A multi-period Stackelberg game is adopted to study a green procurement relationship between manufacturers and suppliers in a supply chain. The manufacturers are considered as leaders, while the suppliers are modelled as followers in this Stackelberg game. Accordingly, a mixed binary linear bi-level programming model is developed to elaborate the game in consideration of carbon tax scheme. The upper level (the leader) aims at selecting a proper number of suitable suppliers to provide heterogeneous raw materials at the lowest operational cost. The objective of the lower level (the follower) is to find optimal purchasing quantities of raw materials. In addition, two lemmas are introduced to transform the mixed linear bi-level programming model into a single level linear programming model. The numerical example illustrates that: (1) the manufacturer prefers to adopt the multiple sourcing strategy due to the flexibility; (2) keeping stable supplies and large order volumes could effectively reduce carbon emissions for the suppliers and make the supply chain greener.
Original scientific paper High uncertainty and variability of acquirable cores can lead to some difficulties of operations management in the remanufacturing process. Two acquisition models with quantity discount and carbon tax scheme were established to analyze the effect of quality variability and condition uncertainty and to reduce these difficulties. In the first model, quality variability was considered. The optimal acquisition policy was determined by a single closed-form expression because the average cost of remanufactured products is independent of the acquisition quantity for a given discount segment. In the second model, both quality variability and condition uncertainty were considered. The properties of the model were analyzed, and a single algorithm was developed to obtain the optimal acquisition policy based on the bisection method. Finally, numerical simulation examples were provided to explore the effect of quantity discount on the optimal acquisition policy. Results show that the quantity discount schedule impels remanufacturers to acquire more cores and enhances the chances of remanufacturers to select the best cores. Moreover, the total expected cost decreases, especially in the case with both quality variability and condition uncertainty. The proposed model can effectively solve the acquisition problem in remanufacturing systems.
Keywords: carbon emission; core acquisition; remanufacturing; quantity discount; quality variability
Optimalna politika akvizicije u sustavima preradbe s diskontom na količinu i planom poreza na ugljikIzvorni znanstveni članak Velika nesigurnost i promjenljivost akvizicijskih temelja, mogu stvoriti poteškoće kod upravljanja operacijama u procesu preradbe. Postavljena su dva modela akvizicije s popustom na količinu i planom poreza na ugljik u svrhu analize učinka promjenljivosti kvalitete i nesigurnosti uvjeta i smanjenja tih problema. U prvom se modelu razmatrala promjenljivost kvalitete. Optimalna politika akvizicije određena je pojedinačnim izrazom zatvorenog oblika jer prosječna cijena prerađenog proizvoda ne ovisi o dobivenoj količini za dati segment diskonta. U drugom su modelu uzeti u obzir i promjenljivost kvalitete i nesigurnost uvjeta. Analizirana su svojstva modela i razvijen je algoritam za postizanje optimalnog načina akvizicije na temelju metode bisekcije. Konačno, dani su primjeri numeričke simulacije kako bi se istražio učinak diskonta na količinu na optimalni način akvizicije. Rezultati pokazuju da se politikom diskonta na količinu prerađivači potiču na dobivanje više osnova i povećavaju im se mogućnosti da izaberu najbolju osnovu. Štoviše, smanjuje se ukupno očekivani trošak, naročito kad se radi i o promjenljivosti kvalitete i o nesigurnosti uvjeta. Predloženi model može uspješno riješiti problem akvizicije u prerađivačkim sustavima.
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