Browsing by Author "Tonelli, M."

Now showing 1 - 2 of 2

Open Access
A bilevel uncapacitated location/pricing problem with Hotelling access costs in one-dimensional space
(International Conference on Information Systems, Logistics and Supply Chain, 2016) Arbib, C.; Pınar, Mustafa Ç.; Tonelli, M.
We formulate a spatial pricing problem as bilevel non-capacitated location: a leader first decides which facilities to open and sets service prices taking competing offers into account; then, customers make individual decisions minimizing individual costs that include access charges in the spirit of Hotelling. Both leader and customers are assumed to be risk-neutral. For non-metric costs (i.e., when access costs do not satisfy the triangle inequality), the problem is NP-hard even if facilities can be opened at no fixed cost. We describe an algorithm for solving the Euclidean 1-dimensional case (i.e., with access cost defined by the Euclidean norm on a line) with fixed opening costs and a single competing facility.
Open Access
Competitive location and pricing on a line with metric transportation costs
(Elsevier, 2020-04-01) Arbib, C.; Pınar, Mustafa Ç.; Tonelli, M.
Consider a three-level non-capacitated location/pricing problem: a firm first decides which facilities to open, out of a finite set of candidate sites, and sets service prices with the aim of revenue maximization; then a second firm makes the same decisions after checking competing offers; finally, customers make individual decisions trying to minimize costs that include both purchase and transportation. A restricted two-level problem can be defined to model an optimal reaction of the second firm to known decision of the first. For non-metric costs, the two-level problem corresponds to Envy-free Pricing or to a special Net- work Pricing problem, and is APX -complete even if facilities can be opened at no fixed cost. Our focus is on the metric 1-dimensional case, a model where customers are distributed on a main communica- tion road and transportation cost is proportional to distance. We describe polynomial-time algorithms that solve two- and three-level problems with opening costs and single 1 st level facility. Quite surpris- ingly, however, even the two-level problem with no opening costs becomes N P -hard when two 1 st level facilities are considered.