The stochastic matching problem

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.Comment: Published version has very minor change

Risk Assessment Plan for Petroleum Underground Storage Tanks in Kentucky, Part ll: Diesel, Heating Oil, Other Middle Distillates and Waste Oil

This report consists of an appendix :Risk Assessment Plan for Petroleum Underground Storage Tanks in Kentucky and a second appendix: Environmental Half-Life and Ecological Effects of PAH

Trade credit, risk sharing, and inventory financing portfolios

As an integrated part of a supply contract, trade credit has intrinsic connections with supply chain coordination and inventory management. Using a model that explicitly captures the interaction of firms' operations decisions, financial constraints, and multiple financing channels (bank loans and trade credit), this paper attempts to better understand the risk-sharing role of trade credit - that is, how trade credit enhances supply chain efficiency by allowing the retailer to partially share the demand risk with the supplier. Within this role, in equilibrium, trade credit is an indispensable external source for inventory financing, even when the supplier is at a disadvantageous position in managing default relative to a bank. Specifically, the equilibrium trade credit contract is net terms when the retailer's financial status is relatively strong. Accordingly, trade credit is the only external source that the retailer uses to finance inventory. By contrast, if the retailer's cash level is low, the supplier offers two-part terms, inducing the retailer to finance inventory with a portfolio of trade credit and bank loans. Further, a deeper early-payment discount is offered when the supplier is relatively less efficient in recovering defaulted trade credit, or the retailer has stronger market power. Trade credit allows the supplier to take advantage of the retailer's financial weakness, yet it may also benefit both parties when the retailer's cash is reasonably high. Finally, using a sample of firm-level data on retailers, we empirically observe the inventory financing pattern that is consistent with what our model predicts

Trade credit in supply chains: multiple creditors and priority rules

Priority rules determine the order of repayment to different creditors when the debtor cannot repay all of his debt. In this chapter, we study how different priority rules influence trade credit usage and supply chain efficiency under the risk-sharing role of trade credit. We find that with only demand risk, when the wholesale price is exogenous, trade credit with high priority can lead to high chain efficiency, yet trade credit with low priority allows more retailers to obtain trade credit and suppliers to gain higher profits. When the supplier has control of wholesale price, however, the supplier should extend unlimited trade credit, deeming priority rules irrelevant. When other non-demand risks, especially those with longer terms in nature, are present, we show several scenarios when the optimal trade credit policy should change according to different risks, and that in general, trade credit with low priority results in higher chain efficiency

Glassy freezing of orbital dynamics in FeCr2S4 and FeSc2S4

We report on a thorough dielectric investigation of the glass-like freezing of the orbital reorientation-dynamics, recently found for the crystalline sulpho-spinels FeCr2S4 and FeSc2S4. As the orbital reorientations are coupled to a rearrangement of the surrounding ionic lattice via the Jahn-Teller effect, the freezing of the orbital moments is revealed by a relaxational behaviour of the complex dielectric permittivity. Additional conductivity (both dc and ac) and contact contributions showing up in the spectra are taken into account by an equivalent circuit description. The orbital relaxation dynamics continuously slows down over six decades in time, before at the lowest temperatures the glass transition becomes suppressed by quantum tunnelling.Comment: J. Non-Cryst. Solids, in press. 6 pages, 4 figure

Two-stage stochastic minimum s − t cut problems: Formulations, complexity and decomposition algorithms

We introduce the two‐stage stochastic minimum s − t cut problem. Based on a classical linear 0‐1 programming model for the deterministic minimum s − t cut problem, we provide a mathematical programming formulation for the proposed stochastic extension. We show that its constraint matrix loses the total unimodularity property, however, preserves it if the considered graph is a tree. This fact turns out to be not surprising as we prove that the considered problem is NP-hard in general, but admits a linear time solution algorithm when the graph is a tree. We exploit the special structure of the problem and propose a tailored Benders decomposition algorithm. We evaluate the computational efficiency of this algorithm by solving the Benders dual subproblems as max-flow problems. For many tested instances, we outperform a standard Benders decomposition by two orders of magnitude with the Benders decomposition exploiting the max-flow structure of the subproblems

Sublinear upper bounds for stochastic programs with recourse

Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47918/1/10107_2005_Article_BF01582286.pd