## Doctoral Theses

### Some Optimization Problems.

February 2011

2-28-2012

#### Institute Name (Publisher)

Indian Statistical Institute

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

Mathematics

#### Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

#### Abstract (Summary of the Work)

In this thesie we have considered two optimisntion problems optinal Erouping in inventory control and optimal cuttine procedures for produots whach are produced in contimous length. The motivation for these two pieces of reseorch work wme actual plant problems encountered in industry. In part I, we have introduced the approach of Group Bcononic Order Qunntity (ECQ) in inventory control and developed optiraum grouping procedures. In Fart II, we have derived a statistical distribution which can te put to use to solve a variety of imuatrial problens. In particular, we have used this diatribution to develop optiman outting parocedures. A brief sunrary of the contents of Farts I and II 1s given below.PART I : GROUP BOQ REPLENISHLEN? POLICY Let A be the per order cost of ordering ard I the cont of ordering expre ased ns rate of interest. We aseume that A and I are the sane for all the itens. The Eeononie Ã¶rder Quantity (EOQ) in tertas of morey value for an individunl iten with money value of yenrly deunni equal to y is given by the well/square-root formula * - / 24Y (1) Then we use the aquare-root formala (1) to calculate the order quantity seperately for each iten, we refer te such a situntion as Individuol BQ Hoplenishnent Policy.Suppoee now that we have a group of N iteme and that the average noney volue of yearly demmnd for the group is y. It is deeised to uoe a oommon ordering rule (nither in terna of money value or of the freyuency of ordera) for all the itema in the group instend of the Individual BOQ Replenishunent Policy. For exxample, for every itea in tlhe group an order of Rs.5000/- war th of aterial may be placed, or every iten in the group nay be ordered 10 times a year. The optiman common group ordering rule in terms of noney value ie the shown to be sivon by when we use a formula of type (2), to caloulate the connon group ordering rule, we refer to the aituation as Group BOQ Replenishment Policy. Use of Group EOQ approach will always mean additioral coss t na compared to Individual EOQ appronch.Let - 0 = yã€‚ãY1ãY2ã€‚ ã-1

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