Cash flow optimization in delivery scheduling

The paper examines the inventory routing problem from the perspective of the present value of the cash flow associated with the distribution of a commodity such as propane. We analyze this problem for both deterministic and stochastic customer demands and validate our results on data from a real life distribution operation of propane. The analysis based on the present value of the cash flow indicates that optimization of propane deliveries based on efficiency/cost criteria alone will generate inferior solutions and it would be more advantageous for the company to set deliveries for a large percentage of the customers based on the present value of cash flow. In addition, in the case of stochastic demands, deliveries based on the cash flow consideration will tend to reduce the number of stockouts (i.e. improve both profit and service).     

Inverse Pattern Matching

Let a textstringTofnsymbols from some alphabet Σ and an integerm < nbe given. A patternPof lengthmover Σ is sought such thatPminimizes (alternatively, maximizes) the total number of pairwise character mismatches generated whenPis compared with allm-character substrings ofT. Two additional variants of the problem are obtained by adding the constraint thatPbe (respectively, not be) a substring ofT. Efficient sequential algorithms are proposed in this paper for the problem and its variants.     

A discrete-time model of failure and repair

In this paper the authors introduce and study a model of failures and repairs of units with discrete lifetimes. They suppose that a unit has a sequence of tasks to perform and that its lifetime is measured by the number of tasks performed before its final, fatal failure. Upon a failure the unit may be repaired (with some probability) and then it may attempt again to perform the current task. The unit dies when (with some probability) a repair cannot be completed. We derive some stochastic comparisons of pairs of such models. The stochastic comparisons are then applied for obtaining results regarding the inheritance of several aging properties by the repaired unit. Various examples illustrate the applicability of the model. Some variants of the model of this paper can be viewed as discrete analogues of the notion of imperfect repair.     

Maximal solutions of semilinear elliptic equations with locally integrable forcing term

We study the existence of a maximal solution of −Δu+g(u)=f(x) in a domain Ω ∈ ℝ ^N with compact boundary, assuming thatf ∈ (L _loc ¹ (Ω))₊ and thatg is nondecreasing,g(0)≥0 andg satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classicalC _1,2 Wiener criterion, then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition, we discuss the question of uniqueness of large solutions. This research was partially supported by an EC Grant through the RTN Program “Front-Singularities”, HPRN-CT-2002-00274.     

Two dimorphs of 5‐methyl­sulfanyl‐1H‐tetrazole

5‐Methyl­sulfanyl‐1H‐tetrazole, C₂H₄N₄S, crystallizes in dimor­phic forms; the α‐form crystallizes at room temperature in the monoclinic crystal system, space group P2₁/m, and the β‐form crystallizes by sublimation at 423 K in the orthorhombic crystal system, space group Pbcm. In both forms, the mol­ecules occupy crystallographic mirror planes and are connected to one another via N—H⋯N hydrogen bonds, the amino H atoms being disordered. The two forms differ from one another in their packing; there are polar layers in the α‐form and non‐polar layers in the β‐form.