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• Freddie sells a wide variety of newspapers and magazines. The most expensive of the newspapers is the Financial Journal.
• The day’s copies of the Financial Journal are brought to the newstand each morning. Any copies unsold at the end of the day are returned to the distributor the next morning. To encourage ordering a large number of copies, the distributor gives a small refund for unsold copies.
• Freddie pays $1.50 per copy delivered.
• Freddie sells it at $2.50 per copy.
• Freddie’s refund is $0.50 per unsold copy.
• Freddie sells 9 copies on 30% of the days, 10 copies on 40% of the days, and 11 copies on 30% of the days.
Assumptions for an Inventory Model for Perishable Products
• Each application involves a single perishable product.
• Each application involves a single time period because the product can’t be sold later.
• However, it will be possible to dispose of any units remaining at the end of the period, perhaps receiving a salvage value for the units.
• The only decision to be made is how many units to order (the order quantity).
• The demand during the period is uncertain. However, the probability distribution of demand is known (or at least estimated).
• If the demand exceeds the order quantity, a cost of underordering is incurred. In particular, cunder = decrease in profit from failing to order a unit that could have been sold during the period.
• If the order quantity exceeds the demand, a cost of overordering is incurred. In particular, cover = decrease in profit from ordering a unit that could not be sold during the period.
• Freddie now wishes to find the optimal order quantity for another newspaper. This more popular newspaper has daily sales in the range from 100 copies to 200 copies, with roughly equal probabilities over this range.
• The makings of fresh food to be prepared in a restaurant.
• Produce, including fresh fruits and vegetables, to be sold in a grocery store.
• Christmas trees.
• Seasonal clothing, such as winter coats, where any goods remaining at the end of the season must be sold at highly discounted prices to clear space for next season.
• Seasonal greeting cards.
• Fashion goods that will be out of style soon.
• New cars at the end of a model year.
• Any product that will be obsolete soon.
• Vital spare parts that must be produced during the last production run of a certain model of a product for use as needed throughout the lengthy field life of that model.
• Reservations provided by an airline for a particular flight. Reservations provided in excess of the number of seats available (overbooking) can be viewed as the inventory of a perishable product.
• Niko Camera is a Japanese company that specializes in producing high quality cameras.
• One of Niko’s newer models is an inexpensive disposable panoramic camera After the customer shoots the film, it is returned to the camera store, the film developed, and the camera sent to a American factory for recycling.
• Niko’s American factory has been selling an average of 8,000 of the recycled cameras per month to wholesale distributors.
• Distributors only submit purchase orders occasionally, leading to sales that fluctuate widely from month to month.
• Because of sales fluctuations, the camera is only produced on a sporadic basis.
• The run size has been set at 20,000, which covers sales for 2.5 months on the average.
• Once the decision has been made to initiate a production run, the lead time for setup and production is about one month.
• Since average sales over the lead time of one month are 8,000, it has become routine to order another production run when the number of cameras in inventory drops to 8,000
• Several distributors have complained about delays in shipping.
• Complaints have been received from the production floor about frequent interruptions in the production of other models caused by setting up for a production run for the disposable panoramic camera every two or three months.
• Proposal: have much longer production runs much less frequently.– This would provide larger inventories to reduce delayed shipments.
– This would substantially reduce setups and the associated disruptions.
When reordering, a cushion of extra inventory (safety stock) needs to be provided in addition to the amount needed to cover the average sales during the lead time.
Even when the amount of safety stock provided still permits occasional short stockouts, this safety stock can dramatically improve the service to customers by greatly reducing both the number and length of the delays in filling customer orders.
• How important is it to reduce delays in filling customer orders?
• Considering that larger inventories would be needed to reduce delays, how would you compare the importance of reducing delays with the inportance of holding inventory levels down?
• Considering that unacceptably large inventories would be needed to completely eliminate any delays, what would you consider tolerable in terms of the frequency, size, and length of stockouts?
• Conclusion: Management feels that providing a safety stock of roughly 4,000 cameras is needed to provide an adequate level of service to customers. Considering the company’s just-in-time philosophy regarding the need to hold down inventories, management does not want the safety stock raised higher than this.
• The average monthly setup costs are decreased by increasing the order quantity because this decreases the average number of setups required per month.
• The average monthly holding costs are decreased by decreasing the order quantity, since this decreases the average inventory level.
• However, the average monthly shortage costs are decreased by increasing the order quantity because this decreases the average number of opportunities for stockouts per month.
• The EOQ model with planned shortages addresses these same tradeoffs.
• The EOQ model with planned shortages addresses exactly these same tradeoffs.
• The average monthly holding costs are decreased by decreasing the order quantity, since this decreases the average inventory level.
• However, the average monthly shortage costs are decreased by increasing the order quantity because this decreases the average number of opportunities for stockouts per month.
Recommended inventory policy: Whenever the number of disposable panoramic cameras in inventory drops to 12,000, order a production run of 25,675 cameras.
• The model is for stable products (products that will remain sellable indefinitely) as opposed to perishable products (sellable for only a limited time).
• The model is a continuous-review model because it assumes inventory level is monitored on a continuous basis so that a new order can be placed as soon as the inventory level drops to the reorder point. This is as opposed to a periodic-review inventory system where the inventory level is only monitored periodically such as at the end of each week.
• The traditional method of implementing a continuous-review inventory system was to use a two-bin system. All the units would be held in two bins. The capacity of one bin would equal the reorder point. The units would be withdrawn from the other bin until empty, triggering a reorder.
• In more recent years, two-bin systems have been largely replaced by computerized inventory systems where each sale is recorded electronicaly, so that the current inventory level is always in the computer.
• A common approach to choosing the reorder point R is to base it on management’s desired level of service to customers.
• Alternative measures of service level:– The probability that a stockout will not occur between the time an order is placed
and the order quantity is received.– The average number of stockouts per year.– The average percentage of annual demand that can be satisfied immediately.– The average delay in filling backorders when a stockout occurs.– The overall average delay in filling orders (where the delay without a stockout is 0).
• The first measure is the most convenient, so we will focus on this case:– L = management’s desired probability that a stockout will not occur between the
time an order quantity is placed and the order quantity is received.
Larger Inventory Systems in Practice• Multiproduct Inventory Systems
– It is common to apply the appropriate single-product model to each product individually.
– The ABC Control Method is commonly applied to divide the products into categories, where the A group must be monitored carefully while the C group need only be informally monitored.
– It may not be appropriate to apply the single-product model if there are interactions between products.
• Multi-Echelon Inventory Systems– Inventory may be stored initially at the points of manufacture (one echelon), then at
regional warehouses (a second echelon), then at field distribution centers (a third echelon), etc.
– Some coordination is needed between the inventories at the different echelon.
• Supply Chain Management– A supply chain is a network of facilities that procure raw materials, transform them
into intermediate goods and then final products, and finally deliver the products to customers through a distribution system that includes a (probably multiechelon) inventory system.
– To fill orders efficiently, it is necessary to understand the linkages and interrelationships of all the key elements of the supply chain.