SCM Inventory Part-III

Inventory ManagementPart-III

Aggregating Multiple Products in a Single OrderCycle inventory is proportional to lot size.Lot size can be reduced by reducing ordering costs for a given demand.

Fixed ordering costs can be reduced either directly or by aggregation

Aggregating orders and deliveries across multiple products spreads ordering costs across multiple products.

This helps in reducing the lot size for each product and cycle inventory.

Illustration:Best Buy purchases four computer models . Demand for each of the model is 1000 units per month. Best Buy incurs a fixed order placement, transportation and receiving cost of $4000 each time an order is placed. Each Computer costs Best Buy $ 500 and it incurs a holding cost of 20 percent. All four models originate from the same supplierWhat is the lot size and cycle inventory if all four models are ordered separately.What is the lot size and cycle inventory if all four models are aggregated in a single order.

4-*Aggregating Multiple Products in a Single Order

a)For each model, D = 12 x 1000 = 12000, Co (or S) = 4000, C= 500, i (or h) = 20 %, Cc = 500 x .20 = 100Q* = 980 for each model, cycle inventory for each model = 980 / 2 = 490Total Cycle inventory (for all models)= 4 x 490 = 1960 4-*Aggregating Multiple Products in a Single Order

b) Since all models originate from same supplier, benefit of aggregation can be obtained e.g. all orders can arrive in the same truck

Now we have single order which contains all four modelsD = 4 x 12 x 1000 = 48000, Co (or S) = 4000, C= 500, i (or h) = 20 %, Cc = 500 x .20 = 100Q* = 1960, Total Cycle inventory (for all models)= 1960/ 2 = 980Note a single order contains 490 (=1960/4) units of each model as compared to 980 for each model in previous case.Thus lot size and cycle inventory and costs are reduced.

4-*Aggregating Multiple Products in a Single Order

Aggregating Multiple Products in a Single OrderAggregation can be achieved by :Aggregating multiple products from single supplierAggregating deliveries from multiple suppliers into a single truckAggregating deliveries to multiple retailers into a single trucke.g. In Wal Mart, typically each supplier sends full truck load to cross docking DC which contains aggregated delivery destined for multiple retail stores. Each out bound truck contains products aggregated from several suppliers destined for single storeThus,Aggregating replenishment across multiple products, retailers or suppliers in a single order allows for reduction in lot size for individual products and thereby cycle inventory & costs.

This happens because fixed costs including transportation costs are spread across multiple products, retailers, suppliers

Lot Sizing and Costs with Multiple Products or Customers Impact of AggregationCombining multiple products in a single order increases varietyPart of ordering costs i.e. transportation costs are independent of varietyOther part of ordering costs i.e. receiving and loading costs increases with variety of products in a single order.Hence, S:Common order cost - Order cost incurred each time an order is placed, independent of the variety of products in the order si:Product specific order cost - Additional order cost incurred if product i is included in the order (can be different for different product) Di: Annual demand for product i

Lot Sizing with MultipleProducts or Customers Impact of AggregationIn general there can be three approaches in ordering of multiple products

1. Each product manager orders his or her model independently

Each product is ordered independentlyEach product is delivered independently in a separate truckNo aggregation is doneEasy to coordinateResults in high costs

Lot Sizing with MultipleProducts or Customers Impact of AggregationIn general there can be three approaches in ordering of multiple products- Complete Aggregation

2. The product managers jointly order every product in each lotMultiple products are ordered jointlyEach order contains all the different products Multiple product s are delivered jointly in same truckDisadvantage is low demand products can be aggregated with high demand products in every order.However , it is better to order low demand product less frequently than high demand products.Easy to administer / coordinate but can result in high costs

Lot Sizing with MultipleProducts or Customers Impact of Aggregation

3. Product managers order jointly Tailored AggregationIt is not necessary that every order contains every productEach lot contains a selected subset of the productsSelective approachComplex to administer / coordinate but results in low costs

In all the above three approaches to ordering in case of multiple products , third approach leads to minimum costs.

Illustration-

Best Buy sells three models of computers, the Litepro, the Medpro and the Heavypro. Annual demand for the three products are 12,000/yr, 1,200/yr and 120/yr respectively. Each model costs Best Buy $500. A fixed transportation cost of $4000 is incurred each time an order is delivered. For each model ordered and delivered on the same truck, an additional fixed cost of $1000 is incurred for receiving and storage. Beat Buy incurs a holding cost of 20 percent.

Evaluate lot sizes that Best Buy manager should order Also evaluate the annual costs of such policy by employing three approaches to ordering as discussed before.

4-*Lot Sizing with MultipleProducts or Customers Impact of Aggregation

Approach 1 : Multiple Products Ordered and Delivered IndependentlyApproach 1 : lots for each product are ordered and delivered independently.

Demand DL = 12,000/yr, DM = 1,200/yr, DH = 120/yr

Common order cost S = $4,000

Product-specific order cost sL = $1,000, sM = $1,000, sH = $1,000

Holding cost h = 0.2

Unit cost CL = $500, CM = $500, CH = $500

Multiple Products Ordered and Delivered Independently Total annual cost = $155,140

LiteproMedproHeavyproDemand per year12,0001,200120Fixed cost/order$5,000 $5,000$5,000Optimal order size1,095346110Cycle inventory54817355Annual holding cost$54,772$17,321$5,477Order frequency11.0/year3.5/year1.1/yearAnnual ordering cost$54,772$17,321$5,477Average flow time2.4 weeks7.5 weeks23.7 weeksAnnual cost$109,544$34,642$10,954

Approach 2 : Illustration- Lots/Products are ordered and delivered jointly for all the three models. All models are included each time an order is placed.

Evaluate lot sizes and the annual costs of such policy


Lots Ordered and Delivered Jointly

Lots / Products Ordered and Delivered JointlyAnnual order cost = 9.75 x 7,000 = $68,250Annual ordering and holding cost= $61,512 + $6,151 + $615 + $68,250 = $136,528

Products Ordered and Delivered Jointly Total annual cost = $ 136,528, Note this approach which utilizes aggregation reduces total costs by about 12 % (as compared to Approach 1 without any aggregation)

LiteproMedproHeavyproDemand per year (D)12,0001,200120Order frequency (n)9.75/year9.75/year9.75/yearOptimal order size (D/n)1,23012312.3Cycle inventory61561.56.15Annual holding cost$61,512$6,151$615Average flow time2.67 weeks2.67 weeks2.67 weeks

Approach 3 : Illustration- Lots/Products are ordered and delivered jointly for a selected subset of products. All models are not included each time an order is placed.

Selective in aggregating or combining different products that are ordered jointly in a single order

Each lot contains only selected product orders with a aim to minimize costs

Evaluate lot sizes and the annual costs of such policy


In Approach 3:

It utilizes a heuristic, solution not optimal but close to it. First identify the most frequently ordered product that will be included in every order.The common order cost is then entirely allocated to this productFor each of the less frequently ordered products i, the ordering frequency is determined using only the product-specific ordering costs Si.Each product i is included in every mi orders, mi is an integer which is calculated4-*Lot Sizing with MultipleProducts or Customers Impact of Aggregation

Let product are indexed by ii varies from 1 to l (total nos. of products are l)Each product i has:annual demand of Di , product specific order cost of si, unit cost CiCommon order cost is SAll n denotes ordering frequencymi is an integer4-*Lot Sizing with MultipleProducts or Customers Impact of Aggregation

Lots Ordered and Delivered Jointly for a Selected SubsetStep 1:Identify the most frequently ordered product assuming each product is ordered independentlyThe most frequently ordered product is i* which is included each time order is placed

represents the desired order frequency if product i incurs product specific fixed order cost only each time it is ordered. 4-*Lots Ordered and Delivered Jointly for a Selected Subset

Lots Ordered and Delivered Jointly for a Selected SubsetStep 3:For all i i*, evaluate the frequency of product i relative to the most frequently ordered product i* to be mi

Goal is to include each product i i* with the most frequently ordered product after an integer nos. of orders. This integer no. is denoted by mimi is obtained by rounding off to nearest integerProduct i shall be included with most frequently ordered product i* every mi ordersNote for most frequently ordered product mi = 1For less frequently ordered product mi shall be greater than more frequently ordered product

4-* Note now with most frequently ordered product, in each order, we are also including some other product i.This shall have impact on holding as well as ordering costs.This need to be taken into account for a better estimate of ordering frequency of most frequently ordered product. Lots Ordered and Delivered Jointly for a Selected Subset

Lots Ordered and Delivered Jointly for a Selected SubsetStep 5:Evaluate an order frequency of ni = n/mi with n calculated in Step 4. Also calculate the total cost of such an ordering policyThe above heuristic results in Tailored aggregation Higher-demand products ordered more frequently and lower-demand products ordered less frequently

Ordered and Delivered Jointly Frequency Varies by OrderApplying Step 1Approach 3: Steps 1 to 5 applied to Best Buy problem

Ordered and Delivered Jointly Frequency Varies by OrderApplying Step 2

Ordered and Delivered Jointly Frequency Varies by OrderApplying Step 4Annual Holding Costs = $ 65,383.5

Ordered and Delivered Jointly Frequency Varies by Order Total annual cost = $ 130,767Note this approach which utilizes tailored aggregation reduces total costs by about 4 % (as compared to Approach 2 with complete aggregation)

LiteproMedproHeavyproDemand per year (D)12,0001,200120Order frequency (n)11.47/year5.74/year2.29/yearOptimal order size (D/n)1,04620952Cycle inventory523104.526Annual holding cost$52,307$10,461$2,615Average flow time2.27 weeks4.53 weeks11.35 weeks

Note: As discussed before, Approach 1 is no aggregation, Approach 2 is complete aggregation and Approach 3 is Tailored Aggregation

If product specific ordering costs are small relative to common fixed ordering costs, then tailored aggregation provides little additional value, in this case complete aggregation is effective.

If product specific ordering costs are high relative to common fixed ordering costs, then tailored aggregation provides is effective.


Optimal Order Frequency when aggregating k nos. of items is given by:

Truck capacity for a single delivery need to be compared with total load for the optimal order frequency.

If optimal load exceeds truck capacity, n* should be increased until load equals truck capacity

4-*Aggregation and Capacity Constraint

Managing MultiechelonCycle InventoryMulti-echelon supply chains have multiple stages with possibly many players at each stage

Lack of coordination in lot sizing decisions across the supply chain results in high costs and more cycle inventory than required

The goal is to decrease total costs by coordinating orders across the supply chain

Managing MultiechelonCycle InventoryFigure 11-6

Integer Replenishment PolicyDivide all parties within a stage into groups such that all parties within a group order from the same supplier and have the same reorder interval

Set reorder intervals across stages such that the receipt of a replenishment order at any stage is synchronized with the shipment of a replenishment order to at least one of its customers

For customers with a longer reorder interval than the supplier, make the customers reorder interval an integer multiple of the suppliers interval and synchronize replenishment at the two stages to facilitate cross-docking

Integer Replenishment PolicyFor customers with a shorter reorder interval than the supplier, make the suppliers reorder interval an integer multiple of the customers interval and synchronize replenishment at the two stages to facilitate cross-docking

The relative frequency of reordering depends on the setup cost, holding cost, and demand at different parties

These polices make the most sense for supply chains in which cycle inventories are large and demand is relatively predictable

Integer Replenishment PolicyFigure 11-7

Integer Replenishment PolicyFigure 11-8

Managing Safety Inventory in a Multi-echelon Supply ChainIn multiechelon supply chains stages often do not know demand and supply distributions

Inventory between a stage and the final customer is called the echelon inventory

Reorder points and order-up-to levels at any stage should be based on echelon inventory

Decisions must be made about the level of safety inventory carried at different stages

**Notes:*Notes:

SCM Inventory Part-III

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