconsumption of each single site of primary industries:

__ _

( _ / _ )

ee BreakingOff BreakingOff eff h period

NP h maint h period

=

(2)

This parameter is multiplied by a minimum tolerance factor SelectedTolerance and

compared to the consumption limitP_BreakingOff, which is assigned a priori:

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4 F. Manenti and D. Manca

__

_

BreakingOff effRatio BreakingOff

SelectedTolerance P BreakingOff =

(3)

The consumption limit is similar to the Breaking-Off Threshold. Note that the

discount is granted only ifRatio_BreakingOffis not lower than one:

_BreakingOff Ratio BreakingOff (4)

Inequality constraint (4) is the necessary condition to achieve the Breaking-Off

discount, but it is not a sufficient condition. Actually, it may sometimes happen thatother scenarios with reduced productions (and not contemplating any discount) are

economically more attractive on the specific time horizon. In this case, the Booleanvariable BreakingOff is kept null even if the Ratio_BreakingOff value is greater than

one.

3.2. Take or Pay agreementsTake or Pay clauses, i.e. sale and purchase clauses, are generally offered tomanufacturing societies by primary industries. Aiming at a reduction in the primary

product price, the manufacturing industry assures to buy a minimum amount of goodsfrom the primary industry for a specified period and, in case of reduced purchase,

guarantees the minimum established payment. In this case, the solution of a nestedsupply chain problem must be accounted for, since the business-wide optimization can

evaluate the optimal goods amount for each manufacturing process, whereas theenterprise-wide algorithm investigates the best Take or Pay proposal. The binary

variableX_TOPis defined as follows:

( )1,_

0,t

if ManufacturingSample < MinimumLimitX TOP

otherwise

(5)

It assumes a value of 1 if the goods amount is smaller than the assigned minimum one.

By considering the following generic objective function:

1

( )NP

t t

t

PROFIT REVENUES COSTS=

= (6)

the enterprise-wide revenues, simplified for a single manufacturing site (equation 7), areequal to the minimum negotiated payment if the manufacturing client requires a reduced

amount of goods, otherwise effective supplies are considered in the evaluation of the

overall profit.

]

1 1

( (1 _ )

_ _

NP NPD

y t t

t y

t

REVENUES SalesPrice ManufNeeds X TOP

Limit TOP X TOP

= =

=

+

(7)

where y index represents the commodities produced by primary industries.

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Enterprise-wide Optimization under Tight Supply Contracts & Purchase Agreements 5

4. Preliminary results

Due to space limitations, it is possible to show only a few trends related to an industrial

case in study, which has been already proposed in the literature [6]. It deals with thefield of air separation and industrial gases production and distribution. Figure 2 shows

the cumulative cost trend for the power consumption of an air separation unit. Thediagram presents a linear trend, characterized by negligible oscillations, except for the

last day of the month, where a discontinuity can be observed. It corresponds to the

discount applied by the NEES. Figure 3 shows the final product storage. Note thatduring the week-end the final storage reaches the highest levels. It is especially due to

two reasons: firstly, the demand is generally low or null and the whole production is

stocked. Secondly, the electric energy has a reduced price and the production is pushedto the maximum limit allowed by the air separation unit.

However, since storages are considered as costs, a minimum level at the end of the timehorizon is expected. Conversely, an overproduction can be noted during the last two

days, apparently against the basic principles of supply chain management. Actually, bymeans of the final overproduction, the Breaking-Off Threshold is reached at the 29 th

day of the month, with a consequent large discount in the energetic bill.

5. Conclusions

The horizontal hierarchy (as reported in Figure 1) in the supply chain management is a

multifaceted problem. This manuscript investigated an aspect that has not yet got largeattention by the academic world, but it has a strong weight in the long-term enterprise

strategies. The paper illustrated also how it is possible to implement specific contractclauses in a MILP model and how these clauses can systematically modify the

enterprise operational planning.

0

0,2

0,4

0,6

0,8

1

1,2

0 7 14 21 28

Cumulativecostofpower

consumption[M

]

Time [days]

Figure 2: Monthly energetic costs.

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6 F. Manenti and D. Manca

0

50

100

150

200

250

300

0 7 14 21 28

Volume[1000xNm3]

Time [days]

0

20

40

60

80

Figure 3: Storage volume (top) and market demand (bottom) of the final product.

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