Contract farming is a growing practice in developing countries and first-world economies, alike. It generates necessary guarantees to sustain the continued operations of vulnerable farmers while enabling the manufacturers to manage the aggregate supply and price risk. We consider a single manufacturer who owns several manufacturing plants, each with a random demand for the crop. The manufacturer selects a set of farmers to offer a menu of contracts, which is exogenously specified or endogenously determined. Each "selected" farmer chooses a contract from this menu in advance of the growing season. After the growing season, under known demands and supplies, the manufacturer minimizes the distribution costs from the selected farmers to the production facilities. We formulate this problem as a Stackelberg game with asymmetric information, where the manufacturer is the leader and the farmers are followers. The manufacturer's problem is a two-stage stochastic planning program for which we develop two solution approaches. We have applied our model to problem instances anchored on data from a large manufacturer of potato chips contracting with thousands of small farmers in India. We report on the performance of the solution methods compared to a lower bound based on the Lagrangean dual of the problem and show that the optimality gap is below 1%, for problem instances with 1,000 potential farmers. We also show how our model can be used to gain managerial insights.
I n many markets, it is common for headquarters to create a price list but grant local salespeople discretion to negotiate prices for individual transactions. How much (if any) pricing discretion headquarters should grant is a topic of debate within many firms. We investigate this issue using a unique data set from an indirect lender with local pricing discretion. We estimate that the local sales force adjusted prices in a way that improved profits by approximately 11% on average. A counterfactual analysis shows that using a centralized, data-driven pricing optimization system could improve profits even further, up to 20% over those actually realized. This suggests that centralized pricing-if appropriately optimized-can be more effective than field price discretion. We discuss the implications of these findings for auto lending and other industries with similar pricing processes.
W e consider pricing problems when customers choose under the Markov chain choice model. In this choice model, a customer arriving into the system is interested in a certain product with a certain probability. Depending on the price charged for this product, the customer decides whether to purchase the product. If the customer purchases the product, then she leaves the system. Otherwise, the customer transitions to another product or to the no purchase option with certain transition probabilities. In this way, the customer transitions between the products until she purchases a product or reaches the no purchase option. We study three fundamental pricing problems under this choice model. First, for the monopolistic pricing problem, we show how to compute the optimal prices efficiently. Second, for the competitive pricing problem, we show that a Nash equilibrium exists, prove that Nash equilibrium prices are no larger than the prices computed by a central planner controlling all prices and characterize a Nash equilibrium that Pareto dominates all other Nash equilibria. Third, for the dynamic pricing problem with a single resource, we show that the optimal prices decrease as we have more resource capacity or as we get closer to the end of the selling horizon. We also consider a deterministic approximation formulated under the assumption that the demand for each product takes on its expected value. Although the objective function and constraints in this approximation do not have explicit expressions, we develop an equivalent reformulation with explicit expressions for the objective function and constraints. Dong, Simsek, and Topaloglu: Pricing under the Markov Chain Model Dong, Simsek, and Topaloglu: Pricing under the Markov Chain Model Production and Operations Management 28(1), pp. 157-175,
We develop an expectation-maximization algorithm to estimate the parameters of the Markov chain choice model. In this choice model, a customer arrives into the system to purchase a certain product. If this product is available for purchase, then the customer purchases it. Otherwise, the customer transitions between the products according to a transition probability matrix until she reaches an available one and purchases this product. The parameters of the Markov chain choice model are the probability that the customer arrives into the system to purchase each one of the products and the entries of the transition probability matrix. In our expectation-maximization algorithm, we treat the path that a customer follows in the Markov chain as the missing piece of the data. Conditional on the final purchase decision of a customer, we show how to compute the probability that the customer arrives into the system to purchase a certain product and the expected number of times that the customer transitions from a certain product to another one. These results allow us to execute the expectation step of our algorithm. Also, we show how to solve the optimization problem that appears in the maximization step of our algorithm.Our computational experiments show that the Markov chain choice model, coupled with our expectation-maximization algorithm, can yield better predictions of customer choice behavior when compared with other commonly used alternatives.
T his paper empirically investigates using the e-mail channel to target customers with a delayed incentive promotionspecifically, gift card promotion-and derives data-driven e-mail targeting policies. Gift card promotions are popular across retailers because they incentivize customers to spend more than a fixed expenditure level on regularly priced products by rewarding customers with a gift card to be redeemed against a future purchase. The e-mail channel provides retailers with new sources of customer-level data, which enables better prediction of customers' responsiveness to e-mails (e.g., clicking) and the sales promotion that comes with it (e.g., participation in the promotion). We formulate the retailer's promotion e-mail targeting problem by maximizing two objectives-the promotion's profitability (i.e., profit-based targeting) and e-mail click-through rate (i.e., CTR-based targeting). We also take into account the retailer's promotion budget and exclusivity concerns in targeting e-mails. We use a comprehensive dataset from a Fortune 500 luxury fashion retailer's online channel and utilize both parametric and non-parametric methods to predict customers' response to promotion e-mails. Our data-driven targeting policies improve the promotion's profitability by 5.57% and e-mail CTR by 472.57%, on average, compared to our partner retailer's current e-mail policy. We also find that the CTR-based targeting policy lowers the promotion profitability by, on average, 9.09% compared to the profit-based one. However, the CTR-based policy recuperates the short-term losses in the long-term and increases the long-term profitability by 3.94%, on average, compared to the profit-based targeting policy.
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