Optimizing a dynamic order-picking process

This research studies the problem of batching orders in a dynamic, finite-horizon environment to minimize order tardiness and overtime costs of the pickers. The problem introduces the following trade-off: at every period, the picker has to decide whether to go on a tour and pick the accumulated orders, or to wait for more orders to arrive. By waiting, the picker risks higher tardiness of existing orders on the account of lower tardiness of future orders. We use a Markov decision process (MDP) based approach to set an optimal decision making policy. In order to evaluate the potential improvement of the proposed approach in practice, we compare the optimal policy with two naïve heuristics: (1) “Go on tour immediately after an order arrives”, and, (2) “Wait as long as the current orders can be picked and supplied on time”. The optimal policy shows a considerable improvement over the naïve heuristics, in the range of 7–99%, where the specific values depend on the picking process parameters. We have found that one measure, the slack percentage of the picking process, associated with the difference between the promised lead time and the single item picking time, predicts quite accurately the cost reduction generated by the optimal policy. Since relatively small-scale problems could be solved by the optimal algorithm, a heuristic was developed, based on the structure and properties of the optimal solutions. Numerical results show that the proposed heuristic, MDP-H, outperforms the naïve heuristics in all experiments. As compared to the optimal solution, MDP-H provides close to optimal results for a slack of up to 40%.     

An exactly conservative particle method for one dimensional scalar conservation laws

A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of area. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.     

On-line steiner trees in the Euclidean plane

Suppose we are given a sequence ofn points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the total sum of lengths of its edges. The points appear one at a time, and at each step the on-line algorithm must construct a connected graph that contains all current points by connecting the new point to the previously constructed graph. This can be done by joining the new point (not necessarily by a straight line) to any point of the previous graph (not necessarily one of the given points). The performance of our algorithm is measured by its competitive ratio: the supremum, over all sequences of points, of the ratio between the total length of the graph constructed by our algorithm and the total length of the best Steiner tree that connects all the points. There are known on-line algorithms whose competitive ratio isO(logn) even for all metric spaces, but the only lower bound known is of [IW] for some contrived discrete metric space. Moreover, for the plane, on-line algorithms could have been more powerful and achieve a better competitive ratio, and no nontrivial lower bounds for the best possible competitive ratio were known. Here we prove an almost tight lower bound of Ω(logn/log logn) for the competitive ratio of any on-line algorithm. The lower bound holds for deterministic algorithms as well as for randomized ones, and obviously holds in any Euclidean space of dimension greater than 2 as well. Noga Alon was supported in part by a USA-Israeli BSF grant.     

The relationship between DEA efficiency and the type of production function, the degree of homogeneity, and error variability

In this paper, we use simulations to investigate the relationship between data envelopment analysis (DEA) efficiency and major production functions: Cobb-Douglas, the constant elasticity of substitution, and the transcendental logarithmic. Two DEA models were used: a constant return to scale (CCR model), and a variable return to scale (BCC model). Each of the models was investigated in two versions: with bounded and unbounded weights. Two cases were simulated: with and without errors in the production functions estimation. Various degrees of homogeneity (of the production function) were tested, reflecting a constant increasing and decreasing return to scale. With respect to the case with errors, three distribution functions were utilized: uniform, normal, and double exponential. For each distribution, 16 levels of the coefficient of variance (CV) were used. In all the tested cases, two measures were analysed: the percentage of efficient units (from the total number of units), and the average efficiency score. We applied a regression analysis to test the relationship between these two efficiency measures and the above parameters. Overall, we found that the degree of homogeneity has the largest effect on efficiency. Efficiency declines as the errors grow (as reflected by larger CV and of the expansion of the probability distribution function away from the centre). The bounds on the weights tend to smooth the effect, and bring the various DEA versions closer to one other. The type of efficiency measure has similar regression tendencies. Finally, the relationship between the efficiency measures and the explanatory variables is quadratic.     

Following the growth of surface films on lithium and their thermal behavior in standard LiPF6 solutions using differential scanning calorimetry

In this paper, we report on attempts to use differential scanning calorimetric measurements of aged Li electrodes for the study of the kinetics of the growth of surface films on the active metal. Standard, commonly used alkyl carbonate solutions such as ethylene and di-methyl carbonates with LiPF6 were explored. Heating Li samples in solutions after aging by DSC, resulted in well-resolved curves of reaction heats vs temperature. Exothermic reactions occurring at temperatures below 150 degrees C could be attributed to changes related to the surface films and their heat evolved, increased as a function of storage time, and hence these heats represent the thickness of the surface films that grow upon storage. Scanning electron microscopy of the Li surfaces as a function of storage and heating to different temperatures confirmed that the thermal reactions of Li surfaces in these solutions up to 150 degrees C relate to the surface films only. XPS studies revealed that these processes of the surface films change the metastable organic Li salts to more stable inorganic compounds such as LiF and Li2O. Massive red-ox reactions, between the salt anion and the solvents and between the solution species and the active metal, occur at temperatures higher than 150 degrees C. The kinetics of growth of the surface films on Li show an inverse logarithmic behavior, expected for thin surface films with which the rate-limiting step of their growth depends on ions transport across the film.     

Approximating Probability Distributions Using Small Sample Spaces

We formulate the notion of a "good approximation" to a probability distribution over a finite abelian group ?. The quality of the approximating distribution is characterized by a parameter ɛ which is a bound on the difference between corresponding Fourier coefficients of the two distributions. It is also required that the sample space of the approximating distribution be of size polynomial in and 1/ɛ. Such approximations are useful in reducing or eliminating the use of randomness in certain randomized algorithms. We demonstrate the existence of such good approximations to arbitrary distributions. In the case of n random variables distributed uniformly and independently over the range , we provide an efficient construction of a good approximation. The approximation constructed has the property that any linear combination of the random variables (modulo d) has essentially the same behavior under the approximating distribution as it does under the uniform distribution over . Our analysis is based on Weil's character sum estimates. We apply this result to the construction of a non-binary linear code where the alphabet symbols appear almost uniformly in each non-zero code-word. Received: September 22, 1990/Revised: First revision November 11, 1990; last revision November 10, 1997     

Catalytic degradation of the nerve agent VX by water-swelled polystyrene-supported ammonium fluorides

The catalytic degradation of the nerve agent VX (O-ethyl S-2-(diisopropylamino)ethyl methylphosphonothioate) by water-swelled polymer-supported ammonium fluorides is described. VX (0.06-0.53 mol/mol F(-)) is rapidly degraded (t(1/2) ～ 10-30 min) to form the "G-analogue" (O-ethyl methylphosphonofluoridate), which hydrolyzes (t(1/2) ～ 1-1.5 h) to the nontoxic EMPA (ethyl methylphosphonic acid). The toxic desethyl-VX is not formed. The catalytic effect of fluoride is maintained even when 6 equiv of VX are loaded. GB (O-isopropyl methylphosphonofluoridate) and desethyl-VX agents are also degraded under these conditions.     

DNA-CNT nanowire networks for DNA detection

The ability to detect biological analytes in a rapid, sensitive, operationally simple, and cost-effective manner will impact human health and safety. Hybrid biocatalyzed-carbon nanotube (CNT) nanowire-based detection methods offer a highly sensitive and specific platform for the fabrication of simple and effective conductometric devices. Here, we report a conductivity-based DNA detection method utilizing carbon nanotube-DNA nanowire devices and oligonucleotide-functionalized enzyme probes. Key to our sensor design is a DNA-linked-CNT wire motif, which forms a network of interrupted carbon nanotube wires connecting two electrodes. Sensing occurs at the DNA junctions linking CNTs, followed by amplification using enzymatic metalization leading to a conductimetric response. The DNA analyte detection limit is 10 fM with the ability to discriminate single, double, and triple base pair mismatches. DNA-CNT nanowires and device sensing gaps were characterized by scanning electron microscopy (SEM) and confocal Raman microscopy, supporting the enhanced conductometric response resulting from nanowire metallization.