1 / 5

Inventory Theory Continuous Review Math 305

Inventory Theory Continuous Review Math 305. 12/7/08. Continuous Review. Previous model: periodic review orders placed at the begining of periods Continuous review: an order may be placed at any time What is an inventory policy? when to order more how much to order Costs

gretel
Download Presentation

Inventory Theory Continuous Review Math 305

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inventory TheoryContinuous ReviewMath 305 12/7/08

  2. Continuous Review Previous model: periodic review • orders placed at the begining of periods Continuous review: an order may be placed at any time What is an inventory policy? • when to order more • how much to order Costs • ordering /production (paperwork, delivery charges, per unit charges) • holding (storage, spoilage, opportunity • shortage (possible loss of sale, cost of filling back order) • revenues (not usually counted) • salvage value (at end of inventory period)

  3. Deterministic Example, No Shortages My factory needs 8000 speakers/month for the TVs it makes • speakers are produced in batches • setup cost per batch: $12,000 per run (retooling, startup,...) • per speaker cost of $10 How much do I produce/order at a time? (Q) Q (speakers) Q/a (time) In general K = set up cost c = per unit cost → production cost/cycle = K + cQ a = rate of demand → cycle length = Q/a h = holding cost → holding cost per cycle = (Q/a)(Q/a) h = (hQ2)/2a

  4. No Shortages Total cost per cycle = K + cQ + (hQ2)/2a Cost per unit time T(Q) = K + cQ + (hQ2)/2a = aK/Q + ac + hQ/2 Q/a T(Q) dT/dQ = -aK/Q2 +h/2 Q* = √2aK/h = EOQ t = Q/a = √ 2K/ah Q* Q TVs: T(Q) = (8000)(12,000)/Q + 8000 + .30Q/2 Q* = 25,298 t* = 3.2 months

  5. Shortages Allowed Shortage cost p per unfilled unit of demand per unit time S Q S/a Q/a shortage: p(Q/a-S/a)(Q-s)/2 = p(Q-S)2 /2a T(Q,S) = K + cQ - hS2/2a + p(Q-S)2/2a = aK/Q + ac + hS2/2Q + p(Q-S) 2/2a Q/a (... messy partial derivatives...) S* = √2aK/h √ p/(p+h) Q* = √2aK/h √(p+h)/p What happens as p → ∞? as p↓ P for speakers = 1.10 S* = EOQ(√ 1.1/(1.1+.3) = 22,424 Q* = EOQ(√ (1.1+.3)/1.1) = 28,540 Q-S = max shortage = 6116

More Related