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**Chapter 11. Order Point Inventory Control Methods**

Homework problems: 1, 2, 3, 5.

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**Order Point Inventory Control Methods**

Order point methods are used to determine appropriate order quantities and timing for individual independent-demand product items that are characterized by random customer demand. Performed well, these inventory management functions can provide appropriate levels of customer service without excess levels of inventory and/or cost.

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**1. Basic Concepts Independent Demand Dependent Demand**

When item’s demand is influenced by market conditions and is not related to (i.e., is “independent” of) production decision for any other item. Wholesale and retail merchandise (finished goods), service industry inventory, end-item and replacement-part inventories, spare-parts, MRO (maintenance, repair, and operating) supplies. Demand must be forecast Dependent Demand When item’s demand derives from (i.e., “depend” on) the production decisions for its parents. All intermediate and purchased items in manufacturing. Demand must be derived.

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**Functions of the 4 Types of Inventory**

Cycle Stock/Inventory Created when we place orders LESS frequently. The longer the cycle, the bigger the Q (order quantity). Helps with customer service, ordering cost, setups, transportation rates, and material costs. Equal to Q/2, when demand rate is constant and uniform. Safety Stock/Inventory Created when we place an order sooner than when it is needed, or more than the expected demand during lead time. . Protects against three types of uncertainty: demand, lead time, and supply. Helps with customer service and missing parts.

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**Functions of Inventory**

Anticipation Stock/Inventory Created by overproducing during the slack season or overbuying before a price increase or capacity shortage. Helps absorb uneven rates of demand and supply. Pipeline (transit) Stock/Inventory Created by the time spent to move and produce materials. Can be in any of three stages: Inbound, within the plant, outbound Equal to d x L, where, d: avg. demand per period L: the # of periods in the lead time to move between two points.

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**Functions of Inventory Example**

Management has decided to establish three distribution centers (DCs) in different region of the country to save on transportation costs. For one of the products, the average weekly demand at each DC will be 50 units. The product is valued at $650 per unit. Average shipment sizes into each DC will be 350 units per trip. The average lead time will be two weeks. Each DC will carry one week’s supply as safety stock, since the demand during the lead time sometimes exceed its average of 100 units (50x2). Anticipation inventory should be negligible. How many dollars of cycle inventory will be held at each DC, on the average? How many dollars of safety stock will be held at each DC? How many dollars of pipeline inventory will be in transit for each DC, on the average? How much inventory, on the average, will be held at each DC? Which type of inventory is your first candidate for reduction?

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**Functions of Inventory Example**

Solution: Cycle Inventory = (350/2)($650)=$113,750. Safety stock = (1)(50)($650)=$32,500. Pipeline inventory = (2)(50)($650)= $65,000 Inventory at DC = cycle + safety + pipeline = $211,250 Cycle inventory

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**Inventory Reduction Type Primary Lever Secondary**

Cycle Reduce Q Reduce ordering and setup costs. Safety Place orders closer Improve forecasting. to the time when Reduce lead time. they must be received Reduce uncertainty. Anticipation Vary production rate Level out demand rates. to follow demand rate Pipeline Cut production- Forward inventory positioning. distribution lead time Selection of suppliers and carriers. Reduce Q.

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**Where are the Inventories?**

Inventories are held in: manufacturing (36%), retail trade (25%), wholesales trade (23%), farm (8%), other (8%). Inventory Total: 3.6 monthly sales in 1970s 3.1 monthly sales in 1980s 2.7 monthly sales in 1990s (> $1 trillion)

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**2. Management Issues – Two Fundamental Inventory Questions/Decisions**

How Much? When? See. Figure 11.2 for models

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**Inventory System Performance**

Inventory Measures Start with physical count in units, volume, or weight. Average aggregate inventory value (total value of all items held in inventory) Weeks of Supply. Divide average aggregate inventory value by weekly sales (at cost, i.e., cost of goods sold) of finished goods. Inventory Turnover (turns). Divide annual sales (at cost, i.e., cost of goods sold) by average aggregate inventory value. Fill Rate. The % of units immediately available when requested by customers, measuring customer service level.

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**Inventory System Performance Example**

A recent accounting statement showed average aggregate inventories (RM+WIP+FG) to be $6,821,000. This year’s cost of goods sold is $19.2 million. The company operates 52 weeks per year. How many weeks of supply are being held? What is the inventory turnover? Solution: Weeks of supply= ($6,821,000)/($19,200,000)/52=18.5 weeks. Inventory turnover= ($19,200,000)/($6,821,000)= 2.8 turns.

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Inventory Costs = Ordering costs: physical counting, paperwork, fax/phone, receipt verification, etc. e.g., $95/order vs. $7/order +Holding/carrying costs: cost of capital (5~35%), taxes, insurance, obsolescence, warehousing, etc. Typically annual holding costs = 20~40%. +Stockout/shortage costs: back order, lost sales, lost goodwill. Customer service level ↔ inventory investment + Cost of items

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**Five Assumptions of EOQ**

Demand is known and constant Whole lots ordering Only two relevant costs Item independence Certainty in lead time and supply

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**Economic Order Quantity (EOQ)**

A: annual demand Q: order quantity CP: ordering (preparation) cost per order CH: carrying cost per unit per year Annual inventory carrying cost= (Q/2)·CH Annual ordering cost= (A/Q) ·CP Total annual cost (TAC) = (A/Q)·CP + (Q/2)·CH Finding the optimal order quantity that minimizes TAC using Calculus Observation (Fig 11.4) Economic time between order (TBO) in weeks = EOQ/(A/52)

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EOQ Sensitivity What happens to cycle inventory if the demand rate increases? What happens to lot sizes if setup/ordering cost decreases? What happens to lot size if interest rates drop? How critical are errors in estimating A, CP, CH ? Overestimate A by 300% → overestimate EOQ by 100% Total cost curve is relatively “flat” around the minimum cost ordering quantity, implying total cost performance is relatively insensitive to small changes in order quality around the optimal order quantity. EOQ is robust. When setup cost → 0, EOQ → small → small lot production in JIT.

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**Reorder Timing Decisions**

Under the (Q,R) rule, an order for a fixed quantity (Q) is placed whenever the stock level reaches a reorder point (R). Reorder point = average demand during the average replenishment lead time + safety stock. Reorder point is influenced by demand, lead time, demand uncertainty, and lead time uncertainty. When both demand and lead time are constant, reorder point = expected demand during lead time, and no safety stock is needed. R= d + S

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**Reorder Point Decisions: Discrete Distribution of Demand during Lead Time**

Safety Stock can be determined using (1) stockout risk or probability or (2) customer service level (fill rate). Stockout Risk: the probability of not meeting demand during ANY given replenishment order cycle. e.g., 5% stockout; See Figure 11.5. Fill Rate (Customer Service Level): the % of demand, measured in units, that can be supplied directly out of inventory. See Fig. 11.7 Normal Distribution provides a close approximation to a given discrete distribution, facilitating and simplifying the reorder point (and thus safety stock) calculations.

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**Reorder point and Stockout Probability**

Reorder point of 7 units will provide 5% chance of stockout during a one day lead time With a lead time of one day, 95% of cycles will experience demand for 7 or fewer units Sum of demand probability is 0.05 (5%)

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**Introducing Safety Stock for variable demand**

Average demand=5 units/day Lead time= 1 day During the replenishment lead time (1 day), demand can range from 1 through 9 units. If demand during lead time is less than 5 units, inventory reaches a point between b and c. If demand during the 1 day lead time exceeds 5 units, inventory level reaches a point between c and e.

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**Fig. 7 Determining safety stock for specified service levels**

Know how to construct this table * Calculated by ⱡ Assuming order quantity (Q) is 5 units; annual demand=1,250 P(d) = probability of a demand of d units during the replenishment lead time dMax = maximum demand during the replenishment lead time

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**Reorder Point Decisions: Continuous Distribution of Demand during Lead Time**

The ROP based on a Normal distribution of lead time demand Note. Service level is defined differently with continuous demand.

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**Reorder Point Decisions: Continuous Distribution of Demand during Lead Time**

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**Reorder Point Decisions: Continuous Distribution of Demand during Lead Time**

Probability of Stocking Out Criterion Constant demand and variable lead time R= d x LT + Z·d·σLT Variable demand and constant lead time R= d x LT + Z· √LT · σd (cf. equation 11.18) Variable demand and variable lead time R= d x LT + Z·√LT· σd2 + d 2 · σ2LT (cf. equation 11.20) Where d= average daily or weekly demand, σd = standard deviation of demand per day or week, σLT = standard deviation of lead time per day or week

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**Reorder Point Decisions: Continuous Demand Example**

The injection molding department of a company uses 40 ponds of a powder a day. Inventory is reordered when the amount on hand is 240 pounds. Lead time averages 5 days. It is normally distributed and has a standard deviation of 2 days. a). What is the probability of a stockout during lead time? b). What reorder point would provide a 5% stockout?

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**Reorder Point Decisions**

Note that while discrete demand distributions (e.g., Figure 11.5) can be approximated by the continuous Normal distribution for reorder point decisions (e.g., discussions in the section of Continuous Distribution on page 433 and Customer Service Criterion on page 435), the results won’t be optimal. Thus, when demand is discrete, equation 11.8 should be used. When demand is continuous, the formulas on slide 21 should be used.

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Principles The difference between dependent and independent demand must serve as the first basis for determining appropriate inventory management procedures. Organizational criteria must be clearly established before we set safety stock levels and measure performance. Savings in inventory-related costs can be achieved by a joint determination of the order point and order quantity parameters. The functions of inventory are useful principles to apply in determining whether or not inventory reductions can be made.

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11 Inventory Management CHAPTER

11 Inventory Management CHAPTER

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