F IGURE 23 C ALCULATION EXAMPLE FOR FORMULAS (4.1), (4.2) AND (4.3)

A subassembly X consists of 100 part types and needs to be assembled in Hal 04. Pre-assembly. These 10 part types can be divided into 50 part types from Lift pick area, 30 from POD pick area and 20 from Heavy pick area.

There is no advantage of picking multiple parts at once for Kit in this example, so the amount of reckoned picks remains respectively 50, 30 and 20 picks. Thus L2.i = 50, P2.i = 30 and H2.i = 20. However, for Kanban there is a picking advantage, the amount of reckoned picks becomes respectively 30, 20 and 20 picks. Thus L1.i = 30, P1.i = 20 and H1.i = 20.

As there is an advantage of Kanban due to the amount of reckoned picks, the average amount of storage locations to be visited is also lower. The travel time in Warehouse (1) for subassembly X when Kanban is used is 60 seconds. Thus T1.i = 60. The travel time in Warehouse (1) for subassembly

X when Kit is used is 90 seconds. Thus T2.i = 90.

The amount of pallets for Kanban replenishment needed per subassembly X is 1.5 for coated parts and 1 for uncoated parts. Thus UCPi = 1 and CPi = 1.5. The amount of Kits needed for coated and uncoated parts are both equal to 1. Thus UCKi = 1 and CKi = 1.

The fixed parameters, see table 2, are the parameters given by PP1, PP2, Pick1, Pick2, Pick3, Pick4. Cost of picking and preparing Kanban parts for one subassembly X in Warehouse (1):

𝐶𝑝𝑖𝑐𝑘.𝑘𝑏𝑛1 = 𝑇1.𝑖+ ∑ (𝑃𝑃𝑖 1∙ (𝑈𝐶𝑃𝑖+ 𝐶𝑃𝑖) + 𝐿1,𝑖∙ 𝑃𝑖𝑐𝑘1+ 𝑃1.𝑖∙ 𝑃𝑖𝑐𝑘2+ 𝐻1.𝑖∙ 𝑃𝑖𝑐𝑘3)

𝐶𝑝𝑖𝑐𝑘.𝑘𝑏𝑛1 = 60 + 60 ∙ (1 + 1.5) + 30 ∙ 36 + 20 ∙ 72 + 20 ∙ 225 = 7230 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 Cost of picking and preparing Kit parts for one subassembly X in Warehouse (1):

𝐶𝑝𝑖𝑐𝑘.𝑘𝑖𝑡= 𝑇2.𝑖+ ∑ ((𝑃𝑃𝑖 1+ 𝑃𝑃2) ∙ (𝑈𝐶𝐾𝑖+ 𝐶𝐾𝑖) + 𝐿2.𝑖∙ 𝑃𝑖𝑐𝑘1+ 𝑃2.𝑖∙ 𝑃𝑖𝑐𝑘2+ 𝐻2.𝑖∙ 𝑃𝑖𝑐𝑘3)

𝐶𝑝𝑖𝑐𝑘.𝑘𝑖𝑡= 90 + (60 + 90) ∙ (1 + 1) + 50 ∙ 36 + 30 ∙ 72 + 20 ∙ 225 = 8850 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 Cost of picking Kanban far parts for one subassembly X in Hal 04. Pre-assembly (4):

𝐶𝑝𝑖𝑐𝑘.𝑘𝑏𝑛2 = ∑ ((𝐿𝑖 2.𝑖+ 𝑃2.𝑖+ 𝐻2.𝑖) ∙ 𝑃𝑖𝑐𝑘4)

41 The total cost of picking is either Cpick.kit or the sum of Cpick.kbn1 and Cpick.kbn2 times the operator cost per

second, OC. Transportation

Transport is facilitated by forklift trucks which can handle (Kit) pallets. Limère et al. (2012) refer to this as a point-to-point transport. On each pallet there is certain available capacity of parts or bins. In literature of Limère et al. (2012) and Sali et al. (2015) most transportation is handled by tugger trains. This is less appropriate at Dewulf because of the size of parts, thus only point-to-point transport is used.

After parts are picked in Warehouse (1), the parts need transportation to either Pre-assembly (4) or Final assembly (5). This transportation time is influenced by the amount and size of parts that do need or do not need coating, the travel distance towards destination, the ratio of the amount of empty and loaded travels, ELT, and the average speed of the forklift truck, V. The travel distances are given by DB for Warehouse (1) to Advanced warehouse (2) via the bridge, D08 for Advanced warehouse (2) to Coating (3), D04 for Advanced warehouse (2) to Pre-assembly (4) and D02 for Advanced warehouse (2) to Final assembly (5). To accommodate the height difference of Warehouse (1) and Advanced warehouse (2) a lift is used with an average lift time per pallet, TL.

The time reckoned for transport of an uncoated (Kit) pallet from Warehouse (1) brought to Hal 04. Pre- assembly (4), α04, is given in formula 4.4 by the amount of travels, including empty travels, ELT, times

the lift time per pallet, TL, added by travel distance DB + D04 divided by average forklift speed V.

𝛼04= (1 + 𝐸𝐿𝑇) ∙ ( 𝐷𝐵+𝐷04

𝑉 + 𝑇𝐿) (4.4)

The time reckoned for transport of an uncoated (Kit) pallet from Warehouse (1) brought to Hal 02. Final assembly (5), α02, is given in formula 4.5 by the amount of travels, including empty travels, ELT,

times the lift time per pallet, TL, added by travel distance DB + D02 divided by average forklift speed

V.

𝛼02= (1 + 𝐸𝐿𝑇) ∙ ( 𝐷𝐵+𝐷02

𝑉 + 𝑇𝐿) ` (4.5)

The time reckoned for transport of a coated (Kit) pallet from Warehouse (1) brought to Hal 04. Pre- assembly (4), β04, is given in formula 4.6 by the amount of travels, including empty travels, ELT, times

the lift time per pallet, TL, added by travel distance DB + 2 ∙ D08 + D04 divided by average forklift speed V. The distance towards Coating, D08, is multiplied by two because parts are brought, but also need to

be picked up after their treatment.

𝛽04= (1 + 𝐸𝐿𝑇) ∙ (

𝐷𝐵+2∙𝐷08+𝐷04

𝑉 + 𝑇𝐿) (4.6)

The time reckoned for transport of a coated (Kit) pallet from Warehouse (1) brought to Hal 02. Final assembly (5), β02, is given in formula 4.7 by the amount of travels, including empty travels, ELT, times

the lift time per pallet, TL, added by travel distance DB + 2 ∙ D08 + D02 divided by average forklift speed V. The distance towards Coating, D08, is multiplied by two because parts are brought, but also need to

be picked up after their treatment.

𝛽02= (1 + 𝐸𝐿𝑇) ∙ (

𝐷𝐵+2∙𝐷08+𝐷02

𝑉 + 𝑇𝐿) (4.7)

Transportation time of pallets for one subassembly i from Warehouse (1) to Pre-assembly (4),Ctpt.kbn04,

42 needed for uncoated parts, UCPi, and coated parts, CPi. These travel times are given by the time

reckoned for transport times the corresponding amount of pallets needed.

𝐶𝑡𝑝𝑡.𝑘𝑏𝑛04 = 𝛼04∙ ∑ (𝑈𝐶𝑃𝑖 𝑖)+ 𝛽04∙ ∑ (𝐶𝑃𝑖 𝑖) (4.8)

The formulations, and corresponding parameters, of UCPi and CPi are described in 4.1.2.3 and 4.1.2.4.

Transportation time of pallets for one subassembly i from Warehouse (1) to Final assembly (5), Ctpt.kbn02,

is given in formula 4.9 by the sum of the amount of the travel time needed for the amount of pallets needed for uncoated parts, UCPi, and coated parts, CPi. These travel times are given by the time

reckoned for transport times the corresponding amount of pallets needed.

𝐶𝑡𝑝𝑡.𝑘𝑏𝑛02 = 𝛼02∙ ∑ (𝑈𝐶𝑃𝑖 𝑖)+ 𝛽02∙ ∑ (𝐶𝑃𝑖 𝑖) (4.9)

The formulations, and corresponding parameters, of UCPi and CPi are described in 4.1.2.3 and 4.1.2.4.

Transportation time of kit pallets for one subassembly i from Warehouse (1) to Pre-assembly (4),Ctpt.kit04, is given in formula 4.10 by the sum of the amount of the travel time needed for the amount

of pallets needed for uncoated parts, UCKi, and coated parts, CKi. These travel times are given by the

time reckoned for transport times the corresponding amount of pallets needed.

𝐶𝑡𝑝𝑡.𝑘𝑖𝑡04= 𝛼04∙ ∑ (𝑈𝐶𝐾𝑖 𝑖)+ 𝛽04∙ ∑ (𝐶𝐾𝑖 𝑖) (4.10)

The formulations, and corresponding parameters, of UCKi and CKi are described in 4.1.2.3 and 4.1.2.4.

Transportation time of kit pallets for one subassembly i from Warehouse (1) to Final assembly (5),Ctpt.kit02, is given in formula 4.11 by the sum of the amount of the travel time needed for the amount

of pallets needed for uncoated parts, UCKi, and coated parts, CKi. These travel times are given by the

time reckoned for transport times the corresponding amount of pallets needed.

𝐶𝑡𝑝𝑡.𝑘𝑖𝑡02= 𝛼02∙ ∑ (𝑈𝐶𝐾𝑖 𝑖)+ 𝛽02∙ ∑ (𝐶𝐾𝑖 𝑖) (4.11)

The formulations, and corresponding parameters, of UCKi and CKi are described in 4.1.2.3 and 4.1.2.4.

A calculation example for usage of the above formulas is described in figure 24 below. Only 4.4, 4.6 and 4.8 are compared, because the other formulas are similar.

43