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1 Logistics Management - Formulas 1 STORAGE SYSTEMS Storage Capacity assessment [FF = forecasting factor; i = product family, item; j = month/period] 𝑁𝑆𝑗 = βˆ‘π‘†πΆπ‘–π‘—π‘– #locations occupied by an item i for a period j [SC = starage capacity] - Random storage 𝑆𝐢 = π‘šπ‘Žπ‘₯𝑗{𝑁𝑆𝑗} βˆ— 𝐹𝐹 -> maximum value that I have considering the sums of all the values of each month - Dedicated storage 𝑆𝐢 = βˆ‘(π‘šπ‘Žπ‘₯𝑗{𝑁𝑆𝑖,𝑗} βˆ— 𝐹𝐹𝑖)𝑖 -> sum of the maximum values that I have for each month - Class based storage π‘†πΆπ‘˜ = βˆ‘(π‘šπ‘Žπ‘₯𝑗{π‘π‘†π‘˜,𝑗} βˆ— πΉπΉπ‘˜)π‘˜ Storage area - Bay design β†’ draw and compute W, H, D 𝑁𝑃𝐡 = ⌊ π‘Šπ‘π‘Žπ‘¦ π‘Šπ‘ƒπΏ βŒ‹ [#pallet locations in a bay] - Module design β†’ π΄π‘šπ‘œπ‘‘π‘’π‘™π‘’ = (2𝐷 + π΄π‘Š) βˆ— π‘Š - Number of levels β†’ 𝑁𝐿= π‘šπ‘–π‘›{⌈ 𝑅𝐻 𝐻 βŒ‰ ; ⌊ 𝐡𝐻 𝐻 βŒ‹} [RH = rack height; BH = building height] - Area utilization rate β†’ π΄π‘ˆπ‘…π‘šπ‘œπ‘‘π‘’π‘™π‘’ = π‘ƒπΏπ‘ π‘šπ‘œπ‘‘π‘’π‘™π‘’ π΄π‘šπ‘œπ‘‘π‘’π‘™π‘’ = 2βˆ—NPBβˆ—NL Amodule - Required area π΄π‘ˆπ‘…π‘šπ‘œπ‘‘π‘’π‘™π‘’ = 𝑆𝐢 𝐴 β†’ 𝐴 = 𝑆𝐢 π΄π‘ˆπ‘…π‘šπ‘œπ‘‘π‘’π‘™π‘’ - if the rack length is fixed (π‘ˆ = 𝑅𝐿) o 𝑁𝐢 = ⌊ 𝑅𝐿 π‘ŠβŒ‹ o 𝑁𝐴= ⌈ 𝑆𝐢 2βˆ—π‘π‘ƒπ΅βˆ—π‘πΏβˆ—π‘πΆβŒ‰ o 𝑉 = π‘π΄βˆ— π‘Šπ‘šπ‘œπ‘‘π‘’π‘™π‘’ - If we do not know the rack length, according to the position of the I/O point β†’ expected path 𝑃 = 2 βˆ— ( π‘ˆ π‘Ž + 𝑉 2) β†’ π‘ˆπ‘œπ‘π‘‘ = π‘Ž 2 βˆ— π‘‰π‘œπ‘π‘‘ o I/O in the middle of the storage front π‘Ž = 4 𝑃 = 2 βˆ— ( π‘ˆ 4 + 𝑉 2) Uopt = 2 Vopt o I/O on the vertex of the storage front π‘Ž = 2 𝑃 = 2 βˆ— ( π‘ˆ 2 + 𝑉 2) Uopt = Vopt o I/O distributed along the storage front π‘Ž = 3 𝑃 = 2 βˆ— ( π‘ˆ 3 + 𝑉 2) Uopt = 1,5 Vopt o Number of aisles 𝑁𝐴= ⌈ π‘ˆπ‘œπ‘π‘‘ π΄π‘Š+2π·βŒ‰ o Number of bay columns 𝑁𝐢 = ⌈ 𝑆𝐢 2βˆ—π‘π΄βˆ—π‘π‘ƒπ΅βˆ—π‘πΏβŒ‰ o π‘ˆπ‘Ÿπ‘’π‘Žπ‘™ = π‘π΄βˆ— (π΄π‘Š+ 2𝐷) [π‘š] o π‘‰π‘Ÿπ‘’π‘Žπ‘™ = π‘πΆβˆ— π‘Š [π‘š] o 𝐴 = π‘ˆ βˆ— 𝑉 - Real storage capacity: π‘†πΆπ‘Ÿπ‘’π‘Žπ‘™ = 2 βˆ— π‘π΄βˆ— π‘πΆβˆ— π‘π‘ƒπ΅βˆ— 𝑁𝐿 2 NB: if we have a block stacking storage areas - π‘π‘ƒπ‘™π‘Žπ‘›π‘’ = ⌈ 𝑆𝐢 #π‘–π‘‘π‘’π‘šπ‘ βˆ—π‘ƒπΏ/π‘ π‘‘π‘Žπ‘π‘˜βˆ—#π‘™π‘Žπ‘›π‘’π‘ /π‘–π‘‘π‘’π‘šβŒ‰ - π‘ˆ = π΄π‘Š+ 2 βˆ— [π‘π‘ƒπ‘™π‘Žπ‘›π‘’ βˆ— (𝐷𝑃𝐿 + π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’π‘ƒπΏ) + π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’π‘ƒπΏ] - 𝑉 = (π‘Šπ‘ƒπΏ + π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’π‘ƒπΏ) βˆ— #π‘™π‘Žπ‘›π‘’π‘  - 𝐴 = π‘ˆ βˆ— 𝑉 - 𝑉𝑇𝑆𝐢𝐢 = π‘ƒπ‘Žπ‘–π‘ π‘™π‘’ 𝑠𝐻,π‘Žπ‘–π‘ π‘™π‘’ + π‘ƒπ‘™π‘Žπ‘›π‘’ 𝑠𝐻,π‘™π‘Žπ‘›π‘’ + 𝑆 𝑠𝑉 o π‘ƒπ‘Žπ‘–π‘ π‘™π‘’β€¦

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