Economic Order Quantity model

Description

This function finds the optimal order policy in the classical Economic Order Quantity (EOQ) model and the EOQ model with planned shortages.

Usage

EOQ(d, k, h, b = 0)

Arguments

Details

The EOQ model, also called Lot-Sizing model, considers that demand is uniform and deterministic. Lead time, the time between the placement of an order and its receipt, is equal to zero.

The optimal order policy in the classical EOQ model minimizes the total cost associated with the ordering and holding costs while meeting all demand (without shortage). When shortages are allowed (b>0) we have the EOQ model with backorders or planned shortages.

Value

A list containing:

References

- Hillier, F. and Lieberman, G. (2001). Introduction to operational research. New York: McGraw-Hill, 7th.

See Also

EPQ, newsboy, WW

Examples

 ## Not run: 
#Classical EOQ model
#Given demand d=8000 items per year; set up cost k=12000; and holding cost h=0.3
#per unit we find that the optimal solution is to order 25298 units every 3.2
#months with a total variable cost of $7589.5
## End(Not run)
 
EOQ(8000,12000,0.3)

## Not run: 
#EOQ model with planned shortages
#Consider now that backorders are allowed with a backorder cost b=1.1 per
#unit and year. Then the optimal solution is to order 28540 units every 3.6 months.
#The total variable cost is $6727.3 and the maximum shortage is 6116 units.
## End(Not run)
   
EOQ(8000,12000,0.3,1.1)

Economic Production Quantity model

Description

Implements the Economic Production Quantity (EPQ) model.

Usage

EPQ(d, p, k, h, b = 0)

Arguments

Details

The EPQ model is an extension of the EOQ model. It considers finite production rate, that is, the inventory is replenished gradually as the order is produced. Note that this assumption requires the production rate to be greater than the demand rate (p>d) otherwise there would be no inventory at any time.

The model considers that a new order is produced incrementally when the inventory reaches zero. During the time that production run, t=Q/p, inventory is accumulated at rate p-d, which implies that when the production of the batch Q is finished the inventory will reach its maximum level I.

Value

EPQ() returns a list containing:

References

- Gallego, G. "IEOR4000: Production Management" (Lecture 2), Columbia (2004).

See Also

EOQ, newsboy, WW

Examples

 ## Not run: 
#Suppose k = 100, h = 5, d = 200, p = 1000. Then the production run at
#t=0.1, the optimal order interval is T = 0.5, the optimal order quantity
#is Q = 100, the maximum inventory level is I=80 and the total cost is
#TC = $400.
## End(Not run)
 
EPQ(d=200,p=1000,k=100,h=5)

The newsboy model

Description

Implements the newsboy (or newsvendor) model with normal demand.

Usage

Newsboy(m, sd, p, c, s = 0)

Arguments

Details

When the demand is a random variable with normal distribution, the optimal stocking quantity that minimize the expected cost is: Q=m+z*sd, where z is known as the safety factor and Q - m=z*sd is known as the safety stock. 'Note that the newsboy problem is not formulated in terms of per unit holding cost h=c-s and penalty cost b=p-c.

Value

A list containing:

References

- Porteus E. L. (2002) Foundations of Stochastic Inventory Theory, Stanford University Press, Stanford, CA.

- Gallego G. (1995) Newsvendor Problem. IEOR 4000 Production Management.

- Ayhan, Hayriye, Dai, Jim, Foley, R. D., Wu, Joe, (2004): Newsvendor Notes, ISyE 3232 Stochastic Manufacturing & Service Systems.

See Also

EOQ, EPQ, WW, SS

Examples

 ## Not run: 
# Example Porteus #
# Suppose demand is normally distributed with mean 100 and standard
# deviation 30. If p = 4 and c = 1, then CR = 0.75 and Q=120.23.
# Note that the order is for 20.23  units (safety stock) more than the
# mean. Note also that ExpC(120.23) = 38.13 and ExpP(120.23)=261.87,
# with FR=0.96.
## End(Not run)

Newsboy(100,30,4,1)

## Not run: 
# Example Gallego #
# Suppose demand is normal with mean 100 and standard deviation 20. The
# unit cost is 5, the holding and penalty cost are 1 and 3
# respectively. From the definition of the holding and penalty
# cost we find that p=4, then CR = 0.75 and Q = 113.49. Notice that the
# order is for 13.49 units (safety stock) more than the mean,
# ExpC(113.49) = 25.42 and ExpP(113.49) = 274.58, with fill rate of
# 97 percent.
## End(Not run)

Newsboy(100,20,4,1)

Reorder Point

Description

ROP computes the reorder point level of inventory. When inventory falls to this amount, a new order must be made.

Usage

ROP(SL, md, sd, L = 1)

Arguments

Value

Reorder point level

See Also

SS

Examples

 ROP(0.9,2500,500,6)

Deprecated functions in the SCperf package

Description

The functions listed below are provided for compatibility with older version of the SCperf package. They have been deprecated and will be defunct in the next version of this package. Help pages for deprecated functions are available at help("-deprecated")

Usage

SCperf(phi, theta, L = L, SL = 0.95)

SSL(method = c("MMSE", "SMA", "ES"), phi, L, p, alpha, SL)

bullwhip(method = c("MMSE", "SMA", "ES"), phi, L, p, alpha)

Details

The SCperf function has been deprecated and will be made defunct; use the bullwhipgame package.

The SSL function has been deprecated and will be made defunct; use the bullwhipgame package.

The bullwhip function has been deprecated and will be made defunct; use the bullwhipgame package.

Supply Chain Performance

Description

Computes the bullwhip effect for an stationary ARMA(p,q) demand process.

Usage

SCperf(phi, theta, L, SL)

Arguments

Details

The SCperf function has been deprecated and will be made defunct; use the bullwhipgame package.

Value

Analytical measure for the bullwhip effect

References

- Zhang, X. (2004b). Evolution of ARMA demand in supply chains. Manufacturing and Services Operations Management, 6 (2), 195-198.

- Silva Marchena, M. (2010) Measuring and implementing the bullwhip effect under a generalized demand process. http://arxiv.org/abs/1009.3977

See Also

pkgSCperf-deprecated

Examples

## Not run: 

#ARMA(1,1) case

SCperf(phi=0.95,theta=0.1,L=2,SL=0.99)

#AR(2) case

SCperf(phi=c(0.8,-0.2),theta=0,L=1)

## End(Not run)

Safety Stock

Description

SS computes the safety stock level over lead-time

Usage

SS(SL, sd, L = 1)

Arguments

Value

Safety stock level over lead-time

Examples

 
 SS(0.95,0.7,2)

Safety stock over lead-time

Description

SSL computes the safety stock level over lead-time for three forecasting methods: Minimum Mean Square Error (MMSE), Simple Moving Average (SMA) and Exponential Smoothing (ES) when the demand follows a stationary AR(1) stochastic process.

Usage

SSL(method, phi, L, p, alpha, SL)

Arguments

Details

The SSL function has been deprecated and will be made defunct; use the bullwhipgame package.

Value

Safety stock level over lead-time

See Also

pkgSCperf-deprecated

Examples

## Not run: 

SSL("MMSE",0.15,2,4,0.7,0.95)

SSL("SMA",0.15,2,4,0.7,0.95)

SSL("ES",0.15,2,4,0.7,0.95) 

## End(Not run)

The Wagner-Whitin algorithm

Description

WW implements the Wagner-Whitin algorithm. Considering time-varying demand, the algorithm builds production plans that minimizes the total setup and holding costs in a finite horizon of time, assuming zero starting inventory and no backlogging

Usage

WW(x, a, h, method = c("backward", "forward"))

Arguments

See Also

EOQ, EPQ, newsboy

Examples

 ## Not run: 
# Example from Hiller, p.952, reproduced bellow:
# An airplane manufacturer specializes in producing small airplanes. It has just received
# an order from a major corporation for 10 customized executive jet airplanes for the use of
# the corporation's upper management. The order calls for three of the airplanes to be delivered
# (and paid for) during the upcoming winter months (period 1), two more to be delivered during
# the spring (period 2), three more during the summer (period 3), and the final two during the fall
# (period 4). Setting up the production facilities to meet the corporation's specifications for
# these airplanes requires a setup cost of $2 million.
# The manufacturer has the capacity to produce all 10 airplanes within a couple of months, when the
# winter season will be under way. However, this would necessitate holding seven of the airplanes in
# inventory, at a cost of $200,000 per airplane per period, until their scheduled delivery times
# (...) Management would like to determine theleast costly production schedule for filling
# this order.
## End(Not run)


x  <- c(3,2,3,2)
a  <- 2
h  <- 0.2
WW(x,a,h,method="backward")

 ## Not run: 
# The total variable cost is $4.8 million (minimum value in the first raw). Since we have two
# minimun values in the first raw (positions 2 and 4), we have the following solutions:
# Solution 1:  Produce to cover demand until period 2, 5 airplanes. In period 3, new decision,
# minimun value 2.4 in period 4 (third raw). Then in period 3 produce to cover demand until 
# period 4, 5 airplanes.
# Solution 2: Produce to cover demand until period 4, 10 airplanes.
## End(Not run)
 
WW(x,a,h,method="forward")

 ## Not run: 
#The total variable cost is $4.8 million (minimum value in the last raw). Since we have two minimun
# values in columns 1 and 3, the solutions are:
# Solution 1: Produce in period 1 to cover demand until period 4, 10 airplanes.
# Solution 2: Produce in period 3 to cover demand until period 4, 5 airplanes.In period 2, new
# decision, minimun value 2.4 in raw 3. Then in period 1 produce to cover demand until
# period 2, 5 airplanes.
## End(Not run)

Bullwhip effect

Description

bullwhip computes the increase of demand variability for a simple two-stage supply chains consisting of a single retailer and a single manufacturer using three forcasting methods: Minimum Mean Square Error (MMSE), Simple Moving Average (SMA) and Exponential Smoothing (ES) when the demand follows a known stationary AR(1) stochastic process.

Usage

bullwhip(method, phi, L, p, alpha)

Arguments

Details

The bullwhip function has been deprecated and will be made defunct; use the bullwhipgame package.

Value

The measure for the bullwhip effect

See Also

pkgSCperf-deprecated

Examples

## Not run: 

bullwhip("SMA",0.9,2,4)

bullwhip("ES",0.9,2,0,0.6)

bullwhip("MMSE",0.9,2) 

## End(Not run)