On the Complexity of the Highway Pricing Problem

The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is (weakly) NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so far it has resisted any attempt for constant-factor approximation algorithms. We relate the tractability of the problem to structural properties of customers' valuations. We show that the problem becomes NP-hard as soon as the average valuations of customers are not homogeneous, even under further restrictions such as monotonicity. Moreover, we derive an efficient approximation algorithm, parameterized along the inhomogeneity of customers' valuations. Finally, we discuss extensions of our results that go beyond the highway pricing problem.\u

Price Strategy Implementation

Consider a situation in which a company sells several different items to a set of customers. However, the company is not satisfied with the current pricing strategy and wishes to implement new prices for the items. Implementing these new prices in one single step mightnot be desirable, for example, because of the change in contract prices for the customers. Therefore, the company changes the prices gradually, such that the prices charged to a subset of the customers, the target market, do not differ too much from one period to the next. We propose a polynomial time algorithm to implement the new prices in the minimum number of time periods needed, given that the prices charged to the customers in the target market increase by at most a factor 1 + δ, for predetermined δ > 0. Furthermore, we address the problem to maximize the revenue when also a maximum number of time periods is predetermined. For this problem, we describe a dynamic program if the numberof possible prices is limited, and a local search algorithm if all prices are allowed. Also, we present the integer program that models this problem. Finally, we apply the obtained algorithms in a practical study.operations research and management science;

On the Complexity of the Highway Pricing Problem

The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is (weakly) NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so far it has resisted any attempt for constant-factor approximation algorithms. We relate the tractability of the problem to structural properties of customers'' valuations. We show that the problem becomes NP-hard as soon as the average valuations of customers are not homogeneous, even under further restrictions such as monotonicity. Moreover, we derive an efficient approximation algorithm, parameterized along the inhomogeneity of customers'' valuations. Finally, we discuss extensions of our results that go beyond the highway pricing problem.operations research and management science;

Optimal Bundle Pricing for Homogeneous Items

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation for the requested bundle that we assume to be known to the seller. The task is to find an envy-free pricing such as to maximize the revenue of the seller. We derive several complexity results and algorithms for several variants of this pricing problem. In fact, the settings that we consider address problems where the different items are `homogeneous'' in some sense. First, we introduce the notion of affne price functions that can be used to model situations much more general than the usual combinatorial pricing model that is mostly addressed in the literature. We derive fixed-parameter polynomial time algorithms as well as inapproximability results. Second, we consider the special case of combinatorial pricing, and introduce a monotonicity constraint that can also be seen as `global'' envy-freeness condition. We show that the problem remains strongly NP-hard, and we derive a PTAS - thus breaking the inapproximability barrier known for the general case. As a special case, we finally address the notorious highway pricing problem under the global envy-freeness condition.operations research and management science;

Optimal Bundle Pricing with Monotonicity Constraint

We consider the problem to price (digital) items in order to maximize the revenue obtainable from a set of bidders. We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we derive a PTAS. We also discuss a special case, the highway pricing problem.operations research and management science;

Improving workplace-based assessment and feedback by an E-portfolio enhanced with learning analytics

Electronic portfolios (E-portfolios) are crucial means for workplace-based assessment and feedback. Although E-portfolios provide a useful approach to view each learner’s progress, so far options for personalized feedback and potential data about a learner’s performances at the workplace often remain unexploited. This paper advocates that E-portfolios enhanced with learning analytics, might increase the quality and efficiency of workplace-based feedback and assessment in professional education. Based on a 5-phased iterative design approach, an existing E-portfolio environment was enhanced with learning analytics in professional education. First, information about crucial professional activities for professional domains and suited assessment instruments were collected (phase 1). Thereafter probabilistic student models were defined (phase 2). Next, personalized feedback and visualization of the personal development over time were developed (phase 3). Then the prototype of the E-portfolio—including the student models and feedback and visualization modules—were implemented in professional training-programs (phase 4). Last, evaluation cycles took place and 121 students and 30 supervisors from five institutes for professional education evaluated the perceived usefulness of the design (phase 5). It was concluded that E-portfolios with learning analytics were perceived to assist the development of students’ professional competencies and that the design is only successful when developed and implemented through the eyes of the users. Feedback and assessment methods based upon learning analytics can stimulate learning at the workplace in the long run. Practical, technological and ethical challenges are discussed

Asymptotic Giant Branch Stars in the Sculptor Dwarf Spheroidal Galaxy

JHK_S photometry is presented for a 35 arcmin square field centred on the Sculptor dwarf spheroidal galaxy. With the aid of published kinematic data definite galaxy members are identified and the width in J-K of the colour-magnitude diagram is shown to be consistent with an old population of stars with a large range in metal abundance. We identify two Asymptotic Giant Branch variables, both carbon Miras, with periods of 189 and 554 days, respectively, and discuss their ages, metallicities and mass loss as well as their positions in the Mira period-luminosity diagram. There is evidence for a general period-age relation for Local Group Miras. The mass-loss rate for the 554-day variable, MAG29, appears to be consistent with that found for Miras of comparable period in other Local Group galaxies.Comment: accepted for publication in MNRA

Glioma Pathogenesis-Related Protein 1: Tumor-Suppressor Activities and Therapeutic Potential

After glioma pathogenesis-related protein 1 (GLIPR1/Glipr1) was identified, the expression of GLIPR1 was shown to be down-regulated in human prostate cancer, owing in part to methylation in the regulatory region of this gene in prostate cancer cells. Additional studies showed that GLIPR1/Glipr1 expression is induced by DNA-damaging agents independent of p53. Functional analysis of GLIPR1 using in vitro and in vivo gene-transfer approaches revealed both growth suppression and proapoptotic activities for mouse Glipr1 and human GLIPR1 in multiple cancer cell lines. The proapoptotic activities were dependent on production of reactive oxygen species and sustained c-Jun-NH2 kinase signaling. It was interesting that adenoviral vector-mediated Glipr1 (AdGlipr1) transduction into prostate cancer tissues using an immunocompetent orthotopic mouse model revealed additional biologic activities consistent with tumor-suppressor functions. Significantly reduced tumor-associated angiogenesis and direct suppression of endothelial-cell sprouting activities were documented. In addition, AdGlipr1 strongly stimulated antitumor immune responses that resulted in specific cytotoxic T-lymphocyte activities in this model. Glipr1-related antitumor immunostimulatory activities were confirmed and extended in subsequent studies. Administration of a novel Glipr1 gene-modified tumor cell vaccine had significant antitumor activity in a mouse model of recurrent prostate cancer. In conclusion, restoration of GLIPR1 function in prostate cancer cells through GLIPR1 gene-based or GLIPR protein-based delivery methods may provide a safe and effective approach for targeted therapy for a range of malignancies