{"product_id":"9781441918536","title":"Linear and Integer Programming vs Linear Integration and Counting","description":"Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.","brand":"Jean-Bernard Lasserre","offers":[{"title":"Default Title","offer_id":46694439387454,"sku":"9781441918536","price":4260.28,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781441918536_a8e2f5c3-e611-4f35-8f79-d480a8269194.jpg?v=1707461828","url":"https:\/\/exclusivebooks.co.za\/products\/9781441918536","provider":"Exclusive Books Online","version":"1.0","type":"link"}