Browsing by Author "Arbib, C."

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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
Codon optimization by 0-1 linear programming
(Elsevier, 2020-02) Arbib, C.; Pınar, Mustafa Ç.; Rossi, F.; Tessitore, A.
The problem of choosing an optimal codon sequence arises when synthetic protein-coding genes are added to cloning vectors for expression within a non-native host organism: to maximize yield, the chosen codons should have a high frequency in the host genome, but particular nucleotide bases sequences (called “motifs”) should be avoided or, instead, included. Dynamic programming (DP) has successfully been used in previous approaches to this problem. However, DP has a computational limit, especially when long motifs are forbidden, and does not allow control of motif positioning and combination. We reformulate the problem as an integer linear program (IP) and show that, with the same computational resources, one can easily solve problems with much more nucleotide bases and much longer forbidden/desired motifs than with DP. Moreover, IP (i) offers more flexibility than DP to treat constraints/objectives of different nature, and (ii) can efficiently deal with newly discovered critical motifs by dynamically re-optimizing additional variables and mathematical constraints.
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.
Open Access
On envy-free perfect matching
(Elsevier, 2019) Arbib, C.; Karaşan, Oya Ekin; Pınar, Mustafa
Consider a situation in which individuals –the buyers –have different valuations for the products of a given set. An envy-free assignment of product items to buyers requires that the items obtained by every buyer be purchased at a price not larger than his/her valuation, and each buyer’s welfare (difference between product value and price) be the largest possible. Under this condition, the problem of finding prices maximizing the seller’s revenue is known to be APX -hard even for unit-demand bidders (with several other inapproximability results for different variants), that is, when each buyer wishes to buy at most one item. Here, we focus on Envy-free Complete Allocation, the special case where a fixed number of copies of each product is available, each of the n buyers must get exactly one product item, and all the products must be sold. This case is known to be solvable in O(n4) time. We revisit a series of results on this problem and, answering a question found in Leonard (1983), show how to solve it in O(n3) time by connections to perfect matchings and shortest paths.