Multiechelon copy

MULTI-ECHELON INVENTORIES

SCM

SCM is the term used to describe the mgmt of materials and info across the entire supply chain - from suppliers to component producer to final assemblers to distribution to final consumer.

Competition is between supply chains than between individual firms

Component Producer(s)Component Producer(s)

Final AssemblyFinal Assembly

WarehouseWarehouse WarehouseWarehouse

Outside Supplier(s)Outside Supplier(s)

Retail outlet

s

Customers

Landfill

Recy

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Gro

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Sto

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Dis

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Bullwhip Effect

Demand signal processing - if demand increases, firms order more in anticipation

Rationing game - expecting a shortage, firm orders more than the forecast expecting a larger share in short supply

Order batching - fixed costs at one location leads to batching of orders

Manufacturer price variations - which encourage bulk orders

EDI and EDLP are counter measures for bullwhip effect

Central WarehouseCentral Warehouse

Branch WarehouseBranch Warehouse Branch WarehouseBranch Warehouse

Outside Supplier(s)Outside Supplier(s)

Retail outlets

Customers

Deterministic Demand

Sequential Stocking Points with Level Demand

D - Deterministic demand

Aw - fixed cost associated with replenishment at warehouse

AR - fixed cost associated with replenishment at retail outlets

vw - unit variable cost at the warehouse

vR - unit variable cost at the retailer

Qw = nQR Where n = 1,2,3.....

Time

Time

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Level

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Qw

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Deterministic Demand

Echelon stock - of echelon ‘j’ as the number of units in the system that are at, or have passed through, echelon ‘j’ but have as yet not been committed to outside customers

Total inventory carrying costs - by placing an value to any specific echelon inventory at only the value added at that particular echelon

So, warehouse echelon inventory is valued at v’w = vw

Retailer echelon inventory is valued at v’R = vR - vw

In general, v’i = vi - ∑vj

Deterministic Demand

TRC (Qw, QR) = AwD/Qw + Qwv’wr/2 + ARD/QR + QRv’Rr/2

But Qw = nQR, so,

TRC (Qw, QR) = AwD/nQR + nQRv’wr/2 + ARD/QR + QRv’Rr/2

TRC (Qw, QR) = D/QR [Aw/n + AR] + QRr/2 [nv’w + v’R]

Find integer values of ‘n’ and QR that minimizes the total relevant cost

n* = √Awv’R/ARv’w

Q* = √2 [Aw/n + AR]D/[nv’w + v’R]r

ExerciseConsider a particular liquid product that a firm buys in bulk, then breaks down and repackages. So in this case, the warehouse corresponds to the inventory prior to the repackaging operation, and the retailer corresponds to the inventory after repackaging operation. The demand for this item can be assumed to be essentially deterministic and level at a rate of 1000 liters per year. The unit value of the bulk material (v’w or vw) = $1/liter, while the value added by the transforming (break and package) operation v’R = (vR - vw) = $4/liter. Aw = $10 and the setup cost for break and repackage AR = $15 and r = 0.24$/$/yr.

COMPLEXITIES OF PROBABILISTIC DEMAND

Central Central WarehoWareho

useuse

Branch Branch WarehoWareho

useuse

RetailerRetailer

3 weeks

1 week

1 week

Sales

replenishments

replenishments

replenishments

Demands

Information(orders)

Information(orders)

Information(orders)

Consider a centralized single stocking site with a (s, Q) system. Using other notations: D = Annual Demand, A = Ordering cost, vr = holding cost per unit per year. σ = std dev of lead time demand, z = number of std. Dev of lead time demand used to determine safety stock.

TRC (s, Q) = AD/Q + Qvr/2 + vr*ss = Sqrt(2ADvr) + vr*zσ

If we have N such stocking points each with annual demand Di and σi, then TRC = Sqrt(2Avr) * ∑(Sqrt[Di]) + vrz(∑ σi)

Instead if we have a single centralized location, then,

TRC = Sqrt(2Avr)*Sqrt(D) + vrzσ

Where sqrt(D) = Sqrt(∑Di) & σ = sqrt(∑ σi)

CENTRALIZATION OF INVENTORIES

CENTRALIZATION OF INVENTORIES

A vr D z σ √D

100 10 1000 1.64 50 31.62

100 10 2000 1.64 50 44.72

3000 70.7 54.77

Level Decomposition Systems

Minimize ∑ (unit value on item i)*(safety stock on item i)

S.t.c. ∑ (item demand rate/aggregate demand rate)*(item fill rate) ≤ 0.95

Two items (A & B) are valued at $10 and $15 respectively with demand rates of 3/day and 7/day. With an aggregate service level objective of 0.95, the problem would be:

Min 10*SS1 + 15*SS2

S.t.c 0.3(fill rate of item A) + 0.7(fill rate of item B) ≥ 0.95

MULTI-ECHELON INVENTORY

Multiechelon Systems

This is best for effective echelon safety stock. There are different distribution problems like:

1. One origin with several destinations.

2. Several origins with one destination.

3. Several origins with several destinations.

4. Several origins with a consolidation terminal to several destinations.

MULTI-ECHELON INVENTORY

1. dijk - quantity of demand from origin ‘i’ to destination ‘j’ for product ‘k’

2. Qic - Quantity shipped from origin ‘i’ to consolidation terminal ‘c’

3. Qcj - Qty shipped from consolidation terminal ‘c’ to destination ‘j’

4. Wic - Capacity of vehicle from source ‘i’ to destination ‘c’

5. Wcj - capacity of vehicle from ‘c’ to destination ‘j’

ALGORITHM FOR SEVERAL ORIGINS WITH A CONSOLIDATION TERMINAL AND SEVERAL DESTINATION

5. Sic - freight cost of a load from source ‘i’ to consolidation terminal ‘c’ (Setup or Ordering cost)

6. Scj - freight cost of a load from consolidation terminal ‘c’ to destination ‘j’

7. pk - cost or price per unit of item/product ‘k’

8. Given all these notations, the shipping quantity from source ‘I’ to consolidation terminal ‘c’ is given by the following:

Min[Qic, Wic]

And shipping quantity from consolidation terminal ‘c’ to destination ‘j’ is given by, Min[Qcj, Wcj]

Where Qic = (Sic[∑∑dijk]*50/r[∑∑pkdijk/∑∑dijk])1/2 &

Qcj = (Scj[∑∑dijk]*50/r[∑∑pkdijk/∑∑dijk])1/2

Assume that the inventory carrying charges are 20% and that the firm operates fifty periods (weeks) per year. Find the economical qty to ship from each source to the terminal and from the terminal to each destination.

Example

Demand/period at

Product Cost/unitDestinat.

.1Destinat..

2Source

1 20 8 4 1

2 25 6 10 1

3 25 5 8 2

4 30 6 8 2

The demand for products at destinations 1 &2 and the source of these are presented in table of previous slide. The capacity of vehicles, Setup costs, lead time between locations and other imp data are given in table below.

From Source 1 Source 2 Terminal Terminal

To Terminal Terminal Destin..1 Destin..2

Setup cost 45 25 30 35

Vehicle Capacity 150 200 150 100

Lead time (days) 4 2 3 4

S = s + Q (After fixing ‘s’ and ‘Q’ using older methods to each echelon)

Echelon Inventory Position = Echelon stock + On order

Echelon stock is the number of units that are at that echelon ‘j’ and also that have passed through ‘j’ but as yet not specifically committed to outside customers

For ex.: Branch warehouse - 50 units

Retail outlet - 20 units; Suppose 5 units of known customer demand have not yet been satisfied. There is no order outstanding from the branch on the central facility and 10 units are in transit between branch and retail.

Base Stock Control System