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Logistics cost. Componenti del costo logistico.

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Componenti del costo logistico
Componenti del costo logistico

Costi di trasporto(in ingresso, intra-company. in uscita) Costi di magazzino(immagazinamento e deposito dei prodotti, localizzazione del deposito e della azienda) Costo di mantenimento scorte(capitale per materie prime, WIP, prodotti finiti, scarti) Costi di acquisto/produzione lotti

(movimentazione materiali, messa a punto linee)

Costo degli imballi per trasporto e movimentazione

(pallet, materiali da imballaggio, altri) Costi amministrativi/di struttura(direzione, personale amministrativo, sistemi informativi, elaborazione ordini)

Time space diagrams




Time space diagrams

Consider a simple Product to Consumption Network

Primary Tradeoffs:

Moving (Handle, Transport)/Holding (Rent, Inventory)

Cumulative count curve


Cumulative count curve

Shipments Arrivals

Horizontal distances

  • Transit time tm

  • Headway hi

Vertical distances

  • Items waiting transport nw

  • Items in transit nt

  • Items at destination nd

Cumulative Count of Items








Logistics cost lc function
Logistics cost LC function

LC (per item) = Holding Costs + Moving Costs

Holding Costs = Rent Cost + Inventory Cost

Moving Costs = Transport Cost + Handling Cost

LC (per item) = (R + I) + (T + H)

Rent cost r item
Rent cost R (€/item)

Function of max inventory

Captures facility costs

Not affected by the item by item flow

AnnualRentCost = cr Dhmax

R = cr hmax

D = Annual demand (items/time)

cr = Rent cost (€/item-time)

hmax = Maximum headway (time)

Inventory cost i item
Inventory cost I (€/item)

Function of delay to items.

Captures capital costs, insurance, etc.

Implies that each time period matters equally

Constant to each time period (linear)

Annual Inventory Cost = ci D(1/2ħ + tm)

I = ci(1/2ħ + tm)

ci = Inventory cost (€/item-time)

ħ = average headway

tm =Transit time

Transport cost t item
Transport cost T (€/item)

Shipment size u has a shipment cost s

s = cf + cvv

the cost of n shipments is

ns =Sn(cf + cvvi) =ncf + cvSnvi =ncf + cvD

The transport cost T is

T = cf (n/D) + cv = cf /ū+ cv

T decreases with increase in average shipment size ū.


cf = Fixed transport cost (€/shipment)

cv = Variable transport cost (€/item)

u = Shipment size (items)

D = Annual number of items shipped = Snu

ū = D/n average shipment size

n = number of annual shipments

Transport costs t with headways h
Transport costs T with headways h

Number of items in an average shipment

ū = Dħ

T decreases with increase in average ħ

I increases with ħ

T = cf /Dħ + cv = cf /ū + cv

cf = Fixed transport cost (€/shipment)

cv = Variable transport cost (€/item)

Transport costs and distance
Transport costs and distance

“Fixed” costs cf are variable with number of delivery stops ns and distance d

Variable costs have a fixed component and a linear component variable with distance d

cf = cfs (1 + ns ) + cfdd

cv = cvs + cvdd

T = cf /ū + cv

T = cfs (1 + ns )/ū + cfdd/ū + cvs + cvdd

Marginal cost of an additional item ignore cvd

Transport costs in relation to capacity

Transport Cost per Shipment

CMAX= Maximum capacity for transport mode (items)




Shipment Size


Transport costs in relation to capacity

ft(u) is sub-additive: ft(u1+u2)≤ ft(u1)+ft(u2)


Transport costs with multiple modes

Mode 1

Transport Cost per Shipment

Mode 2

Mode 3



Shipment Size

Transport costs with multiple modes

Handling costs h item
Handling costs H (€/item)

Loading items into boxes, pallets, containers, etc.

  • If handled individually – linear with each item

  • If handled in batches – fixed & variable components

    H = cfh + cvhCh

    Ch= capacity (items) for load unit h

Moving costs t h item
Moving costs T + H (€/item)

T + H = cf/ū + (cv + cfh /ChMAX + cvh)

T + H= cfs(1+ ns)/ū + cfdd/ū + cvs+ cfh/ChMAX+ cvh

Generally handling costs are subsumed within transport costs as long as D>>ChMAX (total shipment size is much greater than pallet)

Total logistics cost lc function
Total logistics cost LC function

LC(€/item) = crhmax+ 1/2ciħ+ citm + cfs(1+ns)/ū + cfdd/ū + cvs

cr = Rent cost (€/item-time)

ci= Inventory cost (€/item-time)

tm =Transit time

hMAX= Maximum headway (time)

cfs= Fixed cost per stop (€/stop)

cfd= Cost per distance (€/distance)

cvs= Marginal cost per item

ns= Number of delivery stops

d = distance

ū = D/n = Dħ average shipment size

Total logistics cost function
Total logistics cost function

VMAX = Maximum capacity for transport mode (items)

Optimum shipment and headway
Optimum shipment and headway

LC(€/item) = crhmax+ 1/2ciħ+ citm + cfs(1+ns)/ū + cfdd/ū + cvs

ū = D/n = Dħ average shipment size

LC(€/item) = crhmax+ 1/2ciū/D+ citm + cfs(1+ns)/ū + cfdd/ū + cvs

dLC/dv = 1/2ci/D - cfs[(1+ns) + cfdd]/ū2 = 0

ū* = {2cfsD[(1+ns) + cfdd]/ci}1/2

The size ū* increases with respect to the square root of D, and the square root of d.

The optimum delivery frequency D/ū* will increase in proportion to the square root of Dand will fall with respect to the square root of d.