Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

Tax-Optimal Step-Up and Imperfect Loss Offset

In the field of mergers and acquisitions, German and international tax law allow for several opportunities to step up a firm's assets, i.e., to revaluate the assets at fair market values. When a step-up is performed the taxpayer recognizes a taxable gain, but also obtains tax benefits in the form of higher future depreciation allowances associated with stepping up the tax base of the assets. This tax-planning problem is well known in taxation literature and can also be applied to firm valuation in the presence of taxation. However, the known models usually assume a perfect loss offset. If this assumption is abandoned, the depreciation allowances may lose value as they become tax effective at a later point in time, or even never if there are not enough cash flows to be offset against. This aspect is especiallyrelevant if future cash flows are assumed to be uncertain. This paper shows that a step-up may be disadvantageous or a firm overvalued if these aspects are not integrated into the basic calculus. Compared to the standard approach, assets should be stepped up only in a few cases and - under specific conditions - at a later point in time. Firm values may be considerably lower under imperfect loss offset.