The company manufactures systems that perform most of the primary steps in the chip fabrication process. The main customers of the company are semiconductor wafer manufacturers and nonconductor integrated circuit manufacturers, which either use the chips they manufacture in their own products or sell them to other companies downstream, The company owns research, development and manufacturing toxicities in the United States, Europe and Far East and distributes its systems across the globe to world’s leading semiconductor companies.
The company is at the top tot the supply chain for most personal computers and other high technology products. Semiconductor systems are very expensive investments and are very critical to operations of many high technology companies, Unused semiconductor manufacturing capacity due to equipment failures is very costly. In order to provide spare parts and service to customers for equipment failures and scheduled maintenances, the company has an extensive spare parts network, The network consists of more than 70 locations across the globe, that consists of company owned distribution centers and depots.
In addition, the company also has agreements with its leading customers where it manages the stock rooms (for all or a group Of spare parts) in customer facilities (some Of these are consignments). 3 continental distribution centers: one in North America, one in Asia and one in Europe I CHAPTER 1. INTRODUCTION constitute the backbone of the network and are primarily responsible for procuring and distributing spare parts to depots and customer locations.
The depot locations are such that they can provide a our service to customers (those who do not have stock rooms operated by the company) for equipment failures (“down orders. However, the continental distribution centers may also be used as a primary source for Devon orders for certain customers. In addition, the continental distribution center provides a second level of support for down orders that cannot be satisfied from the local depots. The customers also demand spare parts to be used in their scheduled maintenance activities (“lead time order<).
The primary source to meet these demands are usually the continental distribution centers. However local depots can also be used for this purpose for certain customers. Both types of customer orders (down and lead time) go through an order fulfillment engine which searches for available inventory in different locations according to a search sequence specific to each customer. However the down orders need to be satisfied immediately (their request date is the date Of order creation), While the lead time orders need to e satisfied at a future date.
A depot may be facing down and lead time demand from a variety Of customers, While a continental distribution center may be facing down and lead time demand from external customers in addition to the “replenishment orders” requested by internal customers: the depots and stock rooms managed by the company. The operations of this complex network is further complicated by a vast number of parts composed of consumables and non-consumables (more than 50,000 active parts need to be managed) and varying service level requirements by different customers.
While providing an implantable and “good” solution for the whole spares network is a proven challenge, we focus on an important issue where improvements can provide immediate and significant benefits, In the existing practice, for those locations that are taking different types tot demand (down, lead time or replenishment), the company targets to achieve the maximum of the service level requirements while considering the aggregated demand Moreover, the company does not recognize the possible demand lead times (the difference between requested date and ship date in excess of transportation time) for lead time orders and possible slacks (the difference between the replenishment lead time the company uses for planning downstream locations and transportation lead time) for replenishment orders. Obviously, this approach is inefficient. We suggest an inventory model that recognizes both the demand lead times and multiple demand classes, and allows for providing differentiated service levels through rationing.
In Chapter 5, we use representative data from the company to show that our model generates significant savings. Inventory systems have received extensive attention since the first half of the twentieth century. Effective management of inventory using Operations Research tools has been a major concern both in the literature and the industry. Basic, yet crucial questions such as when to replenish and how much to replenish have been the focus of inventory management. Since inventory costs constitute a significant portion of the costs a firms faces, the objective of inventory management has been ensuring a high level of customer service by holding the minimum possible amount tot inventory.
Although the depth of the focus tot inventory management has extended from single locations to multiple locations (mufti-echelon theory) ND from a single product to customized products (product differentiation), in most cases demand from multiple sources is handled in a uniform way, However, just as different customers may require different product specifications, they may also require different service levels particularly, for a single product, different customers may have different stockpot costs and/or different minimum service level requirements or different customers may simply be of different importance to the supplier by similar measures. Therefore, it can be imperative to distinguish between classes of customers thereby offering them different arrive. In this setting, different product demand from different customers can no longer be handled in a uniform way. This, in turn, gives rise to multiple demand classes and customer differentiation. Multiple demand classes occur naturally in many inventory systems. Consider a two-echelon supply network consisting of a warehouse at the upstream and a number of retailers at the downstream.
If the retailers are located in say, different regions and have different demand characteristics, it may be beneficial to assign retailers different priorities and differentiate demand accordingly. A animal example can be a two echelon supply network where the upstream is a warehouse which supplies customers (directly) and the downstream retailers (in the form of replenishment orders). In such a case, the stockpot cost resulting from not being able to supply customers is usually much higher than that of the retailers since the latter one causes only a delay in the replenishment orders which usually results a lower cost. Another example regarding inventory systems is a spare parts system. In a production system, a part may be installed in various equipment some of which being crucial to the continuum of production.
Thus the demand for this spare part can be differentiated into several demand classes. Again, in a production system verse the same component is used in multiple end products Of different criticality (based on measures such as profitability) the demand of the end products can be differentiated accordingly. Observe that, in both examples, the demand does not come from different end customers. Yet, multiple demand classes occur naturally in both examples either in the form of demand for a spare part from equipment Of different criticality or demand for a common component from different end products. Multiple demand classes an also be observed in other systems. Revenue management is a celebrated example.
The underlying assumption here is that some customers are willing to pay more for a room or seat than others. Therefore it can be optimal to refuse a low-price customer in anticipation of a future request from a high-price customer. It is indeed optimal if the customers arrive sequentially (first the low- price than the high-price customers) and the optimal policy has shown to he characterized by a set of protection levels which essentially are the minimum number of rooms reserved for future (high-price) classes, Observe that, in Hess problems the inventory is perishable and this leads to non-stationary control policies which adjust as time to expiration (i. E. , flight date of the plane) approaches.
Another distinguishing fact is that inventory level (capacity) is fixed. Thus, as opposed to most classical inventory systems, the replenishment decisions are irrelevant. Given a system with multiple demand classes the easiest policy would be to use different stockpiles for each demand class. This way, it would be very easy to assign a different service level to each class. Also the practical implementation of this policy would be relatively easy. But the drawback fifths policy is that no advantage would be taken from the so-called portfolio effect. In other words, the advantage of pooling demand from different demand sources together would no longer be utilized.
Therefore, as a result of the increasing variability of the demand, more safety stock would be needed to ensure a minimum required service level which in turn means more inventory. On the other side, one could simply use the same pool of inventory to satisfy demand from various customer classes without differentiating them. In this case, the highest required service bevel would determine the total inventory needed and thus the inventory cost. The drawback of this policy is that we would he offering higher service levels to the rest of the demand classes, a deficiency that would lead to increased inventory costs. Rationing or the so called critical level policy essentially lies between these two extremes.
Rationing has proved to be effective to handle different demand classes with different stockpot costs or service levels. Klein and Decker provide a comprehensive study illustrating various examples where multiple demand classes arise together with a literature review about he applications of rationing in such environments. We will explain this policy assuming there are tuft demand classes but the extension to several demand classes is straightforward. In this setting, certain part of the stock is reserved for high priority demand. This amount is called the critical level and once inventory level reaches this level, demand from lower priority demand class is no longer satisfied.
If demand not satisfied immediately is backorder, how to handle replenishment orders is another problem. Obviously, if there is a backorder for a high priority customer upon the arrival Of a replenishment order, it is optimal o use this replenishment order to satisfy this backorder. In addition, if there is a backorder for a low priority customer upon the arrival of a replenishment order and the inventory level is at or above the critical level, one should use this replenishment order to satisfy this backorder. However, if there is a low priority backorder and the inventory level is below the critical level one can either satisfy this backorder or increase the inventory level.
The latter one is referred to as the priority cleaning mechanism and has been proven to be optimal for specific conditions. Under general conditions, however, whichever of these is optimal depends on the problem settings. Notice that the service level of the low priority class is not affected by the way replenishment orders are handled. The drawback of the priority clearing mechanism is that it increases the average backorder length of a low priority customer. Except for very specific cases, a simple critical level policy with a static critical level will not be optimal. An optimal policy should take into account the remaining time until the arrival of the next replenishment arrival.
As the booking limits adjust to the remaining time until expiration in revenue management, the critical bevel in a rationing policy should also adjust dynamically. For example, if the inventory level is below the critical level, but it is known that a replenishment order will arrive within a short period of time, it may not be optimal to refuse a low priority demand arrival, especially if the probability of a high priority demand arrival within this time is very small. But employing such a dynamic rationing policy would be extremely difficult from a practical point of view. Thus, we prefer to focus on a static rationing policy where the critical level does not change over time.