商品的訂價與推薦問題在現代零售業與電子商務業的經營中是一個重要且廣泛的議題，根據企業所展示的商品與訂定的售價，兩個因素皆能在不同方面影響顧客的購買意願，而良好的商品訂價與推薦策略將是企業能否獲得高額收益的關鍵，然而在相關文獻中，替換成本(switching cost)經常是不被考量的隱藏成本，替換成本泛指企業販售、替換架上商品的同時所產生的人力、物力與時間成本，在企業長期的營運下，替換成本將對企業造成影響，因此我們建構並研究了一個商品推薦與訂價情境，並考量商品替換成本對企業的影響，並研究企業在此情況下是否能藉由更佳的策略獲取更高的收益。我們建構並研究了一個商品推薦與訂價情境，並考量商品替換成本對企業的影響，並研究企業在此情況下是否能藉由更佳的策略獲取更高的收益，具體來說，我們考慮一間企業販售多種不同的商品，且企業並未知曉客戶的 需求函數(demand function)。因此企業必須在銷售過程中透過替換欲販售之商品並對商品進行動態訂價(dynamic pricing) 來學習不同商品的顧客需求函數資訊，進而找出潛在利潤最高的商品。上述過程中，替換成本將影響企業學習商品需求函數資訊的過程，企業可能會為了避免高額的替換成本而減少不同商品的替換，導致企業無法完整學習各類商品的資訊。為了緩解此問題，因此本研究提出考量替換成本之商品推薦與訂價演算法，除了找尋最佳商品外，演算法還藉由控制商品的替換次數來降低總替換成本，並且跟文獻中常用之演算法進行比較。數值分析中，本研究提出的演算法能夠達到相對較低的損失(regret)，並且在大多數情況下，最終會收斂至最佳解，因此損失會收斂到一定值而不會持續增長。本研究表明，企業能藉由延長同商品持續販售時間來避免替換成本的過度影響，並且根據已有資訊來判斷商品的學習程度，以使非最佳商品不過度佔用貨架，進而降低損失，並仍保持對商品的學習。

With more and more people tending to shop on e-commerce websites, many e-commerce enterprises have started to focus on improving the efficiency of product recommender systems, enterprises can quickly get higher revenue by correctly recommender a trending product of this selling season to customers, not only the e-commerce industry, this concept can simply found in many other industries. In this research, we faced a complex joint problem of multi-products recommend problem and dynamic pricing problem, in this model, a seller sells multiple products through the selling season with limited display capabilities, the seller knew that every product has a demand model but he(she) don't know the parameters of the model, so it's hard to estimate the potential revenue of every product. The seller wants to figure out which product is the optimal one, the way is to sell these products at different prices through the selling season and learn products information by observing the customer's demand, but the seller will face the switching cost while switching the product from one to another in the selling horizon, which decreases the revenue. In this research, we propose a dynamic pricing strategy and a product recommend algorithms to solve this joint problem, for dynamic pricing, we use a pricing method based on the CILS method from Keskin Zeevi (2014). For the product recommend algorithm, we develop a switch cost-adapted algorithm to solve this problem by controlling the selling time of every product. In the experiments, the performance of our solution is quite better than the ε-greedy algorithm.

Agrawal, S., Avadhanula, V., Goyal, V., & Zeevi, A. (2019). Mnl-bandit: A dynamic learning approach to assortment selection. Operations Research, 67(5), 1453–1485.
Aviv, Y., & Pazgal, A. (2002). Pricing of short life-cycle products through active learning. Under Revision for Management Science, (pp. 1–32).
Bernstein, F., Ko ̈k, A. G., & Xie, L. (2015). Dynamic assortment customization with limited inventories. Manufacturing & Service Operations Management, 17(4), 538–553.
Besbes, O., & Zeevi, A. (2009). Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Operations Research, 57(6), 1407–1420. Caro, F., & Gallien, J. (2007). Dynamic assortment with demand learning for seasonal consumer goods. Management Science, 53(2), 276–292.
Caro, F., Mart ́ınez-de Albe ́niz, V., & Rusmevichientong, P. (2014). The assortment packing problem: Multiperiod assortment planning for short-lived products. Management Science, 60(11), 2701–2721.
Cope, E. (2007). Bayesian strategies for dynamic pricing in e-commerce. Naval Research Logistics (NRL), 54(3), 265–281.
Den Boer, A. V. (2014a). Dynamic pricing with multiple products and partially specified demand distribution. Mathematics of Operations Research, 39(3), 863–888.
Den Boer, A. V. (2014b). Dynamic pricing with multiple products and partially specified demand distribution. Mathematics of Operations Research, 39(3), 863–888.
Den Boer, A. V. (2015). Dynamic pricing and learning: historical origins, current research, and new directions. Surveys in Operations Research and Management Science, 20(1), 1–18.
Federgruen, A., & Heching, A. (1999). Combined pricing and inventory control under un- certainty. Operations Research, 47(3), 454–475.
Gallego, G., & Van Ryzin, G. (1994). Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Science, 40(8), 999–1020.
Gomez-Uribe, C. A., & Hunt, N. (2015). The netflix recommender system: Algorithms, business value, and innovation. ACM Transactions on Management Information Systems (TMIS), 6(4), 1–19.
Greenleaf, E. A. (1995). The impact of reference price effects on the profitability of price promotions. Marketing Science, 14(1), 82 104.
Harrison, J. M., Keskin, N. B., & Zeevi, A. (2012). Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Science, 58(3), 570– 586.
Kao, Y.-M., Keskin, N. B., & Shang, K. (2020). Bayesian dynamic pricing and subscription period selection with unknown customer utility. Available at SSRN 3722376.
Keskin, N. B., & Zeevi, A. (2014). Dynamic pricing with an unknown demand model: Asymptotically optimal semi-myopic policies. Operations Research, 62(5), 1142–1167.
Kök, A. G., Fisher, M. L., & Vaidyanathan, R. (2008). Assortment planning: Review of literature and industry practice. Retail Supply Chain Management, 122(1), 99–153.
Kök, A. G., Fisher, M. L., & Vaidyanathan, R. (2015). Assortment planning: Review of literature and industry practice. Retail Supply Chain Management, (pp. 175–236).
Lazear, E. P. (1984). Retail pricing and clearance sales. Tech. rep., National Bureau of Economic Research.
Nguyen, D. (1984). The monopolistic firm, random demand, and bayesian learning. Opera- tions Research, 32(5), 1038–1051.
Qu, H., Ryzhov, I. O., & Fu, M. C. (2013). Learning logistic demand curves in business-to- business pricing. In 2013 Winter Simulations Conference (WSC), (pp. 29–40). IEEE.
Robbins, H. (1952). Some aspects of the sequential design of experiments. Bulletin of the American Mathematical Society, 58(5), 527–535.
Russo, D. (2016). Simple bayesian algorithms for best arm identification. In Conference on Learning Theory, (pp. 1417–1418). PMLR.
Sauré, D., & Zeevi, A. (2013). Optimal dynamic assortment planning with demand learning. Manufacturing & Service Operations Management, 15(3), 387–404.
Smith, B., & Linden, G. (2017). Two decades of recommender systems at amazon. com. IEEE Internet Computing, 21(3), 12–18.