Logistics

Warehousing

OverviewExamplesPurposes and functionsStrategic decisionsWarehouse layoutReceiving and Shipment Zones: SizingStorage Zone: CapacityStorage Zone: Sizing (Length, Width, Height)Product Allocation Dedicated SpaceOrder batchingOrder pickingRecent developments

Typical covered warehouse

Purposes and functionsReceivingHoldingPickingShippingReceivingHoldingPickingReceivingHoldingPickingReceivingHoldingPickingBatch formingPackagingShipping

Strategic issuesType of storage racks / type of palletMaterial handlingWarehouse lay-out

Storage racksStandard Pallet RackingNarrow Aisle Pallet RackingDouble Deep Pallet RackingPower-mobile pallet racksDrive-In Pallet RackingEtc.

Standard Pallet Racking Offers direct and fast accessibility to each individual pallet.

Low space utilisation.

Utilises standard fork trucks and hand trucks.

Narrow Aisle Pallet Racking Offers direct and fast accessibility to each individual pallet.

The aisle width needs only to be slightly larger than the pallet load, therefore high utilisation of warehouse space.

Double Deep Pallet Racking Using a double deep lift truck, the operator places the back pallet into the system first, then places another pallet in front of it. This gives twice as many pallets stored for a given number of aisles and offers a similar space utilization to Narrow Aisle Racking, however, individual access to every pallet is compromised.

Mobile Pallet Racking Pallet racks are mounted on mobile bases, these travel on tracks laid into the floor. Offers direct but slow accessibility to each individual pallet.

Very high space utilisation.

Drive-In Pallet Racking Works on a first in / last out (FILO) basis. Limited access to individual pallets.

Maximum utilisation of warehouse space.

Uses standard pallet trucks.

Material handlingManualForklift trucks (Straddle truck, Reach truck, Counterbalanced truck, Free-path narrow-aisle machine, Rising cabs, Two-deep reach, Stacker cranes)Conveyors

Articulated CB truck

Counterbalanced fork-lift truck

Reach truck

High track stacker truck very narrow aisle

Powered pallet truck

Conveyor

AGV with Conveyor

Warehouse layout

Warehouse layout: ZonesUsually 3 types of zones in a warehouse:receiving zone(s)storage zone (sometimes divided into reserve and forward zone)shipping zone(s)

Warehouse layout: IssuesReceiving and Shipment Zones: SizingStorage Zone: CapacityStorage Zone: Sizing (Length, Width, Height)Product Allocation Dedicated Space

Order batchingOrder picking

Sizing the Receiving and Shipment Zonesreceiving zone usually larger than the shipping zone

determine the number of truck docksddaily demand of ordersttime for load/unload a truckq(average used) truck capacityTdaily time available to load/unload

Storage Capacitydedicated spaceeach product is stored in a specific areaassign storage location to productsrandom space: products can be stored anywherethe products are randomly distributed over the warehouse

Inventory of product j at time t

Tabelle1

space

productbatch sizesafety stockdedicatedrandom

110002001200700

2250040029001650

3116001250128507050

48503001150725

5175050022501375

64500100055003250

7260095035502250

total space:2940017000

Tabelle2

Tabelle3

Storage Zone Length, Width, Height (1)Height is usually determined by the S/R (Storage / Retrieval) technology12345678910111225643

Lagrangean relaxation (LR)minsuch that

Storage Subsystem Length, Width, Height (2)

Product Allocation Dedicated Space (1)divide the warehouse into M (square) grids of same storage capacityeach product j (j=1,..,n) requires mj grid squaresassume(add dummy product)

pj is the total loads moved per time unit for product j

Product Allocation Dedicated Space (2)

Product Allocation Dedicated Space (3)Integer program:

minimize:

subject to

Product Allocation Dedicated Space (4)Without loss of generality (we can always set ), we assume that

Product Allocation Dedicated Space (5)Binary program:

minimize:

subject to

Product Allocation Dedicated Space (6)Rewriting objective: minimize

Product Allocation Dedicated Space (7)Optimal Solution

[Order Grids]: Compute the tk for all grids and sort them in non-decreasing order, such that t[1] t[2] t[3] [Order Products]: Put the products in non-increasing order, such that p[1] / m[1] p[2] / m[2] p[3] / m[3] [Assign Products]: For j=1,n assign product j to the first mj grid squares still available.

Product Allocation Dedicated Space (8)Optimality Proof

Take any solution with a different order. Then there must be two grids stocking products k and l with t[k] < t[l] and p[k] / m[k] < p[l] / m[l].

Swapping the grids increases cost by

t[k] p[l] / m[l] + t[l] p[k] / m[k] t[k] p[k] / m[k] - t[l] p[l] / m[l]

= ( t[k] t[l] )( p[l] / m[l] p[k] / m[k] )

< 0So, the suggested solution cannot be optimal. Q.E.D.

Example (1)

Example (2)I/Otk4.51.5

Example (3)I/OI/Otkproductsp[2] / m[2] p[3] / m[3] p[1] / m[1]

558844773366

336644775588

Product Allocation Dedicated Space (8)Other issuesClustering of products with correlated demandBalancing of workload for pickers/machinesMinimising risk of damage

Order batching (orders are combined to batches) HeuristicsMost start with a seed order and then expand the batch with orders in close proximity so long as vehicle capacity is not exceeded.Different proximity measures: number of common locations/aisles, sum of distances for each location/aisles in candidate order to closest location/aisles already in batch.Some rules have been proposed that consider due dates.Remark: order batching may not always be possible, in which case each order is retrieved individually.

Order Picking (1)xxxxxTravelling Salesman Problem (TSP):How to determine the travelling times?StartOne-dimensional presentation of Two-dimensional situation!

Order Picking (2) crossovers only allowed at ends of aislesxxxxxStart

Order Picking (3) Routing methodsS-shape, start aisle 1Optimal, start aisle 1Largest gap, start aisle 1

Largest gap: (go into an aisle until the largest gap) for warehouses without cross aisles.

S-shape: (traverse always through an aisle if products in it need to be picked) if many locations have to be visited (more than 3 picks per aisle). Also to prevent congestion or to enforce one-way traffic.

Optimal methodOrder Picking (4) Routing methods

Order PickingSo far, we have assumed a Picker-to-product environment, but sometimes it is Product-to-picker (Order-to-picker):AS/RSCarousel

Automated Storage Retrieval Systems AS/RS: S/R machine for each aisle; pick-up and delivery station located at the end of each aisleWalk/ride and pick system (W/RPS) (may visit multiple aisles)

Product to picker: Horizontal carousel

Horizontal carousel

Horizontal carouselPicking placeWhat is the optimal route?

Horizontal carouselPicking placeThe optimal route admits at most one turn!

Horizontal carouselPicking placeWhere to place fast moving (frequently demand) and slow moving items?

Horizontal carouselPicking placeWhere to place fast moving (frequently demand) and slow moving items?

Small orders: fast movers close to the picking place.Large orders: slow movers close to the picking place.

Horizontal carousel: large ordersxxxxxxxxxxxFast moversSlow moversxxxxxxxxxxxFast moversSlow moversLarge orders: Better to putslow movers close to the picking place.

Horizontal carousel: small ordersxxxxxFast moversSlow moversxxxxxxFast moversSlow moversSmall orders:Better to putfast movers closeto the picking place.

Horizontal carousel:Nearest neighbour heuristicIn practice, the nearest neighbour heuristic is often applied for carousels. On average, that performs quite well.

But what is the worst case behaviour?

Recent developments

pick-to-light, pick-to-belt

SortingUse of high capacity sortation systems withautomatic scanningRingsorter

Enabling technologies: Sorting & DispatchSource: PSB, 2000Source: VanderLande

CrossdockingIn a crossdock, goods arriving from the vendor already have a customer assigned, so workers need only move the shipment from the inbound trailer to an outbound trailer bound for the appropriate destination.Crossdocking essentially eliminates the inventory-holding function of a warehouse while still allowing it to serve its consolidation and shipping functions.Shipments typically spend less than 24 hours at the facility, sometimes less than an hour.

Merge-in-transitMerge-in-transit is similar to cross-docking, but differs in the way orders are fulfilled. With merge-in-transit, it is essential to identify all the component/shipments of a single order in the merging terminal and to ensure that all the components are delivered at once, delaying the earliest shipments if necessary.

In a cross-docking situation the emphasis is more on process efficiency, as the shipments incoming to a terminal are forwarded with the next delivery to the customer, often regardless of the order they belong to.

The operational efficiency achievable with merge-in-transit is not as high as with cross-docking, but it can be economically performed with a wide product offering and a large customer-base.