! " # $ % % & $'( # ) * 1

Transcription

1 ! " # $% %&$'( # ) * 1

2 +,+ #+ ' Percent of annual dollar usage A Items B Items &( &( + C Items Percent of inventory items Figure 1.

3 ' - %. &( + / / / + # # % " / / 3 3

4 ' 4 ' "! " Inventory level Order quantity = (maximum inventory level) Minimum inventory Usage rate Average inventory on hand Time Figure 1.3 4

5 # Objective is to minimize total costs Minimum total cost Curve for total cost of holding and setup Annual cost Table 11.5 Optimal order quantity Holding cost curve Setup (or order) cost curve Order quantity $ Annual setup cost = S = Number of pieces per order * = Optimal number of pieces per order (EO) = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) = Annual demand Number of units in each order = (S) Setup or order cost per order $ Annual holding cost = = Number of pieces per order * = Optimal number of pieces per order (EO) = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity = (Holding cost per unit per year) = (H) S Annual setup cost = H 5

6 $ = Number of pieces per order * = Optimal number of pieces per order (EO) = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual setup cost = S Annual holding cost = H Optimal order quantity is found when annual setup cost equals annual holding cost Solving for * S = H S = H = S/H * = S/H % etermine optimal number of needles to order = 1,000 units S = $10 per order H = $.50 per unit per year * = * = S H (1,000)(10) 0.50 = 40,000 = 00 units % etermine optimal number of needles to order = 1,000 units * = 00 units S = $10 per order H = $.50 per unit per year Expected number of orders emand = N = = Order quantity N = 1, * = 5 orders per year 6

7 % etermine optimal number of needles to order = 1,000 units * = 00 units S = $10 per order N = 5 orders per year H = $.50 per unit per year Expected time between = T = orders T = Number of working days per year 50 5 N = 50 days between orders % etermine optimal number of needles to order = 1,000 units * = 00 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = S + H 1, TC = ($10) + ($.50) 00 TC = (5)($10) + (100)($.50) = $50 + $50 = $100 & The EO model is robust It works even if all parameters and assumptions are not met The total cost curve is relatively flat in the area of the EO 7

8 ' EO answers the how much question The reorder point (ROP) tells when to order ROP = d = emand per day = d x L Lead time for a new order in days Number of working days in a year ' Inventory level (units) * ROP (units) Slope = units/day = d Figure 1.5 Lead time = L Time (days) ' % emand = 8,000 Vs per year 50 working day year Lead time for orders is 3 working days d = ROP = d x L Number of working days in a year = 8,000/50 = 3 units = 3 units per day x 3 days = 96 units 8

9 ' ' Inventory level Maximum inventory Part of inventory cycle during which production (and usage) is taking place emand part of cycle with no production t Time Figure 1.6 ' = Number of pieces per order p = aily production rate H = Holding cost per unit per year d = aily demand/usage rate t = Length of the production run in days Annual inventory holding cost = (Average inventory level) x Holding cost per unit per year Annual inventory level = (Maximum inventory level)/ Maximum inventory level Total produced during = the production run = pt dt Total used during the production run 9

10 ' = Number of pieces per order p = aily production rate H = Holding cost per unit per year d = aily demand/usage rate t = Length of the production run in days Maximum inventory level = Total produced during the production run = pt dt However, = total produced = pt ; thus t = /p Maximum inventory level = p d = 1 p p d p Total used during the production run Maximum inventory level d Holding cost = (H) = 1 H p ' = Number of pieces per order H = Holding cost per unit per year = Annual demand p = aily production rate d = aily demand/usage rate Setup cost = (/)S Holding cost = 1/ H[1 - (d/p)] (/)S = 1/ H[1 - (d/p)] = S H[1 - (d/p)] * = S H[1 - (d/p)] ' % = 1,000 units S = $10 H = $0.50 per unit per year p = 8 units per day d = 4 units per day * = S H[1 - (d/p)] * = = 80,000 (1,000)(10) 0.50[1 - (4/8)] = 8.8 or 83 hubcaps 10

11 ' When annual data are used the equation becomes * = S annual demand rate H 1 annual production rate ( Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost H TC = S + + P ( A typical quantity discount schedule &6( 4 &( 5 Table 1. 11

12 ( Steps in analyzing a quantity discount 1. For each discount, calculate *. If * for a discount doesn t qualify, choose the smallest possible order size to get the discount 3. Compute the total cost for each * or adjusted value from Step 4. Select the * that gives the lowest total cost ( Total cost curve for discount 1 Total cost curve for discount Total cost $ a b Total cost curve for discount 3 * for discount is below the allowable range at point a and must be adjusted upward to 1,000 units at point b 1st price break nd price break 0 1,000,000 Order quantity Figure 1.7 ( % Calculate * for every discount * = S IP 1 * = * = 3 * = (5,000)(49) (.)(5.00) (5,000)(49) (.)(4.80) (5,000)(49) (.)(4.75) = 700 cars order = 714 cars order = 718 cars order 1

13 ( % Calculate * for every discount 1 * = (5,000)(49) (.)(5.00) * = = 700 cars order S IP * = 3 * = (5,000)(49) (.)(4.80) (5,000)(49) (.)(4.75) = 714 cars order 1,000 adjusted = 718 cars order,000 adjusted ( % " 3 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit Table 1.3 % ' 13

14 /71 % 9 ' "1 14