Consider the choice between two alternative pipeline capacities with no reserve capacity, i.e., the initial line capacity is fully implemented with matching pumping capacity (reserves will be considered in the stage II and stage III experiments) :
Pipeline 1 the smaller pipeline, to be operated at capacity \(Y_1 = Q_1\) with (zero reserve, or expansion capacity), total investment cost is \(K_1\), and per unit (average) investment cost is \(IC_1\).
Pipeline 2 the larger pipeline, with a larger capacity \(Y_2 = Q_2 > Q_1\), with zero reserve. Total investment cost is \(K_2 > K_1\), and per unit (average) investment cost is \(IC_2 < IC_1\) (assumes economies of scale).
Define \(Q\) as the total pipeline throughput capacity of gas in MMcf/d. Efficiency is greatest for the \(Q\) that maximizes :
\begin{equation} \int V(Q_{1}) dQ_{1} - K_1, \qquad \int V(Q_{2}) dQ_{2} - K_2 \end{equation}
We describe a possible bidding choice mechanism between the two discrete alternatives pipeline one and pipeline two.
Each bidder \(i\) submits a bid \((b_i, q_i)\) (dollars per unit capacity, number of capacity units); \(q_i\) includes \(i\)’s proportionate share of \(Q\); i.e. if \(\sum _i q_i = Q_1\) is the auction outcome, then \(s_i = q_i\) is allocated for each \(i\) whose bid is accepted; if \(\sum _i q_i > Q_2\) is the auction outcome and \(\sum _i q_i = 0.8 Q_2\), then \(s_i = 0.8 q_i\) is allocated for each accepted bid \(i\).
Bids are arrayed from highest to lowest (lexical graphically) on price for each capacity bid to determine total capacity as expressed by the bids. Higher bids have priority over lower bids for acceptance.
If the total sum of bids (\(\sum _i q_i b_i, \quad \text {for } \quad b_i > IC_1\)) exceeds \(K_1\) but not \(K_2\), the outcome is \(Q_1\); if the sum exceeds \(K_2\), the outcome is \(Q_2\).
If outcome \(Q_1\) is chosen, then all bids \(b_i > IC_1\) are accepted; all bids below \(IC_1\) are rejected; ties are broken at \(IC_1\) by sequential random selection, with only the last tied bid winner having his quantity request rationed. If outcome \(Q_2\) is chosen, then all bids \(b_i > IC_2\) are accepted; all bids below \(IC_2\) are rejected; ties are broken at \(IC_2\) by sequential random selection, with only the last tied bid winner having his quantity request rationed.
Each accepted bid pays the same price—a price per unit capacity equal to \(IC_1\) or \(IC_2\); this is a well-established behavioral rule normally intended to provide incentives for all bidders to enter their best bid, discouraging gaming and strategizing on the part of all.
As appealing as this rule set appears, a there is one fatal flaw in this application; that is, there is no disciplining action on the individual’s bid \(b_i\). There is no disincentive for bidders to enter a bid as large as possible, since there is no possibility that the bidder will have to pay the bid. The bidder always pays \(IC_1\) or \((IC_2)\).
We consider two discrete capacity options on each leg of the Y pipeline (see Figure 5) with no reserves, as for the single pipeline above. All rights seekers must bid on leg A with subsets of these bidders also bidding on B and/or C, if they want through transmission rights to their respective markets.
This would be a three node connected line version of the bidding example above with bidders bidding on different combinations of capacity on the various legs. Thus, a bidder wanting to get North Slope gas to Anchorage bids for equal amounts of capacity on legs A and C, and no capacity on B. Another bids on all three wanting gas in both Anchorage and Chicago, etc. . The discrete alternatives might assume that \(Q_A \geq Q_B\) and \(Q_A \geq Q_C\) with, for example two sizes offered on each leg, say (42 inches and 36 inches), (36 inches and 30 inches), or (30 inches and 24 inches).
Unit Capacity costs are now :
\( \seteqnumber {2} \)
\begin{align} ICA_1 & > & ICA_2 & \quad & QA_1 & < & QA_2 \\ ICB_1 & > & ICB_2 & \quad & QB_1 & < & QB_2 \\ ICC_1 & > & ICC_2 & \quad & QC_1 & < & QC_2 \end{align}
Let \(I\) be the set of bidders for links A and C, each \(i \in I\) bids (dollars offered; capacity request for leg A, capacity request for leg C) \((B_i; a_i, c_i)\); i.e., \(B_i\) is the dollar bid for capacity \(a_i\) on leg A and for capacity \(c_i\) on leg C.
Let \(J\) be the set of bidders for links A and B, each \(j \in J\) bids (dollars offered; cap A and cap B) \((B_j; a_j, b_j)\).
Let \(H\) be the set of bidders for links A, B and C, each \(h \in H\) bids (dollars offered; cap A, cap B and cap C) \((B_h; a_h, b_h, c_h)\)
\(i\)’s share of capacity on A is \(a_i (QA_1 / \sum _i a_i)\) if bid \(i\) accepted, similarly for \(j\) and \(h\).
In the sealed bid auction optimization, algorithms are applied to the set of all bids for choosing the pipeline telescope configuration that maximizes the total value of the project. Note that in the single pipeline example above the algorithm chooses the area under the submitted bid schedule that is greatest (subject to the feasibility constraint that cost is covered).