Dynamic and targeted bundle pricing of two independently valued products

Bundling is when two or more products are offered as a single unit and at a price lower than the sum of the individual prices of the products. We study a multi-segment market in which a retailer aims to clear the inventory of an item by bundling it with a second product which is independently valued. We investigate the question of how dynamic and segment-specific bundle pricing impacts retailer’s revenue. We develop a revenue model that integrates the dynamic and segment-specific aspects of the pricing decisions, and present a computational study to analyze their revenue impact relative to a price promotion for the individual item only. The computational results indicate that the bundle offers are most effective when the initial inventory of the item under consideration is high. The results also demonstrate that dynamic pricing is beneficial when the initial inventory of the item is low. An additional revenue improvement is observed when the price of the bundle is dynamically optimized. In the computational study, segment-specific pricing is observed to have no direct impact on revenue when prices are static; segment-specific and dynamic pricing, however, can bring about substantial revenue improvements that are an increasing function of the initial inventory level of the item. We consider the correlation in consumers’ valuations of the bundled products, and show that dynamically priced and segment-specific bundle offers yield a robust revenue performance, mitigating the potentially revenue-diminishing impact of positive correlation in consumers’ valuations of the products

Minimization of number of tool switching instants in automated manufacturing systems

This study addresses the problem of minimizing tool switching instants in automated manufacturing systems. There exist a single machine and a group of jobs to be processed on it. Each job requires a set of tools, and due to limited tool magazine capacity, and because it is not possible to load all available tools on the machine, tools must be switched. The ultimate goal, in this framework, is to minimize the total number of tool switching instants. We provide a mathematical programming model and two constraint programming models for the problem. Because the problem is proven to be NP-hard, we develop two heuristic approaches, and compare their performance with methods described in the literature. Our analysis indicates that our constraint programming models perform relatively well in solution quality and execution time in small-sized problem instances. The performance of our greedy approach shows potential, reaching the optimal solution in 82.5% of instances. We also statistically demonstrate that the search algorithm enhances the quality of the solution obtained by the greedy heuristic, particularly in large sets. Hence, the solution approach, i.e., the greedy heuristic and the search algorithm proposed in this study is able to quickly reach near-optimal solutions, showing that the method is appropriate for manufacturing settings requiring sudden adjustments

Randomized pricing of a storable good in the presence of consumer stockpiling

In a retail setting with a storable product and customers that are heterogeneous in their product valuations and stockpile-up-to levels, intertemporal price discrimination is a key revenue driver. This study considers price randomization as an intertemporal price discrimination scheme that can bring in revenues comparable to those of the third-degree price discrimination. A mathematical model that captures the retailer’s expected revenue maximization problem in a two-segment setting over an infinite horizon is developed. We show that when product valuations are uniformly distributed, price randomization generates at least 89 of the revenue the retailer can achieve with the third-degree price discrimination strategy. The computational analysis indicates that price randomization can be an effective price discrimination option in the presence of segments having similar sizes and marked differences in product valuations. Moreover, the computational analysis illustrates that price randomization can recover a significant portion of the revenue that the retailer could achieve through deterministic cyclic policies with two price levels. We describe how a retailer should optimally design its price randomization strategy and identify market structures where randomized pricing can be an effective option

Minimization of number of tool switching instants in automated manufacturing systems

This study addresses the problem of minimizing tool switching instants in automated manufacturing systems. There exist a single machine and a group of jobs to be processed on it. Each job requires a set of tools, and due to limited tool magazine capacity, and because it is not possible to load all available tools on the machine, tools must be switched. The ultimate goal, in this framework, is to minimize the total number of tool switching instants. We provide a mathematical programming model and two constraint programming models for the problem. Because the problem is proven to be NP-hard, we develop two heuristic approaches, and compare their performance with methods described in the literature. Our analysis indicates that our constraint programming models perform relatively well in solution quality and execution time in small-sized problem instances. The performance of our greedy approach shows potential, reaching the optimal solution in 82.5% of instances. We also statistically demonstrate that the search algorithm enhances the quality of the solution obtained by the greedy heuristic, particularly in large sets. Hence, the solution approach, i.e., the greedy heuristic and the search algorithm proposed in this study is able to quickly reach near-optimal solutions, showing that the method is appropriate for manufacturing settings requiring sudden adjustments

Integrated optimisation of pricing, manufacturing, and procurement decisions of a make-to-stock system operating in a fluctuating environment

Manufacturers experience random environmental fluctuations that influence their supply and demand processes directly. To cope with these environmental fluctuations, they typically utilise operational hedging strategies in terms of pricing, manufacturing, and procurement decisions. We focus on this challenging problem by proposing an analytical model. Specifically, we study an integrated problem of procurement, manufacturing, and pricing strategies for a continuous-review make-to-stock system operating in a randomly fluctuating environment with exponentially distributed processing times. The environmental changes are driven by a continuous-time discrete state-space Markov chain, and they directly affect the system's procurement price, raw material flow rate, and price-sensitive demand rate. We formulate the system as an infinite-horizon Markov decision process with a long-run average profit criterion and show that the optimal procurement and manufacturing strategies are of state-dependent threshold policies. Besides that, we provide several analytical results on the optimal pricing strategies. We introduce a linear programming formulation to numerically obtain the system's optimal decisions. We, particularly, investigate how production rate, holding cost, procurement price and demand variabilities, customers' price sensitivity, and interaction between supply and demand processes affect the system's performance measures through an extensive numerical study. Furthermore, our numerical results demonstrate the potential benefits of using dynamic pricing compared to that of static pricing. In particular, the profit enhancement being achieved with dynamic pricing can reach up to 15%, depending on the problem parameters