Tedarik zincirinde işbirlikçi oyun kuramı kullanılarak adil kâr paylaşımının yapılması ve enerji sektöründe uygulamalar
Fair profit sharing using cooperative game theory in a supply chain and energy market applications
Yazar: HÜSEYİN KUTAY TİNÇ
Danışman: PROF. DR. MEHMET NAHİT SERARSLAN ; PROF. DR. ELMKHAN MAHMUDOV
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Endüstri Mühendisliği Ana Bilim Dalı / Endüstri Mühendisliği Bilim Dalı
Derece: Doktora, 2018
Konu: Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering ; Enerji = Energy

Özet:
Yirmi birinci yüzyılda rekabetçi şirketler için maliyetleri azaltmak en önemli başarı kriterlerinden biri olarak ortaya çıkmıştır. Bunun en büyük nedeni küreselleşen piyasaların satış fiyatları üzerinde ciddi bir düşüşe neden olmasıdır. Benzer kalitede ve birbirinin muadili olan ürünler arasında fiyat müşteri tercihini belirleyen en kuvvetli unsur haline gelmiştir. Bu da rekabetin yüksek olduğu ürünlerde fiyatların ucuzlamasına ve dolayısıyla maliyetlerin azaltılmasının en önemli kâr odaklarından biri olmasına neden olmuştur.
Maliyetlerin azaltılması için şirketler bir yandan gereksiz faaliyetlerini azaltırken bir yandan da hammadde veya kaynak ihtiyaçlarını daha ucuza karşılamanın yollarını ararlar. Gereksiz faaliyetlerin azaltılması şirketin kendi uzmanlık alanında yoğunlaşıp geri kalan pek çok hizmeti dışarıdan alması ile, hammadde ve kaynak maliyetlerinin azaltılması ise planlı kaynak yönetimi veya daha ucuz hammadde tedariği ile gerçekleşir.
Bu tez çalışmasında daha ucuz hammadde tedariği için hammadde satıcısı ile alıcısı arasında kurulacak bir işbirlikçi oyun kuramı uygulaması ile her iki taraf için de kârın nasıl arttırılabileceği incelenmiştir. Tezin ilk aşamalarında bu modelin kurulması için gereken alt yapıdan bahsedilmiş ve modelin bir uygulaması olarak seçilen enerji sektörü ile ilgili genel bilgiler verilmiştir. Bu kısımlarda oyun kuramı ve tedarik zinciri kavramlarının yanısıra ek ödeme kavramı da tanıtılmıştır.
Ek ödeme kavramı tanıtılırken modelde ve uygulamalarda kullanılacak olan yöntemden de bahsedilmiştir. Adil kâr paylaşımında ise, ek ödeme ile arttırılan toplam kârın iki taraf arasında nasıl paylaşılabileceği tartışılmıştır. Ek ödeme ile ortaya çıkan kârın paylaştırılmasının ek ödemesiz kullanılan Nash ve Kalai-Smorodinsky pazarlık çözümleri ile karşılaştırması yapılmıştır. Ayrıca ek ödemelerin paylaşımı için sözleşmelerin nasıl tasarlanması gerektiği anlatılmış ve özel sözleşme gerektiren bir durum örneği verilmiştir.
Daha sonraki aşamalarda sırasıyla, kâr modeli ve elektrik piyasasında uygulamalar anlatılmıştır.
Kâr modeli bölümünde hammadde satıcısı ve alıcısının kâr modelleri kurulmuştur. Hem Stackelberg hem de işbirliği modeli için çözümler verildikten sonra ek ödemeli model için çözüm yapılmıştır. İşbirliği modelinde analitik çözüm olmadığı gibi ek ödemeli modelde de analitik çözüm bulunamamıştır. Her iki modelin de sayısal çözümlerinin mevcut olduğu görülmüştür.
Elektrik piyasasında uygulama bölümünde iki farklı piyasa oyuncusu için farklı ek ödemeli işbirliği modeli incelenmiştir. İlk modelde bir doğalgaz santrali ile doğalgaz satıcısı arasındaki fiyat anlaşmasının her iki tarafın kârına etkisi gösterilmiştir. 
Doğalgaz santrallerinin üretim maliyetlerinin düşmesi, piyasaya sattıkları elektriğin daha düşük fiyattan satılması anlamına gelmektedir. Bu da piyasa takas fiyatını düşürecektir. Piyasa takas fiyatındaki bu düşüşün ne kadar olabileceği başka bir çalışma ile incelenebilir.
İkinci modelde ise Pazar payını büyütmek isteyen bir küçük girişimci perakende satış şirketinin büyük bir toptan satış şirketi ile imzalayacağı ikili anlaşmada ek ödeme kullanarak satış miktarını ve dolayısıyla kârını, nasıl arttırabileceği gösterilmiştir. Artan kârdan toptan satış şirketine yapılacak ek ödeme için birer alt ve üst sınır belirlenmiştir.
Bu sınırlar dahilinde yapılacak olan ikili anlaşma ile piyasaya daha ucuz elektrik sunma fırsatı yaratılmaktadır. Bu da son kullanıcının daha ucuza elektrik alabilmesi anlamına gelmektedir.

Abstract:
In the twentyfirst century, one of the most critical factors of success for competitive companies has become the ability to reduce costs. This is in part due to the globalization of markets and its impact on sales prices. Customers are prefering cheaper products when similar quality items that can be used as each others replacement are on the same market. This preference has led to a drop on prices for competitive markets with high supply and the rise of importance of cost reductions to increase profits.
This cost reduction fight was fought on two fronts. First of all, companies started getting rid of their unnecassary processes and activities to reduce costs. Reducing unnecessary activities has resulted in more focused companies that outsource its non-value added needs. Second of all, finding cheaper resources and raw materials has become an important necessity. Efficient resource planning led to cheaper or better use of resources and raw materials. All of which has helped companies reduce their costs and increase their profits.
In this study, supply chains are analyzed using cooperative game theory with side payments to maximize their total profit and find a way to share that profit in a just manner. This work entails finding the total profit by an analytical process and formulating profit sharing systems and comparing them to well known bargaining methods like Nash Bargaining or Kalai-Smorodinsky Bargaining solutions. 
Game theory encompasses any decision making process with more than one decision maker and it seeks to find equilibrium states and bargaining solutions to better understand the decision making system, namely the game. 
Cooperative game theory is taken into account in the bargaining side of the coin. Players usually have their own strategies for the game. This strategy, while ensures a personal best regardless of other players' choices, usually can yield low utility values which might mean low profits for companies. Using cooperative game theory, in games where it can be applied, players might find better solutions which yield more utility to one or more sides. 
Side payments are utility transfers between players that come into play during strategy selection and players have an inkling of what they can attain via different strategies. Side payments can be as simple as direct profit transfer between parties of a supply chain or they can take the forms of buyback options or price discounts. Side payments create new strategies for supply chain members.
Just as every production company needs to either mine or harvest raw materials themselves or buy raw materials from a seller, each seller needs a buyer that can use their raw material to produce and sell goods. This type of interaction creates a supply chain between a buyer and a seller where materials, money and information can flow on both sides.
In this study, cooperative game theory is supported with side payments for tradeable utilities, which results in players giving up some of their profits as an incentive for other players to follow a certain strategy that increases the overall profit of the supply chain although it is possibly worse for them utility-wise. The values that the side payments can take are analyzed and some bargaining solutions are presented.
To better understand the solutions, the difference between the total profit that total profit maximization using cooperative game theory with side payments achieve and the total profit from the original strategies is calculated and shared between players as an extra profit added to their original utilities. Those solutions are:
Equal Shares, which shares the extra profit equally between any number of companies and hence adding the same amount of extra profit to their own original profit values. This is the most basic sharing method and is usually shunned by the stronger sides in the supply chain.
Proportional Shares, which shares the extra profit in proportion to their original utilities between the players. This is the suggested solution for most situations and is useful to keep every member of the supply chain satisfied with their extra profits gained from the bargaining process.
Dominational Shares, which shares the profit among the players as a ratio of their dominance of the supply chain, which can be found in any number of ways including their Shapley values. This solution is useful to appease the stronger side in the supply chain which in turn helps with the chain's longevity.
Investment Oriented Shares, which shares the profit in favor of the company that needs to grow to make the supply chain more effective and more profitable. This solution focuses on the long run and any agreement between companies must be binding for the long run reflect that goal.
The cooperative game this study focuses on is between a buyer and a seller where both sides have two decision variables that affect their profits. For the buyer, who manufactures and sells a good, the variables are the price of the good and the marketing expenditure they are willing to make per unit of good. For the seller the the variables are the price of the raw material and the lot size. These four variables can be used to maximize each player's own profit. Other parameters that are used in the formulation include scaling constants for both the demand function and production function, price and marketing expenditure elasticity of the demand function, seller's production and setup costs, buyer's ordering cost, inventory cost, seller's production rate and demand rate. The optimal values of the four variables for the noncooperative game can be found using first order conditions and eliminating other variable from the derivatives, in which case each variable will become a function of the other two player's variables. 
The cooperative game that we want to use will use the total profit's first order conditions. With four variables in the first order conditions it will not be possible to solve derivatives for any one variable analytically, though numerical solutions will be obvious. This is also the same for similar cases of cooperative games in a buyer seller supply chain.
The rest of the study focuses on two applications for the Turkish Energy Market. The first game has a natural gas seller and a natural gas power plant as players and the second game has an energy wholesale company and an energy retail company as players.
In the first game the natural gas seller can decide on the price of the natural gas and the power plant can decide the amount of natural gas in standard cubic meters it will buy for a year. Two types of natural gas power plants are analyzed in the game, turbine and natural gas engine.
As natural gas power plants are the most expensive electricity generation option in Turkey, the discount on natural gas prices affect the strategy and amount bought for the power plant drastically, resulting in huge profit gains for the power plant that can later be transferred to the natural gas seller as a side payment. These gains are more obvious in the natural gas engine type power plants as their generation costs are much higher than turbine type power plants.
In a competitive market this strategy would result in a drop in market clearing prices as high cost natural gas power plants would reduce their prices to be able to generate and sell when their production costs were lowered. Independent gas traders would compete with each other to sell more gas than others and to secure volume rights or meet their quotas. This strategy would both give natural gas sellers an advantage over their competitions and lower the price that users would have to pay for electricity as the market clearing prices dropped. The amount of reduction in market clearing prices caused by this strategy can be the subject of another study.
In the second game, a startup energy retail company's bilateral contract with an energy wholesale company is analyzed. The aim of this contract is to help the energy retail company to grow without the need for huge investments and increase its monthly total profits.
Startup energy retail companies in Turkey are fledgling companies that are not backed by large corporations. Although counter examples of this statement exist, most energy retail companies are left to fend for themselves in an ever increasingly competitive market. Even though the number of eligible customers raise yearly, energy retail companies with no financial backing cannot hope to cultivate a big enough portfolio to compete with their regional counterparts, distribution company owned energy retail companies and other corporate backed competitors.
This difference in size becomes apparent when a bidding war for a particularly good customer starts. Larger companies can lower their price as much as they want just to keep the customer in their portfolio without regards for the loss they might incur, but startup energy retail companies have to take into account their immediate profit and low prices might mean they can go bankrupt in a very short time. Instances of this situation has already been observed during 2016 and 2017 where many energy retail companies have failed to pay for the energy they have bought and their portfolio was taken away from them.
The problem with portfolio growth when an energy company buys electricity from the day ahead market is the collateral they have to keep in the trade bank. This collateral, when added to the daily energy cost and the effect of late bill returns, creates a need for capital that might overwhelm small companies. To overcome this immediate need for capital, a bilateral agreement with a larger energy wholesale company can be used.
This bilateral agreement must ensure that the energy wholesale company cannot incur a loss from the trade, hence the trade price for the bilateral contract should always be above the hourly market clearing price. This condition can be satisfied with a lower limit that will be set for the side payment which will be added to the market clearing price. This lower limit will be a function of the minimum attractive rate of return for both any money used to buy energy by the energy wholesale company and any collateral it has to keep in trade bank for the trade.
The upper limit for the side payment will be the total profit the energy retail company will earn by selling the energy it buys in the bilateral trade to its customers. This upper limit will be affected by various market costs like renewable taxes or imbalance costs.
Any value between these two limits can be agreed on by the energy companies to realize this trade and as the energy retail company grows, profits for both sides would climb.
As this strategy would increase competitiveness, retail prices across other retailers would tend to drop, resulting in better prices for end users.  So this strategy can claim to be useful for the welfare of the public.