In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a tradeoff between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable.
We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a 'common assortment' that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store.
Concerning the computational complexity, we show that the APP is strongly NP-complete. The core of this hardness result lies in the selection of the common assortment. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances.
Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores.
In this paper we introduce a binary autoregressive model. In contrast to the typical autoregression framework, we allow the conditional distribution of the observed process to depend on past values of the time series and some exogenous variables. Such processes have
potential applications in econometrics, medicine and environmental sciences. In this
paper, we establish stationarity and geometric ergodicity of these
processes under suitable conditions on the parameters of the model. Such properties are
important for understanding the stability properties of the model as well as for deriving the
asymptotic behavior of the parameter estimators.
Capital budgeting or investment decisions have an essential influence on companies’ performance. Instead of a rational choice, capital budgeting might be regarded as a process of reality construction. Research suggests that decision makers have only limited control over their own cognitive biases in this construction process. It is in this perspective that this paper intends to answer the following research question: What are behavioral determinants for a successful capital-budgeting decision process? The authors identify and discuss three behavioral success factors (reflective prudence, critical communication and outcome independence) for five stages of the capital budgeting process against the backdrop of the findings of the managerial and organizational cognition theory and cognitive psychology.
The Comparative Manifesto Project (CMP) dataset is the only dataset providing information about the positions of parties for comparative researchers across time and countries. This article evaluates its structure and finds a peculiarity: A high number of zeros and their unequal distribution across items, countries and time. They influence the results of any procedure to build a scale, but especially those using factor analyses. The article shows that zeroes have different meanings: Firstly, there are substantial zeroes in line with saliency theory. Secondly, zeroes exist for non-substantial reasons: The length of a manifesto and the percentage of uncoded sentences, both strongly varying across time and country. We quantify the problem and propose a procedure to identify data points containing non-substantial zeroes. For the future comparative use of the dataset we plead for a theoretical selection of items combined with the information about the likelihood that zeroes are substantially meaningful.
Ion energy spectra of a laser-produced Ta plasma have been investigated as a function of the flight distance from the focus. The laser (Nd:YAG, 20 ns, 210 mJ) is incident obliquely (45°) and focused to an intensity of about 10^11 W cm-2. The changes in the ion distributions have been analysed for the Ta+ to Ta6+ ions in an expansion range 64 - 220 cm. With increasing distance from the target, a weak but monotonic decrease is observed for the total number of ions, which is essentially due to the decrease in the number of the more highly charged species. For the Ta+ and Ta2+ ions the net changes approximately cancel. A more sophisticated picture of the recombination dynamics is obtained, however, if the changes within individual groups of ions expanding with different velocities are compared. Here, in the same spectrum, both increasing and decreasing ion numbers can be observed. This can be interpreted as direct evidence of recombination and its dependence on temperature, density and charge.
The particle flux produced by an obliquely incident Nd Q-switched pulse (20 ns) on a Ta target has been analysed with regard to its angular distribution resolved for both its neutral and ion components. The laser intensity has been varied in the range between about 10^10 - 10^11 W cm-2, which is appropriate for many low-irradiance applications. It is observed that, at all emission angles and for the whole range of laser intensities, the number of neutral species clearly dominates the composition of the particles. At 1.3 x 10^10 W cm-2 the total number of emitted particles is 4 x 10^14, scaling as E_L^¾ with the laser energy. While for relatively low laser energies the angular distribution shows the usual smooth cos-behaviour, an additional strong directive emission cone, superimposed upon the cos-distribution, develops if the laser energy is enhanced. Both the strength and the width strongly depend on the laser intensity. While at lower intensities a fit by a cos^n function with n ~ 10 seems appropriate, n increases to 26 at an intensity of 10^11 W cm-2 . It can be assumed that secondary energy transfer processes that are not yet fully understood are responsible for this anomalous emission.
The conversion efficiency of laser energy into kinetic ion energy in a laser-produced plasma has been investigated for two quite different targets: graphite and tantalum. The laser energy (intensity) varied from several mJ to 200 mJ (1O^9 to 7 x 10^10 W cm-2) which is appropriate to many applications of a laser produced ion source. The conversion efficiency as a function of the laser energy was directly determined by differential measurements of the charge, kinetic energy and angular emission distribution of the plasma ions in absolute units. Whilst for the Ta target a nearly constant efficiency of about 30% was observed, the graphite result shows an unexpectedly strong enhancement of the transfer efficiency of up to 80% in the laser intensity range around 1.5 x l0^10 W cm-2. It is assumed that the results are related to the difference in the surface roughness of the targets.
The symplectic group of homogeneous canonical transformations is represented in the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states. The intertwining relations between this representation and the algebra of Weyl operators are derived. They confirm the identification of this representation with Bogoliubov transformations.
Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.
This work is concerned with a nonlinear Galerkin method for solving the incompressible Navier-Stokes equation on the sphere. It extends the work of Debussche, Marion,Shen, Temam et al. from one-dimensional or toroidal domains to the spherical geometry. In the first part, the method based on type 3 vector spherical harmonics is introduced and convergence is indicated. Further it is shown that the occurring coupling terms involving three vector spherical harmonics can be expressed algebraically in terms of Wigner-3j coefficients. To improve the numerical efficiency and economy we introduce an FFT based pseudo spectral algorithm for computing the Fourier coefficients of the nonlinear advection term. The resulting method scales with O(N^3), if N denotes the maximal spherical harmonic degree. The latter is demonstrated in an extensive numerical example.