An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

Abstract

W e consider a pricing and short-term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time-dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time-dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non-decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.

Auction-Based Capacity Allocation in Two Parallel Machines with Inclusive Processing Set Restrictions

“…eir market goods were time blocks and then proved that the equilibrium solution always exists but is not unique. Karabat and Yalcn [20] considered the pricing and production capacity allocation problem in the single machine environment and proposed an auction mechanism that uses the finished products as market goods for the private information case.…”

An iterative combinatorialauctionmechanism formulti-agentparallel machinescheduling

“…It has been implemented in some resource allocation problems in recent years. Karabatı and Yalçın (2014) developed an iterative auction mechanism with a single-minded bidding policy to solve the capacity problem in the supply chain. Abrache et al (2013Abrache et al ( , 2014 studied the ICAs for multilateral procurement with a simple bidding language.…”

“…A myopic bidding strategy is adopted, where each bidder seeks to obtain the time blocks that maximise his/her revenue in the current iteration without considering the possibilities of future iterations. This bidding strategy is easy to be applied, and it is a natural choice for self-interested consumer agents who have no knowledge about other agents (Wellman et al 2001;Hall and Liu 2013;Karabatı and Yalçın 2014). An adaptive bid pricing strategy is designed, where the bidding prices of bidders vary with their revenues.…”

Mechanism Design of Unknown Bidding Preference and Discrete Cost Structure in Multi-Attribute Reverse Auctions

“…According to the existing literature, the frequently adopted methods include Lagrangian relaxation [35], heuristics [30] and linear price approximation [7]. In practice, iterative auction has been applied to many areas, such as production planning problem [19], inventory management [29], [42], scheduling [25] and capacity allocation [4], [31], [58]. However, most of these works assumed that the buyer exactly knows the bidder's bidding preferences and the cost function is continuous.…”

“…Since procurement cost and delivery time are the most important factors for firms to achieve the goal of lean manufacturing [13], [32], we assume that each supplier has a limited capacity of the goods and discrete cost values associated with the supply quantity and delivery time. Without loss of generality, the unit cost could be discounted in terms of the supply quantity and delivery time [25]. Also, we assume that the cost structure is common knowledge but the cost values can only be privately observed by each individual supplier.…”