Mathematical Methods of Operations Research

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Single-peakedness was introduced by Black (J Political Econ 56:23–34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The unde...

We study a multiclass many-server queueing system with renewal arrivals and generally distributed service and patience times under a nonpreemptive allocation policy. The status of the system is described by a pair of measure-valued processes to track the residual service and patience times of customers in each class. We establish fluid approximations and study the long-term behavior of the fluid model. The equilibrium state of the fluid model leads to a nonlinear program, which enables us to ide...

We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem in a continuous-time framework where the demand is modeled with a non-homogeneous Poisson process h...

We consider the end-of-life inventory problem for the supplier of a product in its final phase of the service life cycle. This phase starts when the production of the items stops and continues until the warranty of the last sold item expires. At the beginning of this phase the supplier places a final order for spare parts to serve customers coming with defective items. At any time during the final phase the supplier may also decide to switch to an alternative and more cost effective service poli...

We revisit the polyhedral projection problem. This problem has many applications, among them certain problems in global optimisation, polyhedral calculus, problems encountered in information theory and financial mathematics. In particular, it has been shown recently that polyhedral projection problems are equivalent to vector linear programmes (which contain multiple objective linear programmes as a sub-class). In this article, we develop a novel solution concept which provides more detailed ins...

The main results of the paper are a minimal element theorem and an Ekeland-type variational principle for set-valued maps whose values are compared by means of a weighted set order relation. This relation is a mixture of a lower and an upper set relation which form the building block for modern approaches to set-valued optimization. The proofs rely on nonlinear scalarization functions which admit to apply the extended Brezis–Browder theorem. Moreover, Caristi’s fixed point theorem and Takahashi’...

In this paper, we consider the problem of optimal investment-reinsurance with two dependent classes of insurance risks in a regime-switching financial market. In our model, the two claim-number processes are correlated through a common shock component, and the market mode is classified into a finite number of regimes. We also assume that the insurer can purchase proportional reinsurance and invest its surplus in a financial market, and that the values of the model parameters depend on the market...

In this paper new modeling techniques of \((S-1,S)\) inventory systems (continuous review base-stock inventory systems) with state dependent demand rates are proposed. Examples of single-location \((S-1,S)\) inventory systems where the demand, experienced by the system, varies due to the state of the system are, e.g., inventory models with partial backorders, inventory models with lost sales, inventory models with perishable items, inventory models with emergency replenishments etc. Models of su...

While there is vast literature on principal-agent service contracts in which a principal pools the service capacities of multiple agents for economy of scale, here we focus on the case that exists in practice of an agent pooling multiple principals. Since it is reasonable to presume that an agent of good standing attracts multiple contract offers, his main strategic decision is to select his principals. It is generally known that a principal can extract all economic surplus from a risk-neutral a...

The question of measuring and managing systemic risk - especially in view of the recent financial crises - became more and more important. We study systemic risk by taking the perspective of a financial regulator and considering the axiomatic approach originally introduced in Chen et al. (2013) and extended in Kromer et al. (2014). The aim of this paper is to generalize the static approach in Kromer et al. (2014) and analyze systemic risk measures in a dynamic setting. We work in the framework o...

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