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Inventory Management

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**Inventory Raw material Inventory Work in process Inventory**

Finished product Inventory It is one of the dominant costs Goal of effective inventory management in SC is to have correct inventory at right place at right time to minimize system costs while satisfying customer service requirements

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**Inventory is held due to:**

Unexpected changes in Customer Demand (due to short life cycle of products thereby having no historical data of customer demand & many competing products) Many a times significant uncertainty in quantity and quality of supply, supplier costs, delivery times Lead times Economies of Scale offered by transportation Companies

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**An Effective Inventory Policy needs to consider:**

Customer Demand (may be known in advance or random, if random forecasting tools used to estimate average demand & variability in demand based on historical data) Replenishment Lead time No. of different products (compete on budget/space) Length of planning horizon Costs Order Costs (product & transportation cost) Inventory Holding Costs (state & property taxes,insurance,maintenance costs,obsolescence costs,opportunity costs) Service level Requirements

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Single Stage Inventory Control (Inventory Management in a Single Supply chain Stage) (Constant Demand for a single item)

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**Economic Lot Size Model (Ford W.Harris)**

Illustrates trade-offs between ordering and storage costs Assumptions: Constant ‘D’ items/day Fixed order ‘Q’ items/order A fixed cost(setup) ‘K’ incurred everytime warehouse places an order An inventory carrying cost/holding cost ‘h’ per unit/day Zero Lead time Zero initial inventory Long (infinite) planning horizon Goal is to find optimal order policy that minimizes annual purchasing and carrying costs while meeting all demand

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**Consider Inventory level as a function of time**

Total inventory cost in a cycle of length T is K+ hTQ/2 K: fixed cost charged once per order h: per unit per time period holding cost T: length of cycle Q/2: average inventory level Also, Q=TD So, average total cost per unit time: KD/Q + hQ/2

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**Important Insights from model**

Zero inventory ordering property Optimal order quantity(EOQ) is achieved where inventory setup cost per unit of time(KD/Q)equals inventory holding cost per unit of time (hQ/2) Q*=√ 2KD/h As one increases order quantity ‘Q’ inventory setup cost per unit of time(KD/Q) decreases while inventory holding cost per unit of time (hQ/2) increases. While total inventory cost is insensitive to order quantities (Q=bQ*)

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**Effect of Demand Uncertainty**

Principles of all forecasts: Forecast is always wrong (difficult to match supply & demand) Longer the forecast horizon, worse the forecast (difficult to predict customer demand for a long period of time) Aggregate forecasts are more accurate (easier to predict demand across all SKUs within one product family, an example of risk pooling)

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**Single Period Model To understand impact of demand uncertainty**

Consider a product that has short lifecycle and hence firm has only one ordering opportunity(ex. Swimsuits) Inferences: Optimal order qty. is not necessarily equal to forecast/average demand. Rather it depends on relationship between marginal profit achieved from selling an additional unit and marginal cost. If an additional unit is sold: MP= SP /unit – variable ordering(production) cost/unit If an additional unit is not sold: MC= variable ordering(production) cost/unit – salvage value/unit If MC> MP, then optimal quantity in general will be less than average demand Risk/Reward tradeoff: With increase in production qty risk/probability of large losses and probability of large gains increases.

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Initial Inventory Firm already has some inventory of product in hand,may be of previous season Trade off is between having a limited amount of inventory by avoiding paying fixed cost vs. paying fixed cost and having higher inventory level. Min max policy or (s,S): On reviewing if inventory level is below is certain value,s, we order/produce to increase the inventory to level,S. Where ‘s’ is referred as reorder point/min and ‘S’ is referred as order-up-to level/max

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**Multiple Order Opportunities (Random demand, Repeated orders)**

When demand is random, distributor has to hold inventory due to following reasons: To satisfy demand occurring during lead times To protect against uncertainty in demand To balance annual inventory holding costs and annual fixed order costs Two type of Policies: Continous Review Policy Periodic Review Policy

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**Continous Review Policy**

Inventory is reviewed continuously & order is placed when inventory reaches a particular level or reorder point Assumptions: Daily demand is random & follows a normal distribution Every time distributor places order from manufacturer,distributor pays a fixed cost,K, plus an amount proportional to quantity ordered Inventory holding cost is charged per item per unit time After continuous review if an order is placed order arrives after appropriate lead time If a customer order arrives when there is no inventory in hand(distributor is stocked out), order is lost Distributor specifies a reqd. service level (service level is the probability of not stocking out during lead time)

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**AVG=average daily demand**

STD= Standard deviation of daily demand faced by distributor L= Replenishment Lead time h= cost of holding one unit for one day α= service level (probability of stocking out is 1- α)

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Follows (Q,R) Policy i.e. whenever inventory level falls to reorder level,R, place an order for,Q, units. Reorder level consist of 2 components: Average inventory during lead time(product of average daily demand and lead time) L×AVG Safety stock ( amount of inventory distributor needs to keep at warehouse & in pipeline to protect against deviations from average demand during lead times) z×STD×√L Reorder level=L×AVG + z×STD×√L

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**Optimal/Economic Order Quantity**

Q*=√ 2K x AVG/h Average inventory level=Q/2+ z×STD×√L - As between two successive orders,min. level of inventory is right before receiving an order Max level is immediately after receiving the order Expected level before receiving order is safety stock i.e z×STD×√L Expected Level immediately after receiving order Q+ z×STD×√L

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**Variable Lead Times Reorder point will be**

R= AVG x AVGL + z√ AVGL x STD² + AVG² x STD² Avg. demand Std. Deviation of demand during lead time during lead time

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**Periodic Review Policy**

Inventory level is reviewed periodically at regular intervals and an appropriate quantity is ordered after each review In case of short intervals (daily), modified (Q,R) policy should be used i.e (s,S)policy where Q and R values are calculated as if it were a continuous review model and s is set equal to R and S equal to R+Q In case of long intervals, quantity is ordered after each review n then fixed cost of placing an order is sunk cost(zero). Presumably, fixed cost is used to determine the review interval So inventory policy (order quantity) is characterized by a single parameter i.e. base stock level (or target inventory level)

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**Effective Base Stock Level consist of 2 components:**

Average demand during an interval of r+L days (r+L) x AVG Safety stock ( amount of inventory warehouse needs to keep to protect against deviations from average demand during a period of r+L days) z×STD×√r+L Base stock level(quantity to be ordered) =(r+L)×AVG + z×STD×√r+L Average inventory level=rxAVG/2+ z×STD×√r+L

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**Risk Pooling A tool for reducing variability in Supply Chain**

It suggests that demand variability is reduced if one aggregates demand across locations,as high demand from one customer will be offset by low demand from other Reduction in variability allows decrease in safety stock and therefore reduces average inventory

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Few Critical Points: Centralized Inventory reduces both safety stock and average inventory in the system as there are possibilities of reallocation of inventory from the centralized warehouse from one market area of having low demand to other having high demand Higher the coefficient of variation, greater the benefit from centralized systems or risk pooling Benefit from risk pooling depends on behavior of demand from one market relative to other. It decreases if demand from both is showing very high positive correlation

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**Centralized Vs. Decentralized Systems**

Parameter Centralized Decentralized Remarks Safety Stock High low Amount of decrease depends on coefficient of variation & correlation between demand from different markets Service Level (at same total safety level stock) Low Amount of increase depends on coefficient of variation & correlation between demand from different markets Overhead Costs High* *due to low economies of scale Customer Lead Time Transportation Cost Outbound Inbound

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