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Inc. and accounts for about 13 percent of Gap’s sales. As Gap shifted its product line to basics such as cropped pants, jeans, and khakis, Banana Republic had to move away from such staples and toward trends, trying to build a name for itself in fashion circles. But fashion items, which have a much shorter product life cycle and are riskier because their demand is more variable and uncertain, bring up a host of operations management issues. In one recent holiday season, the company had bet that blue would be the top-selling color in stretch merino wool sweaters. They were wrong. Marka Hansen, company president noted, “The No. 1 seller was moss green. We didn’t have enough.”
• Inventory is any asset held for future use or sale.
Objectives:
• Inventory Management involves planning, coordinating, and controlling the acquisition, storage, handling, movement, distribution, and possible sale of raw materials, component parts and subassemblies, supplies and tools, replacement parts, and other assets that are needed to meet customer wants and needs.
- Maintain sufficient inventory- Incur lowest possible cost
• Ordering costs or setup costs are incurred as a result of the work involved in placing purchase orders with suppliers or configuring tools, equipment, and machines within a factory to produce an item.
• Inventory-holding costs or inventory-carrying costs are the expenses associated with carrying inventory.
• “A” items account for a large dollar value but relatively small percentage of total items (e.g., 10% to 30 % of items, yet 60% to 80% of total dollar value).
• “C” items account for a small dollar value but a large percentage of total items (e.g., 50% to 60% of items, yet about 5% to 15% of total dollar value). These can be managed using automated computer systems.
The data shows projected annual dollar usage for 20 items. Exhibit 12.3 shows the data sorted, and indicates that about 70% of total dollar usage is accounted for by the first 5 items.Exhibit 12.2
• The process of triggering an order is based on the inventory position.
• Inventory position (IP) is the on-hand quantity (OH) plus any orders placed but which have not arrived (scheduled receipts, or SR), minus any backorders (BO).
• The Economic Order Quantity (EOQ) model is a classic economic model developed in the early 1900s that minimizes total cost, which is the sum of the inventory-holding cost and the ordering cost.
Average cycle inventory = (Maximum inventory + Minimum inventory)/2= Q/2
The EOQ Model
• Cycle inventory (also called order or lot size inventory) is inventory that results from purchasing or producing in larger lots than are needed for immediate consumption or sale.
Safety Stock and Uncertain Demand in a Fixed Order Quantity System
• When demand is uncertain, using EOQ based on the average demand will result in a high probability of a stockout.– Safety stock is additional planned on-
hand inventory that acts as a buffer to reduce the risk of a stockout.
– A service level is the desired probability of not having a stockout during a lead-time period.
When a normal probability distribution provides a good approximation of lead time demand, the general expression for reorder point is:
r = mL + zsL [12.9]Where: mL = Average demand during the lead time.sL = Standard deviation of demand during the lead time.z = The number of standard deviations necessary to achieve the acceptable service level.“zsL” represents the amount of safety stock.
Safety Stock and Uncertain Demand in a Fixed Order Quantity System
We may not know the mean and standard deviation of demand during the lead time, but only for some other length of time, t, such as a month or year. Suppose that mt and st are the mean and standard deviation of demand for some time interval t. If the distributions of demand for all time intervals are identical to and independent of each other, then:
mL = mtL [12.10]
sL = st √L [12.11]
Safety Stock and Uncertain Demand in a Fixed Order Quantity System
• Ordering costs are $45.00 per order. • One ream of paper costs $3.80.• Annual inventory-holding cost rate is 20%. • The average annual demand is 15,000 reams, or
about 15,000/52 = 288.5 per week.• The standard deviation of weekly demand is
about 71.• The lead time from the manufacturer is two
weeks.
Solved Problem
Southern Office Supplies, Inc. distributes laser printer paper.
Inventory-holding cost is Ch = IC = 0.20($3.80) = $0.76 per ream per year.
• Desired service level of 95%, which results in a stockout of roughly once every 2 years. For a normal distribution, this corresponds to a standard normal z-value of 1.645.
• This policy increases the reorder point by 742 – 577 = 165 reams, which represents the safety stock.
• The cost of the additional safety stock is Ch times the amount of safety stock, or ($0.76/ream)(165 reams) = $125.40.
• Commonly hidden in inventory management decisions are the costs to dispose of obsolete, hazardous materials.
• Environmental considerations, material losses, and waste disposal can be included in the EOQ model to improve inventory decisions.
• If a company examines its hazardous waste disposals and observed that some percentage of its material is eventually disposed of instead of used, then the company should incorporate this into their inventory decisions.
• Example: Annual demand for paint is 4000 lbs., item cost is $3/lb., order cost is $50, inventory-holding cost rate is 10%, 5% of paint is not sold and eventually disposed of, and the disposal cost is $1/lb.
• An alternative to a fixed order quantity system is a fixed period system (FPS)—sometimes called a periodic review system—in which the inventory position is checked only at fixed intervals of time, T, rather than on a continuous basis.Two principal decisions in a FPS:1. The time interval between reviews (T),
- cs = The cost per item of overestimating demand (salvage cost); this cost represents the loss of ordering one additional item and finding that it cannot be sold.
- cu = The cost per item of underestimating demand (shortage cost); this cost represents the opportunity loss of not ordering one additional item and finding that it could have been sold.
• A buyer orders fashion swimwear about six months before the summer season.
• Each piece costs $40 and sells for $60. • At the sale price of $30, it is expected that any
remaining stock can be sold during the August sale.
• The cost per item of overestimating demand is equal to the purchase cost per item minus the August sale price per item: cs = $40 – $30 = $10.
• The per-item cost of underestimating demand is the difference between the regular selling price per item and the purchase cost per item; that is, cu = $60 – $40 = $20.
Quantitative models have been developed for other practical situations:
• Backorder Models: It may be desirable from an economic point of view to plan for and allow shortages, such as when the value per unit of the inventory is very high, and hence the inventory-holding cost is high (a new-car dealer’s inventory). Most customers do not find the specific car they want in stock, but are willing to backorder it.
• Quantity Discount Models: Suppliers often offer discounts for purchasing larger quantities of goods. This often occurs because of economies of scale associated with larger quantities or simply as an incentive to increase total revenue.
1. What are good estimates of order cost and inventory holding cost? (State all assumptions and show all computations.)
2. What is the EOQ and reorder point for Strike Disinfectant given your answer to Question 1?
3. Compute the total order and inventory holding costs for a Fixed Quantity System (FQS) and compare to their current order Q's. Can you save money by adopting a FQS?
4. What are your final recommendations? Clearly explain your reasoning.