Exact algorithms for procurement problems under a total quantity discount structure.

In this paper, we study the procurement problem faced by a buyer who needs to purchase a variety of goods from suppliers applying a so-called total quantity discount policy. This policy implies that every supplier announces a number of volume intervals and that the volume interval in which the total amount ordered lies determines the discount. Moreover, the discounted prices apply to all goods bought from the supplier, not only to those goods exceeding the volume threshold. We refer to this cost-minimization problem as the TQD problem. We give a mathematical formulation for this problem and argue that not only it is NP-hard, but also that there exists no polynomial-time approximation algorithm with a constant ratio (unless P = NP). Apart from the basic form of the TQD problem, we describe three variants. In a first variant, the market share that one or more suppliers can obtain is constrained. Another variant allows the buyer to procure more goods than strictly needed, in order to reach a lower total cost. In a third variant, the number of winning suppliers is limited. We show that the TQD problem and its variants can be solved by solving a series of min-cost flow problems. Finally, we investigate the performance of three exact algorithms (min-cost flow based branch-and-bound, linear programming based branch-and-bound, and branch-and-cut) on randomly generated instances involving 50 suppliers and 100 goods. It turns out that even the large instances of the basic problem are solved to optimality within a limited amount of time. However, we find that different algorithms perform best in terms of computation time for different variants.Algorithms; Approximation; Branch-and-bound; Complexity; Cost; Exact algorithm; Intervals; Linear programming; Market; Min-cost flow; Order; Performance; Policy; Prices; Problems; Procurement; Reverse auction; Structure; Studies; Suppliers; Time; Volume discounts;

Load Balancing in the Smart Grid: A Package Auction and Compact Bidding Language

Distribution system operators (DSOs) are faced with new challenges from the continuous integration of fluctuating renewable energy resources and new dynamic customer loads such as electric vehicles, into the power grid. To ensure continuous balancing of supply and demand, we propose procurement package auctions to allocate load flexibility from aggregators and customers. The contributions of this research are an incentive-compatible load flexibility auction along with a compact bidding language. It allows bidders to express minimum and maximum amounts of flexibility along with unit prices in single bids for varying time periods. We perform a simulation-based evaluation and assess costs and benefits for DSOs and balancing suppliers given scenarios of varying complexity as well as computational aspects of the auction. Our initial findings provide evidence that load flexibility auctions can reduce DSO costs substantially and that procurement package auctions are well-suited to address the grid load balancing problem

Exact algorithms for the matrix bid auction.

In a combinatorial auction, multiple items are for sale simultaneously to a set of buyers. These buyers are allowed to place bids on subsets of the available items. A special kind of combinatorial auction is the so-called matrix bid auction, which was developed by Day (2004). The matrix bid auction imposes restrictions on what a bidder can bid for a subsets of the items. This paper focusses on the winner determination problem, i.e. deciding which bidders should get what items. The winner determination problem of a general combinatorial auction is NP-hard and inapproximable. We discuss the computational complexity of the winner determination problem for a special case of the matrix bid auction. We present two mathematical programming formulations for the general matrix bid auction winner determination problem. Based on one of these formulations, we develop two branch-and-price algorithms to solve the winner determination problem. Finally, we present computational results for these algorithms and compare them with results from a branch-and-cut approach based on Day & Raghavan (2006).Algorithms; Bids; Branch-and-price; Combinatorial auction; Complexity; Computational complexity; Exact algorithm; Mathematical programming; Matrix; Matrix bids; Research; Winner determination;

Matrix bids in combinatorial auctions: expressiveness and micro-economic properties

A combinatorial auction is an auction where multiple items are for sale simultaneously to a set of buyers. Furthermore, buyers are allowed to place bids on subsets of the available items. This paper focuses on a combinatorial auction where a bidder can express his preferences by means of a so-called ordered matrix bid. Ordered matrix bids are a bidding language that allows a compact representation of a bidder''s preferences, and was developed by Day (2004). We give an overview of how a combinatorial auction with matrix bids works. We elaborate on the relevance of the matrix bid auction and we develop methods to verify whether a given matrix bid satisfies properties related to micro-economic theory as free disposal, subadditivity, submodularity and the gross substitutes property. Finally, we investigate how a collection of arbitrary bids can be represented as a matrix bid.microeconomics ;

Designing smart markets

Electronic markets have been a core topic of information systems (IS) research for last three decades. We focus on a more recent phenomenon: smart markets. This phenomenon is starting to draw considerable interdisciplinary attention from the researchers in computer science, operations research, and economics communities. The objective of this commentary is to identify and outline fruitful research areas where IS researchers can provide valuable contributions. The idea of smart markets revolves around using theoretically supported computational tools to both understand the characteristics of complex trading environments and multiechelon markets and help human decision makers make real-time decisions in these complex environments. We outline the research opportunities for complex trading environments primarily from the perspective o

Exact algorithms for procurement problems under a total quantity discount structure

In this paper, we study the procurement problem faced by a buyer who needs to purchase a variety of goods from suppliers applying a so-called total quantity discount policy. This policy implies that every supplier announces a number of volume intervals and that the volume interval in which the total amount ordered lies determines the discount. Moreover, the discounted prices apply to all goods bought from the supplier, not only to those goods exceeding the volume threshold. We refer to this cost-minimization problem as the TQD problem. We give a mathematical formulation for this problem and argue that not only it is NP-hard, but also that there exists no polynomial-time approximation algorithm with a constant ratio (unless P = NP). Apart from the basic form of the TQD problem, we describe three variants. In a first variant, the market share that one or more suppliers can obtain is constrained. Another variant allows the buyer to procure more goods than strictly needed, in order to reach a lower total cost. In a third variant, the number of winning suppliers is limited. We show that the TQD problem and its variants can be solved by solving a series of min-cost flow problems. Finally, we investigate the performance of three exact algorithms (min-cost flow based branch-and-bound, linear programming based branch-and-bound, and branch-and-cut) on randomly generated instances involving 50 suppliers and 100 goods. It turns out that even the large instances of the basic problem are solved to optimality within a limited amount of time. However, we find that different algorithms perform best in terms of computation time for different variants.status: publishe

Exact algorithms for procurement problems under a total quantity discount structure

C