经济决策定量方法第三章课件

Deterministic Model
Annual Cost Total cost: TC
Ordering cost: hc(Q/2)
Ordering cost: k(A/Q)
Q 0 Q
Deterministic Model
The value of Q, say Q0, that minimizes TC, is found by setting the first derivative to zero Q A hc ( ) ( ) k 2 Q
Optimal quantity： Q 0
Optimal number of order：
2 Ak hc
A n0 Q0
hcA 2k
Optimal cycle time ：
t0
2k hcA
When the unit holding cost increases, both Q0 and t0decrease (smaller inventory levels). As the demand rate increases, Q0 increases (larger batches) but t0decreases (more frequent setups).
The most basic of the deterministic inventory models is the economic order quantity (EOQ). The variable costs in this model are annual holding cost and annual ordering cost. For the EOQ, annual holding and ordering costs are equal.
Economic Order QuLeabharlann Baiduntity
The Mathematical Model
Inventory Level
Slope = -A
Q
Time (years)
T = Q/A Order points
Figure 3-1 Inventory system for the simple economic order quantity model
Example: Bart’s Barometer Business
Economic Order Quantity Model
Bart's Barometer Business is a retail outlet that deals exclusively with weather equipment. Bart is trying to decide on an inventory and reorder policy for home barometers. Barometers cost Bart $50 each and demand is about 5000 per year distributed fairly evenly throughout the year. Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item.
Inventory Costs
Ordering cost -- salaries and expenses of processing an order, regardless of the order quantity Holding cost -- usually a percentage of the value of the item assessed for keeping an item in inventory (including finance costs, insurance, security costs, taxes, warehouse overhead, and other related variable expenses) Backorder cost -- costs associated with being out of stock when an item is demanded (including lost goodwill) Purchase cost -- the actual price of the items Other costs
Deterministic Model
Asummption：
Order quantity isQ. Number of annual order is n，which equals A/Q。Cost per order is k,so that cost of annual A k . When Unit cost of Order Q procuring an item is c, the annual procurement cost is AC
Chapter3 Inventory Models
★ deterministic model ★ stochastic model
Inventory Models
The study of inventory models is concerned with two basic questions: How much should be ordered each time When should the reordering occur The objective is to minimize total variable cost over a specified time period (assumed to be annual in the following review).
A television manufacturing company produces its own speakers, which are used in the production of its television sets. The television sets are assembled on a continuous production line at a rate of 8,000 per month, with one speaker needed per set. Each time a batch is produced, a setup cost of $12,000 is incurred. The unit production cost of a single speaker is $10.The estimated holding cost of keeping a speaker in stock is $0.30 per month. The product quantity to replenish inventory arrives all at once just when desired.
Economic Order Quantity
The objective is to determine when and how much to replenish inventory so as to minimize the Assumptions total cost. A : Annual number of items demanded, c : Unit cost of procuring an item, T : Time between orders, h : Annual cost per dollar value of holding items in inventory. K：fixed cost per order The order quantity (Q) to replenish inventory arrives all at once just when desired, namely, when the inventory level drops to 0. Planned shortages are not allowed
Average inventory level 2 Q hc holding cost Q Average holding cost 2 hc
1
Deterministic Model
Total Annual Cost:
A Q TC (Q) ( )k hc( ) Ac Q 2
transformed：

Economic order quantity (EOQ) Economic production lot size EOQ with planned shortages EOQ with quantity discounts
Economic Order Quantity (EOQ)
Deterministic Model
Suppose that a Mall sells 12,000 pair of skis each year. For simplicity, we will assume that the ski is sold at a constant rate throughout the year. The net cost of each pair to the Mall is $30. The wholesale supplier charges $10 for each delivery, regardless of how many pairs have been ordered, and delivery always occurs the day after the order is placed. The owner’s only working capital is tied up in inventory, and these funds have been borrowed from the local bank at a simple annual interest rate of 10%. In addition, the owner must pay a state franchise tax of 5% of the annual inventory value, and another 5% for theft insurance. All other operating costs are either fixed in nature or do not depend on the amount of skis ordered. The owner wants to evaluate the present procedure of ordering 1,000 pairs each month and to establish a better inventory policy that will minimize the annual costs of doing business in skis.
A Q TC (Q) ( )k hc( ) Q 2
Deterministic Model
Holding cost curve：
Q hc ( ) 2
Ordering cost curve： ( A ) k
Q
Total cost curve：
A Q TC (Q) ( )k hc( ) Q 2
Deterministic Models
The simplest inventory models assume demand and the other parameters of the problem to be deterministic and constant. The deterministic models covered in this chapter are:
Deterministic Model
★Economic Order Quantity,（EOQ）
A simple model representing the most common inventory situation faced by manufacturers, retailers, and wholesalers is the EOQ (Economic Order Quantity) model. (It sometimes is also referred to as the economic lot-size model.)