Heavy Traffic Analysis of Dynamic Cyclic Policies a Unified Treatment of the S

Cover Heavy Traffic Analysis of Dynamic Cyclic Policies a Unified Treatment of the S
Heavy Traffic Analysis of Dynamic Cyclic Policies a Unified Treatment of the S
David Maxwell Markowitz
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Let the average setup time per cycle s he greater than zero. If region II conditions hold as w -^ oc, then \ (n-) = — u' + o[ic).
where 0' is five . Sef containing the standardized products and the cheapest hackorder product (this product could he customized or standardized) and 9 V Pji^-Pj) -- 2^jee' h;+h; If region III conditions liold as U' — >■ 3c. Then ;o3) V'(»') = - — w + o{w). (54) c 31 Property 2. If the setup cost per cycle I\ = ami all of the products are staudardized. Then the polic
...y at the idling threshold icq satisfies the region II ci)nditions if and only il /), = hj for all i and J. If this condition holds then //■/;, 7^ I) J for some i and j then the idling threshold satisfies the region I conditions and T-{Wo) = 0.
Property 3. If average setup time s is greater than zero, region II conditions hold in the limit as tc — >• oo if and only if the tardiness costs of all the standardized products are ecpial and the cheapest tardiness cost among the customized products is equal to or greater than the standardized tardiness cost (or if the tardiness cost of all of the customized products are equal and there are no standardized products).


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