inventory models n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Inventory Models PowerPoint Presentation
Download Presentation
Inventory Models

Loading in 2 Seconds...

play fullscreen
1 / 13

Inventory Models - PowerPoint PPT Presentation


  • 336 Views
  • Uploaded on

Inventory Models. Planned Shortage Models. PLANNED SHORTAGE MODEL. Assumes no customers will be lost because of stockouts Instantaneous reordering This can be modified later using standard reorder point analyses Stockout costs: C b -- fixed administrative cost/stockout

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Inventory Models' - niveditha


Download Now 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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
inventory models

Inventory Models

Planned Shortage Models

planned shortage model
PLANNED SHORTAGE MODEL
  • Assumes no customers will be lost because of stockouts
  • Instantaneous reordering
    • This can be modified later using standard reorder point analyses
  • Stockout costs:
    • Cb -- fixed administrative cost/stockout
    • Cs -- annualized cost per unit short
      • Acts like a holding cost in reverse
  • Reorder when there are S backorders
proportion of time in out of stock
PROPORTION OF TIME IN/OUT OF STOCK
  • T1= time of a cycle with inventory
  • T2= time of a cycle out of stock
  • T = T1 + T2 = time of a cycle
  • IMAX = Q-S = total demand while in stock.
  • T1/T =Proportion of time in stock.

Multiplying by D/D gives T1D/TD =

(Demand while in stock)/(Demand for cycle) = (Q-S)/Q

  • T2/T = Proportion of time out of stock

Multiplying by D/D gives T2D/TD =

(Demand while out of stock)/(Demand for cycle) = S/Q

average inventory average number of backorders
Average InventoryAverage Number of Backorders
  • Average Inventory =

(Avg. Inv. When In Stock)(Proportion of time in stock)

=(IMAX/2)((Q-S)/Q) = ((Q-S)/2)((Q-S)/Q) =(Q-S)2/2Q

  • Average Backorders =

(Average B/O When Out of Stock)(Proportion of time out of stock)

= (S/2)(S/Q) = S2/2Q

total annual cost equation
TOTAL ANNUAL COST EQUATION
  • TC(Q,S) = CO(Avg. Cycles Per Year) + CH(Average Inv.) + Cs (Average Backorders) + Cb (Number B/Os Per Cycle) (Avg. Cycles Per Year) + CD

= CO(D/Q) + Ch((Q-S)2/2Q) + Cs(S2/2Q) + CbS(D/Q) + CD

optimal order quantity q optimal backorders s
OPTIMAL ORDER QUANTITY, Q*OPTIMAL # BACKORDERS, S*
  • Take partial derivatives with respect to Q and S and set = 0.
  • Solve the two equations for the two unknowns Q and S.
example scanlon plumbing
EXAMPLESCANLON PLUMBING
  • Saunas cost $2400 each (C = 2400)
  • Order cost = $1250 (CO = 1250)
  • Holding Cost = $525/sauna/yr. (Ch = 525)
  • Backorder Goodwill Cost $20/wk (CS =1040)
  • Backorder Admin. Cost = $10/order (Cb = 10)
  • Demand = 15/wk (D = 780)
using the template
Using the Template

OptimalValues

Input

Parameters

Planned Shortage

Worksheet

reorder point analysis
REORDER POINT ANALYSIS
  • Reorder point can be affected by lead time.
  • If lead time is fixed at L years, order is placed accounting for the fact that LD items would be demanded during lead time.
  • Thus order is places when there are S*-LD backorders.
    • If this is a negative number, this implies an order is placed when there are LD - S* items left in ventory.
example what if lead time were 4 weeks
ExampleWhat If Lead Time Were 4 Weeks?
  • Demand over 4 weeks = 4(15) = 60
    • 4 weeks = .07692 years (for template)
  • Want order to arrive when there are 20 backorders.
  • Thus order should be placed when there are 60 - 20 = 40 saunas left in inventory
using template
Using Template

Reorder Point = 40

Enter Lead Time

review
Review
  • In planned shortage models there can be both time-dependent and time-independent shortage costs
  • There are 2 unknowns which are found by taking partial derivatives of the total cost equation
    • Q* -- the amount to order
    • S*-- the number of backorders when order is placed
  • The actual reorder point may be adjusted for lead time.
  • Use of template