{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T23:52:21Z","timestamp":1773705141079,"version":"3.50.1"},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T00:00:00Z","timestamp":1422835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p>The inventory routing problem (IRP) involves the distribution of one or more products from a supplier to a set of customers over a discrete planning horizon. The version treated here, the so\u2010called vendor managed IRP (VMIRP), is the IRP arising when the replenishment policy is decided a priori. We consider two replenishment policies. The first is known as order\u2010up (OU): if a client is visited in a period, then the amount shipped to the client must bring the stock level up to the upper bound. The latter is called maximum level (ML): the maximum stock level in each period cannot be exceeded. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. VMIRP contains two important subproblems: a lot\u2010sizing problem for each customer and a classical vehicle routing problem for each time period. In this paper we present <jats:italic>a priori<\/jats:italic> reformulations of VMIRP\u2010OU and VMIRP\u2010ML derived from the single\u2010item lot\u2010sizing substructure. These reformulations take into account the special nature of the test instances\u2014constant demand for each client over time and stock\/production upper bounds that are fixed small multiples of the client's demand. In addition we introduce two new cutting plane families\u2014the cut inequalities\u2014deriving from the interaction between the lot\u2010sizing and the routing substructures. A branch\u2010and\u2010cut algorithm has been implemented to demonstrate the effectiveness of the single\u2010item reformulations. Computational results on benchmark instances with 50 customers and six periods with a single product and a single vehicle are presented. \u00a9 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(2), 129\u2013138 2015<\/jats:p>","DOI":"10.1002\/net.21586","type":"journal-article","created":{"date-parts":[[2015,2,2]],"date-time":"2015-02-02T10:33:08Z","timestamp":1422873188000},"page":"129-138","source":"Crossref","is-referenced-by-count":27,"title":["Single\u2010item reformulations for a vendor managed inventory routing problem: Computational experience with benchmark instances"],"prefix":"10.1002","volume":"65","author":[{"given":"Pasquale","family":"Avella","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Universit\u00e0 del Sannio Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maurizio","family":"Boccia","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Universit\u00e0 del Sannio Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurence A.","family":"Wolsey","sequence":"additional","affiliation":[{"name":"Center for Operations Research and Econometrics Universit\u00e9 catholique de Louvain Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2015,2,2]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2013.0550"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1100.0439"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.1060.0188"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1050.0223"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13676-012-0016-7"},{"key":"e_1_2_9_7_1","first-page":"1","article-title":"and G. 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