Week 5

• Working stock: Inventory that is actively being processed or moved. Parts being cut on a machine, components being transported in a truck, and consumer loan applications being evaluated by a bank officer are all examples of working stock.

• Congestion stock: Inventory that builds up unintentionally as a consequence of variability in the system. For instance, a queue that builds up behind a highly variable, highly utilized process is a form of congestion stock. Components waiting to be matched with their counterparts to form assemblies are another form of congestion stock.

• Cycle stock: Inventory that results from batch operations. For example, when a purchasing agent orders office supplies in bulk (to obtain a price discount or to save on shipping costs) the excess beyond what is immediately needed becomes cycle stock. A heat-treat furnace that processes batches of wrenches produces a build up of cycle stock at the next downstream station as the batches wait to be split up into a one piece flow.

• Safety stock: Inventory that exists intentionally to buffer variability. Retail inventory held in outlets to accommodate variable customer demand is an example of safety stock.

• Anticipation stock: Inventory that is built up in expectation of future demand. For instance, a plant might build up a stock of lawnmowers to satisfy a seasonal spike in demand. In general, this is done to level production in the face of uneven or cyclic demand to make better use of capacity

Working stock is not generally a problem, because it is required for any production/supply chain system to operate. But the other forms of inventory are not strictly necessary and hence are often classified as “waste” (or “muda” by those with a penchant for Japanese terms). Managing these effectively is fundamental to achieving supply chain efficiency.

• This approach divides items into categories based on dollar usage. Typically a small fraction of the items account for a large fraction of total annual dollar usage. Therefore, it makes sense to devote more attention to those items responsible for the majority of investment.

• Class A items represent the first 5 to 10 percent of items that generally account for 50 percent or more of total annual usage measured in dollars. These should receive the most personalized attention and most sophisticated inventory management.

• Class B items represent the next 50 to 70 percent of items that account for most of the remaining dollar usage. Like Class A items, these should be addressed with sophisticated inventory tools. But they are often too numerous to permit the individual management intervention that can be used for Class A items.

• Class C items represent the remaining 20 to 40 percent of items that represent only a minor portion of total dollar usage. Management of these items should be as simple as possible, because time spent on such parts can have only a small financial impact on the system. However, when inexpensive Class C parts are essential to operations (e.g., lack of a fuse can cause an expensive delay) it makes sense to err on the side of ample inventory.

Demand / Order quantity

order quantity/2

oD/OQ

hOQ/2

• Demand is fairly steady over time.

• The cost to place an order (e.g., purchasing clerk time, fixed shipping expenses, etc.) is reasonably stable and independent of the quantity ordered.

• Replenishments are delivered all at once.

• What policy should we use to control stock levels over time?

• Given a control policy, what level of safety stock is needed to achieve a desired level of customer service?

• The base stock system, in which a replacement is ordered each time an item is removed. A kanban system is essentially a base stock system, because cards represent replenishment orders that are triggered whenever an item is removed from an inbound stock point.

• we assume that demands occur one at a time at random intervals and are either met from stock (if there is inventory) or backordered (if the system is stocked out). Each time a demand occurs a replenishment order is placed to replace the item (also one at a time). Replenishment orders arrive after a fixed lead time, LT

We define net inventory as on-hand inventory minus backorders (i.e., so that it becomes negative whenever we are out of stock and have outstanding customer backorders).

We call the sum of net inventory plus replenishment orders the inventory position and note that it represents the total inventory either on hand or on order.

Because a replenishment order is placed every time a demand occurs, the inventory position remains constant in a base stock system. We call this level the base stock level (BSL). The base stock level can also be thought of as a target inventory level or “order up to” level. We place an order each time inventory position reaches BSL −1

We place an order each time inventory position reaches BSL −1, so we call this the reorder point (ROP)

service is measured by fill rate, the fraction of demands that are met from stock

For the base stock system, we can calculate fill rate by considering the system at a moment when a demand has just occurred and thus a replenishment has just been ordered. This order will arrive after LT time units have elapsed. Because any other orders that were outstanding will also have arrived by this time, the replenishment order will arrive before it is demanded (i.e., will go into stock rather than fill a backorder) if demand during this interval of length LT is less than BSL (i.e., less than or equal to ROP = BSL −1).

The probability that an item will not be back ordered, which is the same as the fraction of orders that will be filled from stock, is therefore equal to the probability that demand during replenishment lead time is less than or equal to ROP

• mean lead time + (z value (for 0.95 = 1.645) x standard deviation)

• Safety stock = ROP - average lead time

• If ROP is:

• Then safety stock is only zσ

• Therefore safety stock is not affected by mean lead time demand

In a base stock system, safety stock increases with both the target fill rate and (for a sufficiently high target fill rate) the standard deviation of demand during replenishment lead time

Periodic review systems, in which stock counts and replenishment orders are made at regular intervals (e.g., weekly), and continuous review systems, in which stock levels are monitored in real time and replenishment orders can be placed whenever needed.

where the distribution of demand is the same from period to period. Use order up policy

If our forecast of weekly demand is the same every week (even though the actual demand may not be), then an orderup-to policy, in which inventory is brought up to the same specified level at the start of each week, is appropriate

To minimize total average cost, we should set the inventory level at the start of the week to a level where expected backorder cost just equals expected holding cost.

• Order-up-to level

• If we order enough stock so that we start the week with OUTL on hand, our probability of meeting all demand during the week will equal b/(b + h).

• Increasing the backorder cost b increases the target probability of meeting demand and hence the necessary order-up-to level, OUTL

where z is a safety factor given by the b/(b + h) percentile of the standard normal distribution, which can be looked up in a normal table or computed in a spreadsheet

• Most systems make use of a reorder point approach, in which a replenishment order is placed whenever inventory drops to a specified level.

• The reorder point (ROP) is equal to 3, while the order quantity (OQ) is equal to 4. Every time the inventory position (on-hand inventory plus replenishment orders minus backorders) reaches the reorder point of 3, a new replenishment order of 4 items is placed. We assume that the replenishment lead time is 6 days, so we see a jump in net inventory 6 days after the order is placed.

OQ and ROP interact with eachother. When increasing either the reorder point, ROP, or the order quantity, OQ, will increase the average level of on-hand inventory. But increasing either ROP or OQ also reduces the average backorder level.

Under this approach we set the safety stock equal to some number of days of demand.

• The reasoning behind the days-of-supply approach is that it provides a uniform level of protection across parts, because a high demand part will have a larger safety stock than a low-demand part. But this reasoning is wrong! Because the formula for ROPi does not consider the cost of the part or the replenishment lead time, this approach can result in serious inefficiencies

The organization and management of inventories consisting of very large numbers of distinct items, referred to as stock-keeping units (SKU’s)

annual dollar volume (demand x price)

Annual demand volume criterion

• The number of different SKUs is too large to implement SKU-specific inventory control methods.

• Service levels are very important for determining ABC

Simplicity

• In service industries, criticality for the functioning of a piece of equipment.

• In practical situations; demand value (price multiplied by demand volume)

• Traditionally one criterion is used.

• According to the article, one single criterion is sufficient. However; However, that criterion does take four system parameters into ac-count: demand volume, holding cost (purchase price),shortage cost (criticality), and average order quantity.

• A measure service is the fill rate, i.e., the fraction of demands that are satisfied directly from stock on hand.

• The main advantage of using the fill rate is that it directly reflects the service as experienced by the customers

• The weighted average of the single-SKU fill rates, where the weights are the fractions of demands for the different SKUs

• This is difficult to analyse, therefore the cost-approach is often used.

Missed demands incur a penalty cost including inventory and penalty costs. The practical validity of this alternative cost approach lies in the fact that it leads to the same set of cost-service efficient solutions as the corresponding service approach

the objective is to minimize the total cost, consisting of inventory holding costs (per SKU and per time unit)and penalty/shortage costs per backordered demand.

It takes shortage cost(or criticality) into account. This implies that it can also be used in situations, such as spare parts management, where criticality is essential.