Slides 2 Inventory Management Global Supply Chain Management Inventory Management

Agenda Inventory Management Intro Economic Lot Size Model Continuous Review Policy Service level optimization Risk Pooling / Centralization Inventory Management

Inventory Management (IM) We will introduce here the basics…. Later, course cases GM, Meditech, Reebok present a diagnosis of a typical problem: low service levels & too high inventory levels. This is actually an Oxymoron….. Solutions: co-ordination within or across, better forecasts, reduction of lead time, use Pull, Push-Pull boundaries, postponement. Emphasis is on quick diagnosis (like a Kaizen event), using simple tools and principles, to identify high leverage points Actual project– specialty industrial chemicals Note – there is not much real information in case, so we’ll need to make some inferences; depending on what one assumes, analysis and rec’s might change. Inventory Management

IM implies Order (or Production) Management Key Question: what, when and how much to order (or: to produce – assume order) Simple models and principles can provide valuable guidance At start not like continuous replenishment policy (case of Tesco): we order, the order arrives before we need to order again. Later: orders are underway when we order. My next session --- Instron case– think about how do you want to run the operation? What are the main tactics and operating polices to use? Inventory Management

Why do we keep Inventory? Logical: incentives for orders or arriving shipments that are larger (and hence less frequent) compared to leaving sales based on demand: think of a grocery retailer Uncertainty in supply levels, in lead times To address uncertainty in demand in combination with long lead times demand may be hard to forecast, demand may suddenly go up, with high “unsatisfied demand” costs we rather keep some stock, especially if it takes a long time to replenish. Risks associated with inventories Shorter lifecycles, more competing products Inventory Management

Typical Inventory Policy Factors Expectations about customer demand Expectations about lead time Length of the planning horizon (e.g. seasonal ?) Costs: Fixed (order) costs, consisting of fixed costs in Materials and components, storage, admin costs, production costs, transportation costs, Assume that variable costs are covered with sales Inventory holding costs and associated costs Taxes and Insurance costs, Maintenance costs Obsolescence costs and Loss of Opportunity costs Service level (availability) requirements Inventory Management

Economic Lot Size Model FIGURE 2-3: Inventory level as a function of time Assumptions - Constant demand rate of D items per unit of time - Q items per order: Order quantities are always the same - Lead Time = 0 : Time between placement of an order and its receipt is assumed to be zero. - Planning horizon is long, infinite (for that product) Inventory Management

Other Assumptions K fixed setup cost: Every time the warehouse places an order, a fixed setup cost of K is incurred h inventory carrying cost: A holding cost of h is incurred per unit held in inventory per unit of time Requested is Q* or EOQ, the Economic Order Quantity Inventory Management

EOQ: Minimizing Total Costs FIGURE 2-4: Economic lot size model: total cost per unit of time as a function of the order quantity Inventory Management

Deriving EOQ Whatever Q is, at the start of cycle time T we order Q units The average inventory during a cycle is: Q/2, see diagram Per T this means a total holding cost of: T * h * Q/2 For every cycle T we also incur a fixed order cost: K So the average total cost per cycle: K + T * h *Q/2 Average total cost per unit of time: K/T + h * Q/2 Total demand during a cycle is Q = D * T, so T = Q/D Average total cost per unit of time: K * D/Q + h * Q/2 This sum of the Order Cost per of unit time and Holding Cost per unit of time can be shown in a Diagram….. Inventory Management

Where is the minimum ? Function f(Q) = K*D/Q + h*Q/2 Gives f ’(Q) = -1*K*D/Q^2 + h/2 This being 0, implies that the optimal order quantity is Example: K = 2000$, D = 180 units per day and h = 0.5$ per unit per day What is Q*? How often will we order? Inventory Management

Sensitivity Analysis Total costs relatively insensitive to order quantities Actual order quantity: Q Q is a multiple b of the optimal order quantity Q*. For a given b, the quantity ordered is Q = bQ* Nevertheless: it makes a difference b 0.5 0.8 0.9 1.0 1.1 1.2 1.5 2.0 Cost Increase 25% 2.5% 0.5% 0% 0.4% 1.6% 8.9% Inventory Management

What if the Manufacturer (or Retailer) has an Initial Inventory? Trying to use the existing inventory to meet the demand has…. Advantage: no need to pay production (order) cost Disadvantage: it may be impossible to meet demand Producing/ordering on the other hand has…. Advantage: more likely to meet demand Disadvantage: implies a production (order) cost, which is relatively high a as we will produce (order) a smaller quantity Inventory Management

Multiple Order Opportunities Suppose: demand is uncertain & lead times exist Question: when and how much to order each time? to balance annual inventory holding costs and annual fixed order costs to satisfy demand occurring during lead time to protect against uncertainty in demand Major strategies Continuous review policy inventory is continuously reviewed (computerized inventory system) and an order is placed when the inventory reaches a particular level, the reorder point Periodic review policy (less relevant today) Inventory Management

Continuous Review Policy An entity faces demand according to a normal distribution, the mean demand is AVG and its standard deviation STD. Every time the entity places an order to its supplier (or decides to manufacture), the entity pays a fixed cost K (plus an amount proportional to the quantity). Inventory holding cost h is charged per item per unit time. Inventory level is continuously reviewed, and if an order is placed, the order arrives after the (constant) lead time L. If customer demand occurs when there is no inventory on hand (i.e. when the entity is stocked out), the order is lost. The entity specifies a required service level α. This implies that the probability of stocking out during L out is 1 – α. Inventory Management

Continuous Review Policy (Q,R) policy – whenever inventory level falls to a reorder level (point) R, place an order for Q units (optimal order quantity) What is the optimal value of R? What is the safety stock level? What is the demand during the lead time ? What is the optimal value of Q? The expected time between orders TBO? How many inventory turns per unit of time? Inventory Management

Inventory development over time Order received Q placed Inventory + Pipeline Time inventory R TBO1 TBO2 TBO3 L

Continuous Review Policy Expected demand during lead time L x AVG Required safety stock Reorder level R= Order quantity Expected time between orders = Q / AVG Inventory Management

Relation between Service Level α and Safety Factor z 90% 91% 92% 93% 94 % 95% 96% 97% 98% 99% 99.9% Z - value 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08 z is chosen from statistical tables to ensure that the probability of stock-outs during lead time is exactly 1 - α Inventory Management

Inventory Level Over Time FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy Inventory level before receiving an order = Inventory level after receiving an order = Average Inventory (AvInv) = Inventory Turn = AVG / AvInv Inventory Management

Continuous Review Policy Example: calculate (Q,R) A distributor of TV sets that orders from a manufacturer and sells to retailers Fixed ordering cost = $4,500 Cost of a TV set to the distributor = $250 Annual inventory holding cost = 18% of product cost (so 18% of $260) Lead time = 2 weeks Expected service level = 97% AVG = 49 per week. STD = √50 per week (variance is 50) Inventory Management

Service Level Optimization Optimal inventory policy assumes a specific service level target. What is the appropriate level of service? May be determined by the downstream customer The customer may require its supplier (the entity), to maintain a specific service level The supplier will use that target to manage its own inventory The Supplier (the Entity) may have the flexibility to choose the appropriate level of service Inventory Management

Service Level Optimization FIGURE 2-11: Service level versus inventory level as a function of lead time Inventory Management

Trade-Offs Everything else being equal: the higher the service level, the higher the inventory level and vice versa (see graph), the lower the inventory level, the higher the impact of a unit of inventory on service level and hence on expected profit (form of curves), for the same inventory level, the longer the lead time to the facility, the lower the service level provided by the facility (dotted curve). Inventory Management

Defining a Retail Strategy Given a target overall service level across all products Determine the service level for each SKU so as to maximize expected profit Everything else being equal, service level will be higher for products with: high profit margin high volume low variability short lead time Inventory Management

Service Level Optimization FIGURE 2-12: Service level optimization by SKU (Example) Note that the size of the circles is an indication of the profitability Inventory Management

Profit Optimization A target service level of 97% across all products combined typically leads to a: Service level > 99% for products with high profit margin, high volume, low variability. Service level < 95% for products with low profit margin, low volume and high variability. Inventory Management

Risk Pooling (based on location) Demand variability is reduced if one aggregates demand across locations. More likely that high demand from one customer will be offset by low demand from another customer. Reduction in variability allows a decrease in safety stock and therefore reduces average inventory. Other RP factors are time and product Inventory Management