(See [2] for a basic de nition.) The TPP property for the triple (S, T, U) is invariant under permutations of the triple, that is, the permuted triples (S,U, T ), (T, S, U), (T,U, S), (U, S, T ), (U, T, S) all satisfy the TPP i (S, T, U) satis es the TPP, ([6], p. 45). We denote by =(G) the set of all TPP triples of G, and by =(G)/Sym3 the set of equivalence classes of =(G) under the equivalenc...

Patients with suspected myocardial infarction (MI) now account for a considerable proportion of acute medical admissions, whose number seems to be rising inexorably. Figure 1 shows the rise in such admissions to the Nottingham hospitals since 1982.1 No sensible provider is going to agree anything with a purchaser, based on the previous year's figures, even though we might have hoped that the nu...

While all of medicine is under pressure to increase transparency and accountability, joint replacement subspecialists will face special scrutiny. Disclosures of questionable consulting fees, a demographic shift to younger patients, and uncertainty about the marginal benefits of product innovation in a time of great cost pressure invite a serious and progressive response from the profession. Cur...

While all of medicine is under pressure to increase transparency and accountability, joint replacement subspecialists will face special scrutiny. Disclosures of questionable consulting fees, a demographic shift to younger patients, and uncertainty about the marginal benefits of product innovation in a time of great cost pressure invite a serious and progressive response from the profession. Cur...

The Traveling Purchaser Problem (TPP) looks for a tour visiting a subset of markets to satisfy a positive discrete demand for some products at minimum traveling and purchasing costs. The problem is known to be NP-hard in the strong sense, and finds application in different real contexts. Frequently, as a static problem, the TPP lacks of realism: different purchasers may compete for the same res...

The Travelling Purchaser Problem (TPP) is a known generalization of the Travelling Salesman Problem, and is defined as follows. Let us consider a set of products and a set of markets. Each market is provided with a limited amount of each product at a known price. The TPP consists in selecting a subset of markets such that a given demand of each product can be purchased, minimizing the routing c...

We present novel branch-and-check and logic-based Benders decomposition techniques for the Travelling Purchaser Problem, an important optimization problem with applications in vehicle routing, logistics, and warehouse management. Our master problem determines a set of markets and directed travel arcs that satisfy product purchase constraints with relaxed travel costs. Our subproblem identifies ...