Optimizing Contracts

Schaefer, A. Huher, C. Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829-5835. 

Schafer, A., Horn, H., Ahlrichs, R., 1992, Fully Optimized Contracted Gaussian Basis Sets for Atoms Li to Kr , J. Chem. Phys., 97, 2571. 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

The greater dependence on basis-set quality of correlated calculations compared to those of the HF variety has prompted many developers of basis sets to optimize contractions via some scheme that includes evaluating results from the former. For instance, the correlation consistent prefix of the cc-pVnZ basis sets discussed in Chapter 6 highlights this feature. 

Bardo, R. D. and Ruedenberg, K., Even-tempered atomic orbitals. VI. Optimal orbital exponents and optimal contractions of Gaussian primitives for hydrogen, carbon, and oxygen in molecules,. 1. Chem. Phys. 60, 918-931 (1974). 

Bechtel Corp., Global Energy, Inc., Nexant, Inc. Gasification Plant Cost and Performance Optimization, Contract DE-AC26-99FT40342, Sep 2003. 

The key issue to be managed in such contracts is the agency effect, as described in the earlier section. The agency effect reflects the fact that only the agent (the supplier) knows the true quality, while the principal (the buyer) experiences the cost of the quality. The associated problem then is similar to the unknown supplier capability discussed in the previous section. Similar to the models discussed there, contracts between the buyer and the supplier can include buyer oversight and buyer-recommended processes that involve buyer costs but may affect supplier costs as well. The optimal contract thus has to account for the extent of buyer oversight and its associated impact on the information rents that have to be paid to suppliers. 

Provasi, P. F., Aucar, G. A., Sauer, S. R A. (2001). The effect of lone pairs and electronegativity on the indirect nuclear spin—spin coupling constants in CH2X(X=CHj, NH, O, S) Ab initio calculations using optimized contracted basis sets. The Journal of Chemical Physics, 115(3), 1324-1334. 

A supply chain is said to be coordinated with a contract if the optimizing actions of the agents under the contract lead to Pareto optimality, that is, no agent in the chain can be better off without making any other agent worse off. The associated contract is said to be a Pareto-optimal contract. By definition, only Pareto-optimal con-... 

In the reminder of this chapter, we first briefly review the standard newsvendor model with the satisficing objective. We then design Pareto-optimal WP, BB, and QF contracts for a supply chain where all agents adopt satisficing objectives. These Pareto-optimal contracts are then evaluated based on whether they can coordinate the supply chain or not. We then proceed to discuss possible extensions to the model by considering different objectives for different agents. Finally we summarize the results obtained in this chapter. 

Design of Pareto-Optimal Contracts under the Satisficing Objectives... 

In the next three subsections, we design the Pareto-optimal contracts— that is, the Pareto-optimal contract parameters—for each contractual form. Moreover, we identify the associated Pareto-optimal order quantity and the maximal probabilities of achieving the target profits for the supplier and the retailer. 

So far we have designed the Pareto-optimal contracts for the three contractual forms under the satisficing objectives. In this section, our goal is to identify the contractual forms that are capable of coordination of the supply chain with satisficing objectives. 

For each contractual form, we first design the Pareto-optimal contracts. By definition, only Pareto-optimal contracts should be selected in practice, no matterwhatthe negotiation process and negotiation powers among the agents. This is due to the feet that if a contract is not Pareto optimal, it is open to a counteroffer that makes no one worse off and at least one of the other agents strictly better off. Furthermore, a contract has to be Pareto optimal first to coordinate a supply chain. 

Schafer A, Horn H, Ahlrichs R (1992) Fully optimized contracted gaussian basis sets for atoms Li to Kr. J Chem Phys 97 2571-2577... 

Before we conclude this section, it is also worthwhile to introduce and summarize the terminology we will be using in the remainder of this chapter. A compensation system is said to induce or implement an action if that action represents the agent s optimal choice. Such action is called incentive compatible. A pair that consists of a compensation system and an action is called a contract. Such a contract is feasible if the prescribed action is incentive compatible and if the compensation system satisfies the participation constraint. The optimal contract is the pair (not necessarily unique) of a compensation system and incentive compatible action that maximizes the principal s expected payoff and satisfies the participation constraint. The action prescribed in the optimal contract is called second-best as opposed to the so-called first-best action that is optimal when the agent s action is observable by the principal. 

P.F. Provasi, G.A. Aucar, S.P.A. Sauer, The effect of lone paiis and electronegativity on the indirect nuclear spin-spin coupling constants in CHX (X = CH,NH,0, S) ah initio calculations using optimized contracted basis sets,. Chem. Phys. 115 (2001) 1324. 

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