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By E. Kay, R Brown, G. Chandler and W. A. Davis (Auth.)

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2. If we evaluate distance in a block of cubicle cells of side 1, in terms of number of cells along, across and upwards, and there are K = aXbXc cells, the average cell distance from origin is given by d = \bc Σ Xi+ac Σ yi+ab £ 0 0 [bc(a-l)a =[ 2 + 0 ac(b-\)b 2 + ζλ/abc J/ ab(c-\)cl 2 \l I f abC (10 la) ' a+b+c—3 / , · * x ~ (a,b,cjCi,yuZi, integers). 3. 1b) should correctly read ίϊ = %[am + gn + dp- {a + g + d\. 1b) is good enough for our purpose. 4. 2) is given by: Minimise £( ax + gy + dz) subject to Hence xyz = K F =- ax-\r gy + dF/dx dF/dy dFldz dF/dk dz~\{xyz~K).

I 42 HANDLING IN A WAREHOUSE \o o o W» o o ^ o o •n o o a s * s * s ■* o o o o o o o o o «N - O SI s \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m \ \ « o o \ o en \ o c> \ o m \ o \ « o \ N « o \ \ trt \ \ «s \ \ \ «M \ \ N N \ \ \ CM \ \ \ N \ \ \ N \ \ \ »S \ \ \ «S \ «s N. \ \ o 1 n \ \ * \ \ * \ \ ■* ■ \ \ ■* \ \ * \ \ * \ \ ■* \ \ -r \ \ \ \ SO \ \o \ \ vO \ \ \o \ \ sO \ \ vC S. \ s© \ \ \o \ \ VO \ •Λ \ \ «O \ \ \ \ «r> \ \ « \ \ "» \ \ *rt \ ' fi 8 S r» 1»· t^ ^ r» r^ ^ r» \ \ \ \ \ \ S.

15. The average maximum stock is given again as (2 — μ)Κ. The old stock which moves relatively rarely, 46 HANDLING IN A WAREHOUSE will on average be μΚ, and movement will take place in the space in front and behind this barrier of old stock, which is centred on the mean line of the cube of volume (2 — μ)Κ. (See Fig. ) I I I I I I FIG. 3. Shaded volume represents space in which on average no movement occurs under LIFO. The average distance for cubical cells can thus be approximated by averaging the average distance in a cube of volume ( 1 — μ)Κ and the average distance of the ( 1 — μ) Κ furthest cells in a cube of volume (2 — μ) Κ.

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