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We construct a generic model for a heat engine using information theory concepts, attributing irreversible energy dissipation to the information transmission channels. Using several forms for the channel capacity, classical and quantum, we demonstrate that our model recovers both the Carnot principle in the reversible limit, and the universal maximum power efficiency expression of nonreversible thermodynamics in the linear response regime. We expect the model to be very useful as a testbed for studying fundamental topics in thermodynamics, and for providing new insights into the relationship between information theory and actual thermal devices.

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Problem definition: We consider an intermediary’s problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. Specifically, there are two disjoint sets of demand and supply types, and a reward for each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform decides on the optimal matching policy to maximize the expected total discounted rewards, given that unmatched demand and supply may incur waiting or holding costs, and will be fully or partially carried over to the next period. Academic/practical relevance: The problem is crucial to many intermediaries who manage matchings centrally in a sharing economy. Methodology: We formulate the problem as a dynamic program. We explore the structural properties of the optimal policy and propose heuristic policies. Results: We provide sufficient conditions on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs. We show that those conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively. Managerial implications: The priority property simplifies the matching decision within a period, and the trade-off reduces to a choice between matching in the current period and that in the future. Then the optimal matching policy has a match-down-to structure when considering a specific pair of demand and supply types in the priority hierarchy.

In this paper we investigate joint pricing and inventory control problems in a finite-horizon, single-product, periodic-review setting with certain/uncertain supply capacities. The demands in different periods are random variables whose distributions depend on the posted price exhibiting the additive form. The order quantity in each period is required to be of integral multiples of a given specific batch size (denoted by Q). Inventory replenishment incurs a linear ordering cost. Referred to as the cost-rate function, the sum of holding and backorder costs can either be convex or quasi-convex. The objective is to determine a joint ordering and pricing decision that can maximize the total expected profit over the planning horizon. We first consider the case in which the cost-rate function is convex and show that the modified (r, Q) list-price policy is optimal for the system with certain and limited capacities, a special case of which is the (r, Q) list-price policy when capacities become unlimited. As supply capacities become random, the optimal policy follows a new structure wherein the optimal order-up-to level and posted price must be coordinated to make the optimal safety stock level follow the (r, Q) policy. We further consider the case of a quasi-convex cost-rate function, which may arise when a service level constraint is used as a surrogate for the shortage cost. We demonstrate that the (r, Q) list-price policy is optimal for the system without supply capacity constraints. In addition, extensions to several other models are discussed. The enabling technique is based on the notion of Q-jump convexity and its variants.