Demand Characteristics: known in advance or random
Number of Different Products Stored in the Warehouse
Economies of scale offered by suppliers & transport companies
Length of Planning Horizon
Service level desired
Economic Order Quantity Model Assuming demand certainty Trade-offs between setup costs and inventory holding costs, but ignores issues such as demand uncertainty and forecasting . 1000 2000 3000 4000 5000 6000 0 50 100 150 200 250 300 350 Ordering (Acquisition)Costs Holding or Carrying Costs Total Costs Economic Order Quantity
But Need to understand risk associated with certain decisions.
A frequency histogram provides information about potential profit for the two given production quantities, 9,000 units and 16,000 units. The possible risk and possible reward increases as we increase the production size.
in which inventory is reviewed every day and a decision is made about whether and how much to order.
Periodic review policy
in which the inventory level is reviewed at regular intervals and an appropriate quantity is ordered after each review.
Variable Demand with a Fixed ROP Reorder point, R Q LT Time LT Inventory level 0 Result of uncertainty
Reorder Point with a Safety Stock The amount of safety stock needed is based on the degree of uncertainty in the lead time demand and desired customer service level Reorder point, R Q LT Time LT Inventory level 0 Safety Stock
The inventory position at any point in time is the actual inventory at the warehouse plus items ordered by the distributor that have not yet arrived minus items that are backordered .
The reorder level, R consists of two components: the average inventory during lead time , which is the product of average daily demand and the lead time; and the safety stock , which is the amount of inventory that the distributor needs to keep at the warehouse and in the pipeline to protect against deviations from average demand during lead time.
Continuous Review Policy –Variable demand & fixed lead time
Average demand during lead time is exactly
Safety stock is
where z is a constant, referred to as the safety factor . This constant is associated with the service level.
The reorder level is
Economic lot size is
Continuous Review Policy –Variable demand & fixed lead time
The expected level of inventory before receiving the order is (lowest level i.e. Safety Stock)
The expected level of inventory immediately after receiving the order is (highest level)
The average inventory level is the average of these two values
In many situation, the lead time to the warehouse must be assumed to be normally distributed with average lead time denoted by AVGL and standard deviation denoted by STDL . In this case, the reorder point is calculated as
where AVG x AVGL represents average demand during lead time, &
is the standard deviation of demand during lead time. The amount of safety stock that has to be kept is equal to
Continuous Review Policy –Variable demand & lead time
Inventory level is reviewed periodically at regular intervals and an appropriate quantity so as to arrive at base stock level is ordered after each review .
Since inventory levels are reviewed at a periodic interval, the fixed cost of placing an order is a sunk cost and hence can be ignored.
This level of the inventory position should be enough to protect the warehouse against shortages until the next order arrives, that is to cover demand during a period of r + L days , with r being the length of review period and L being the lead time.
Questions: Q1: For the same service level, which system will require more inventory? Q2: For the same total inventory level, which system will have better service? Market Two Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One
The idea behind risk pooling is to redesign the supply chain, the production process, or the product to either reduce the uncertainty the firm faces or to hedge uncertainty so that the firm is in a better position to mitigate the consequence of uncertainty.
Advantages / Disadvantages large costs to have flexibility accommodate demand uncertainty Capacity Pooling reduce inventory investment additional transportation costs keep inventory closer to customer extra costs of operating distribution center decrease lead time Lead Time Pooling better performance in terms of matching supply and demand potentially degrades product functionality reduction in demand variability Product Pooling reduce expected inventory investment needed to achieve a target service level creates distance between inventory and customers reduce demand variability Location Pooling Disadvantages Advantages
Risk-pooling strategies are most effective when demands are negatively correlated because then the uncertainty with total demand is much less than the uncertainty with any individual item/location
Risk-pooling strategies do not help reduce pipeline inventory
Risk-pooling strategies can be used to reduce inventory while maintaining the same service or they can be used to increase service while holding the same inventory
Example Decentralized system: total SS = 47.88 total avg. invent. = 179 Safety Stock SS = z · STD · Reorder Point R = AVG · L + SS Order Quantity Q = sqrt(2* C 0 *AVG/h ) Order-up-to-level R + Q Average Inventory SS + Q/2 Service Level:97% k=1.88 Lead Time= 1 week Q/2+SS AVG STD SS R Q Order- up-to Level Average Inventory Warehouse 1 39.3 13.2 25.08 65 132 197 91 Warehouse 2 38.6 12.0 22.8 62 131 193 88 Centralized Warehouse 77.9 20.7 39.35 118 186 304 132
The benefits of risk pooling depend on the behavior of demand from one market relative to the demand from another market .
Warehouse Market 1 Market 2 D 1 +D 2 : ( , 2 ) Calculating demand variability of centralized system Conclusions: 1. Stdev of aggregated demand is less than the sum of stdev of individual demands 2. If demands are independent or negatively correlated, the std of aggregated demand is much less 1. If D 1 , D 2 positively correlated, > 0 2. If D 1 , D 2 are independent, = 0 3. If D 1 , D 2 negatively correlated, < 0 = 1 + 2 = ??
As (safety) stock is based on standard deviation
Square Root Law: stock for combined demands usually less than the combined stocks