Analyzing Inventory Cost and Service in Supply Chains

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A n alyzin g In ve n to ry Co st an d S e rvic e in S u p p ly Ch ain s Garre tt van R yzin

Cop yrigh t ° c 1998 b y Garrett van

Ryzin . All righ ts res erved .

D ecem b er 1998

Supply Chain Cost and Service

i

Contents
1 Introduction 2 What are inventories and why do they occur? 3 Causes of supply/demand imbalances in a supply chain 3.1 Planned imbalances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Time and distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Economies of scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Supply/demand uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Inventory cost accounting 1 1 1 1 2 2 3 3 4 5 5 6 6 6 7 9 9 10 10 11 11 12 12 13

5 Models of inventory cost and service 5.1 Types of inventory control policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The economic order quantity (EOQ) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 A model with random demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 5.3.2 5.3.3 The demand process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The ordering process and inventory position . . . . . . . . . . . . . . . . . . . . . . . . The periodic review, order-up-to policy . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4 Choosing the policy parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Cost and service measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Examples 6.1 Calculating the inventory needed to meet a target ¯ll rate . . . . . . . . . . . . . . . . . . . . 6.2 Determining service provided by a given inventory level . . . . . . . . . . . . . . . . . . . . . 6.3 Determining policy parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Appendix 7.1 Partial expectation, the standard loss function and average back-orders (optional) . . . . . . 7.2 Extension to random lead times (optional) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Supply Chain Cost and Service

1

1

I ntr oduction

Then I(t) = S(0; t] ¡ D(0; t]: (1)

What does a negative unit of inventory look like? Well, a lot like a back-order. If consumers of our output are willing to order without receiving product, then we can allow demand to exceed supply and I(t) can become negative, in which case, ¡I(t) represents But formulating e®ective strategy requires a good the total quantity on back-order. Think of a positive understanding of what drives cost and service in a inventory as a pile of goods waiting for orders and supply chain. This note introduces an inventory a negative inventory as a pile of orders waiting for model that will enable you to quantifying the of- goods. ten subtle impact of both operational and structural changes in a supply chain. In addition - and perhaps more importantly - the model can help sharpen your 3 Causes of supply/demand intuition about what factors a®ect the operating perimbalances in a supply chain formance of a supply chain. Now, the clever reader has no doubt already spotted the solution to eliminating all inventories (and back2 What ar e inventor ies and orders for that matter): simply set S(0; t] = D(0; t] at why do they occur ? all times t (keep supply equal to demand) throughout the supply chain, then - poof! - I(t) = 0 forever! At a very basic level, inventories are merely the by- Alas, in real life things are not quite that simple. product of a universal \accounting law" of material Indeed, the real key to understanding inventory cost and service is to understand what causes imbalances °ow: in supply and demand in the ¯rst place. inventory = cumulative supply - cumulative demand. In other words, if we draw a \black box" around a...
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