This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Finding the EOQ, Total Cost, TBOFinding the EOQ, Total Cost, TBO
EXAMPLE 12.2
For the bird feeders in Example 12.1, calculate the EOQ and its total annual cycle-inventory cost. How frequently will orders betotal annual cycle inventory cost. How frequently will orders be placed if the EOQ is used?
SOLUTION
Using the formulas for EOQ and annual cost, we get
Suppose that you are reviewing the inventory policies on an $80 item stocked at a hardware store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional i f ti iinformation is:
D = 60 units per week, or 3,120 units per year
S = $30 per order
H = 25% of selling price, or $20 per unit per year
Figure 12.6 – Q System When Demand and Lead Time Are Constant and Certain
28-Jun-10
13
Application 12.2Application 12.2
The on-hand inventory is only 10 units, and the reorder point R is 100. There are no backorders and one open order for 200 units Should a new order be placed?200 units. Should a new order be placed?
Demand for chicken soup at a supermarket is always 25 cases a day and the lead time is always 4 days. The shelves were justday and the lead time is always 4 days. The shelves were just restocked with chicken soup, leaving an on-hand inventory of only 10 cases. No backorders currently exist, but there is one open order in the pipeline for 200 cases. What is the inventory position? Should a new order be placed?
SOLUTION
R = Total demand during lead time = (25)(4) = 100 cases
Figure 12.9 – Finding Safety Stock with a Normal Probability Distribution for an 85 Percent Cycle-Service Level
28-Jun-10
17
Reorder Point for Variable DemandReorder Point for Variable Demand
EXAMPLE 12.4
Let us return to the bird feeder in Example 12.2. The EOQ is 75 units. Suppose that the average demand is 18 units per week with a standard deviation of 5 units. The lead time is constant at two weeks. Determine the safety stock and reorder point if management wants a 90 percent cycle-service level.
Reorder Point for Variable DemandReorder Point for Variable Demand
SOLUTION
In this case, σd = 5, d = 18 units, and L = 2 weeks, so dσdLT = σd L = 5 2 = 7.07. Consult the body of the table in the Normal Distribution appendix for 0.9000, which corresponds to a 90 percent cycle-service level. The closest number is 0.8997, which corresponds to 1.2 in the row heading and 0.08 in the column heading. Adding these values gives a z value of 1.28. With this information, we calculate the safety stock and reorder point as follows:
Suppose that the demand during lead time is normally distributed with an average of 85 and σdLT = 40. Find the safety stock, and reorder point R, for a 95 percent cycle-service level.
SOLUTION
Safety stock = zσdLT =
Find the safety stock and reorder point R for an 85 percent
R = Average demand during lead time + Safety stock
d = Average weekly (or daily or monthly) demandL = Average lead timeσd = Standard deviation of weekly (or daily or monthly) demandσLT = Standard deviation of the lead timeσdLT = Lσd
2 + d2σLT2
28-Jun-10
19
Reorder PointReorder Point
EXAMPLE 12.5
The Office Supply Shop estimates that the average demand for e O ce Supp y S op est ates t at t e a e age de a d oa popular ball-point pen is 12,000 pens per week with a standard deviation of 3,000 pens. The current inventory policy calls for replenishment orders of 156,000 pens. The average lead time from the distributor is 5 weeks, with a standard deviation of 2 weeks. If management wants a 95 percent cycle-service level, what should the reorder point be?
Grey Wolf lodge is a popular 500-room hotel in the North Woods. Managers need to keep close tabs on all of the room service items including a special pint-scented bar soap Theservice items, including a special pint-scented bar soap. The daily demand for the soap is 275 bars, with a standard deviation of 30 bars. Ordering cost is $10 and the inventory holding cost is $0.30/bar/year. The lead time from the supplier is 5 days, with a standard deviation of 1 day. The lodge is open 365 days a year.
What should the reorder point be for the bar of soap if management wants to have a 99 percent cycle-service?
Suppose that the current policy is Q = 80 and R = 150. What will be the changes in average cycle inventory and safety stock if your EOQ and R values are implemented?
How Much to Order in a How Much to Order in a PP SystemSystem
EXAMPLE 12.6
A distribution center has a backorder for five 36-inch color TV sets. No inventory is currently on hand, and now is the time tosets. No inventory is currently on hand, and now is the time to review. How many should be reordered if T = 400 and no receipts are scheduled?
That is, 405 sets must be ordered to bring the inventory position up to T sets.
T – IP = 400 – (–5) = 405 sets
28-Jun-10
25
Application 12.6Application 12.6
The on-hand inventory is 10 units, and T is 400. There are no back orders, but one scheduled receipt of 200 units. Now is the time to review. How much should be reordered?
T = d(P + L) + safety stock for protection interval
interval is d(P + L), or
Safety stock = zσP + L , where σP + L = LPd
28-Jun-10
26
Calculating Calculating PP and and TT
EXAMPLE 12.7
Again, let us return to the bird feeder example. Recall that demand for the bird feeder is normally distributed with a meandemand for the bird feeder is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units. The lead time is 2 weeks, and the business operates 52 weeks per year. The Q system developed in Example 12.4 called for an EOQ of 75 units and a safety stock of 9 units for a cycle-service level of 90 percent. What is the equivalent Psystem? Answers are to be rounded to the nearest integer.
We first define D and then P. Here, P is the time between reviews, expressed in weeks because the data are expressed asreviews, expressed in weeks because the data are expressed as demand per week:
With d = 18 units per week, an alternative approach is to calculate P by dividing the EOQ by d to get 75/18 = 4.2 or 4 weeks. Either way, we would review the bird feeder inventory every 4 weeks.
28-Jun-10
27
Calculating Calculating PP and and TT
We now find the standard deviation of demand over the protection interval (P + L) = 6:
it12 2565
Before calculating T, we also need a z value. For a 90 percent cycle-service level z = 1.28. The safety stock becomes
Safety stock = zσP + L = 1.28(12.25) = 15.68 or 16 units
Order quantities vary to keep the inventory position at R
Minimizes cycle inventory, but increases ordering costs
Appropriate for expensive items
Solved Problem 1Solved Problem 1
Booker’s Book Bindery divides SKUs into three classes, according to their dollar usage. Calculate the usage values of the following SKUs and determine which is most likely to be
The annual dollar usage for each item is determined by multiplying the annual usage quantity by the value per unit. Asmultiplying the annual usage quantity by the value per unit. As shown in Figure 12.11, the SKUs are then sorted by annual dollar usage, in declining order. Finally, A–B and B–C class lines are drawn roughly, according to the guidelines presented in the text. Here, class A includes only one SKU (signatures), which represents only 1/7, or 14 percent, of the SKUs but accounts for 83 percent of annual dollar usage. Class B includes the next two SKUs, which taken together represent 28 percent of the SKUs and account for 13 percent of annual dollar
Figure 12.11 – Annual Dollar Usage for Class A, B, and C SKUs Using Tutor 12.2
Solved Problem 2Solved Problem 2
Nelson’s Hardware Store stocks a 19.2 volt cordless drill that is a popular seller. Annual demand is 5,000 units, the ordering cost is $15, and the inventory holding cost is $4/unit/year.
a. What is the economic order quantity?
b. What is the total annual cost for this inventory item?
A regional distributor purchases discontinued appliances from various suppliers and then sells them on demand to retailers in the region. The distributor operates 5 days per week, 52 weeks
O l h it i f b i d bper year. Only when it is open for business can orders be received. Management wants to reevaluate its current inventory policy, which calls for order quantities of 440 counter-top mixers. The following data are estimated for the mixer:
Average daily demand (d) = 100 mixers
Standard deviation of daily demand (σd) = 30 mixers
d. It is time to review the item. On hand inventory is 40 mixers; receipt of 440 mixers is scheduled, and no backorders exist. How much should be reordered?
28-Jun-10
36
Solved Problem 4Solved Problem 4
SOLUTION
a. The time between orders is
EOQ 440P = (260 days/year) =
EOQD
(260) = 4.4 or 4 days440
26,000
b. Figure 12.12 shows that T = 812 and safety stock = (1.41)(79.37) = 111.91 or about 112 mixers. The corresponding Q system for the counter-top mixer requires less safety stock.
The order quantity is the target inventory level minus the inventory position, or
Q = T – IP =
An order for 332 mixers should be placed.
812 mixers – 480 mixers = 332 mixers
28-Jun-10
37
Solved Problem 5Solved Problem 5
Grey Wolf Lodge is a popular 500-room hotel in the North Woods. Managers need to keep close tabs on all room service items, including a special pine-scented bar soap. The daily d d f th i 275 b ith t d d d i ti f 30demand for the soap is 275 bars, with a standard deviation of 30 bars. Ordering cost is $10 and the inventory holding cost is $0.30/bar/year. The lead time from the supplier is 5 days, with a standard deviation of 1 day. The lodge is open 365 days a year.
a. What is the economic order quantity for the bar of soap?
b. What should the reorder point be for the bar of soap if management wants to have a 99 percent cycle-service level?
b. We have d = 275 bars/day, σd = 30 bars, L = 5 days, and σLT = 1 day.
σdLT = Lσd2 + d2σLT
2 = (5)(30)2 + (275)2(1)2 = 283.06 bars
Consult the body of the Normal Distribution appendix for 0.9900. The closest value is 0.9901, which corresponds to a z value of 2.33. We calculate the safety stock and reorder point as follows:
Zeke’s Hardware Store sells furnace filters. The cost to place an order to the distributor is $25 and the annual cost to hold a filter in stock is $2. The average demand per week for the filters is 32
it d th t t 50 k Th klunits, and the store operates 50 weeks per year. The weekly demand for filters has the probability distribution shown on the left below.
The delivery lead time from the distributor is uncertain and has the probability distribution shown on the right below.
Suppose Zeke wants to use a P system with P = 6 weeks and a cycle-service level of 90 percent. What is the appropriate value for T and the associated annual cost of the system?
Figure 12.13 – OM Explorer Solver for Demand during the Protection Interval
Solved Problem 6Solved Problem 6
Given the desired cycle-service level of 90 percent, the appropriate T value is 322 units. The simulation estimated the average demand during the protection interval to be 289 units,
tl th f t t k i 322 289 33 itconsequently the safety stock is 322 – 289 = 33 units.
Consider Zeke’s inventory in Solved Problem 6. Suppose that he wants to use a continuous review (Q) system for the filters, with an order quantity of 200 and a reorder point of 140. Initial i t i 170 it If th t k t t i $5 it d llinventory is 170 units. If the stockout cost is $5 per unit, and all of the other data in Solved Problem 6 are the same, what is the expected cost per week of using the Q system?
SOLUTION
Figure 12.14 shows output from the Q System Simulator in OM Explorer. Only weeks 1 through 13 and weeks 41 through 50 are shown in the figure The average total cost per week is
are shown in the figure. The average total cost per week is $305.62. Notice that no stockouts occurred in this simulation. These results are dependent on Zeke’s choices for the reorder point and lot size. It is possible that stockouts would occur if the simulation were run for more than 50 weeks.