قیمت‌گذاری تعادلی در یک زنجیره تامین سه‌سطحی

در دنیای امروز و در عرصۀ فعالیت‌های اقتصادی، یکی از مهم‌ترین عوامل تعیین‌کننده در سرنوشت شرکت‌ها و سازمان‌ها، رقابت است. در بیشتر موارد، رقابت شرکت‌ها برای تصاحب سهم بازار، به شکل رقابت در قیمت پدیدار می‌شود و قیمت‌گذاری مناسب محصولات و خدمات، تاثیر زیادی بر درآمد شرکت‌ها دارد و تعیین قیمت بهینه نیز سبب ایجاد هماهنگی و تعادل در بین اعضای حاضر در زنجیره ‌تامین می‌شود و درنهایت، کل زنجیره به بیشترین مقدار سود دست می‌یابد. در سال‌های اخیر نیز پژوهشگران به استفاده از مدل‌های انتخاب گسسته برای استخراج تابع تقاضا در مدل‌های رقابت قیمت توجه زیادی کرده‌اند. در مطالعۀ حاضر و در بررسی موردی از زنجیره تامین و فرآوری قهوه، یکی از شرکت‌های داخل کشور برای یافتن مناسب‌ترین مقادیر قیمت و حجم تولید برای حداکثرسازی سود و با کاربرد نظریۀ بازی‌ها بررسی شده است. این مطالعه ازنظر هدف، کاربردی و به‌لحاظ روش جمع‌آوری داده‌ها، توصیفی تحلیلی است. به همین ترتیب، مدل استفاده‌شده، بر رقابت در بین اعضای این زنجیره در فضایی احتمالی تمرکز داشته و بر مبنای مدل‌های انتخاب گسسته پایه‌ریزی شده و در آن، تاثیر هزینه‌های موجودی و مسیریابی در مدل تعیین قیمت، بررسی هم‌زمان شده است. علاوه بر این، برای حل مدل طراحی‌شده نیز از تقریب توزیع نرمال به جای توزیع دوجمله‌ای استفاده شده است. نتایج مدل نشان می‌دهد زمان حل در مدل تقریبی مورد استفاده، با افزایش تعداد مشتریان، تغییری ندارد و مدل، میزان تولید و قیمت بهینه را مشخص می‌کند. مزیت مدل پیشنهادی نسبت به سایر مدل‌های کلاسیک، لحاظ‌کردن هم‌زمان هزینه‌های مسیریابی، کمبود و ذخیرۀ موجودی‌هاست که کاربرد آن در آن دسته از مدل‌های رقابت قیمت که برپایۀ مدل‌های انتخاب گسسته استوار است، نادر است.

Equilibrium pricing in a threelevel supply chain

Purpose: Proper pricing of products or services can have a significant impact on corporate earnings. Therefore, this study aims to address the optimization of price and production quantity to maximize the total profit using game theory in the coffee supply chain (composed of suppliers, retailers and customers) in Isfahan city. Design/methodology/approach: The applied model focuses on competition among members of the chain in probabilistic space. It is based on discrete selection models in which the impact of inventory costs and routing is analyzed on the pricing model simultaneously. In this model, competition between coffee importers (because coffee is not produced in the country) is studied in the probable space. Due to complexity in computation, it could not solve problems with a large number of customers. Therefore, the approximation of the binomial distribution by the normal distribution is used, an approximate model is proposed. Finally, the equilibrium point is determined by solving a system of nonlinear equations using the Newton method. Findings: The maximum profit in noncooperative game conditions is achievable based on the appropriate demand function. Finally, the equilibrium price was calculated. Findings indicated that the computational time of the approximate model did not change with increasing the number of customers, and the model can determine the optimal price and production quantity. The model results implied that the time of solving the approximate model used did not change with the increasing number of customers, and the model was able to determine the optimal quantity and price.Practical implications In the present study, the equilibrium behaviour of suppliers, retailers and customers in a twotier supply chain of the coffee supply and distribution industry was investigated in Isfahan city. A price competition model was proposed, and ten active companies were studied in the Isfahan market. Moreover, the computational speed diagram indicated that the computational time in the original function increased with increasing the number of customers, but this time in the approximation function did not react to the increase in the number of customers and remained constant. Social implications: In the proposed model of the present study, competition among coffee suppliers was investigated in a probabilistic environment in which retailers acted as intermediaries and had no effect on pricing. Holding and shortage costs were also taken into account. Also, routing costs were approximated using the proposed Himovich model. Then, a pricing model was proposed. The proposed model could not solve problems with a large number of customers due to complexity in computation. Originality/value: The advantage of the proposed model over basic models is in considering the inventory costs, which has not been considered yet in price competition models based on discrete selection models. Another significant feature of the price competition problem is the type of demand function. In this paper, to study a competitive model, a stochastic demand function was developed based on the logit model. The advantage of the introduced demand function is that it considers shortage and inventory holding costs in a oneperiod model. Also, in the game theory studies, usually with the increasing number of customers, the model is computationally complicated and less effective to solve realworld problems. For this reason, in this study, the normal distribution approximation was used instead of the binomial distribution.