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Lecture. 6. Inventory Management Chapter 11. Economic Production Quantity (EPQ). Economic production quantity (EPQ) model: variant of basic EOQ model Production done in batches or lots Replenishment order not received in one lump sum unlike basic EOQ model

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slide1

Lecture

6

Inventory Management

Chapter 11

economic production quantity epq
Economic Production Quantity (EPQ)
  • Economic production quantity (EPQ) model: variant of basic EOQ model
  • Production done in batches or lots
  • Replenishment order not received in one lump sum unlike basic EOQ model
  • Inventory is replenished gradually as the order is produced
    • hence requires the production rate to be greater than the demand rate
  • This model's variable costs are
    • annual holding cost, and
    • annual set-up cost (equivalent to ordering cost).
  • For the optimal lot size,
    • annual holding and set-up costs are equal.
epq model assumptions
EPQ Model Assumptions
  • Demand occurs at a constant rate of D items per year.
  • Production capacity is p items per year.
    • p > D
  • Set-up cost: $Coper run.
  • Holding cost: $Ch per item in inventory per year.
  • Purchase cost per unit is constant (no quantity discount).
  • Set-up time (lead time) is constant.
  • Planned shortages are not permitted.
epq model formulae
EPQ Model Formulae
  • Optimal production lot-size (formula 11-16 of book)
  • Run time: Q */p
  • Time between set-ups (cycle time): Q */D years
  • Total cost (formula 11.15 of book)
example non slip tile co
Example: Non-Slip Tile Co.
  • Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tiles annually.
  • The set-up cost is $5,000 per run
  • Holding cost is estimated at 10% of the manufacturing cost of $1 per tile.
  • The production capacity of the machine is 500,000 tiles per month.
  • The factory is open 365 days per year.
  • Determine
    • Optimal production lot size
    • Annual holding and setup costs
    • Number of setups per year
    • Loss/profit that NST is incurring annually by using their present production schedule
management scientist solutions
Management Scientist Solutions
  • Optimal TC = $28,868
  • Current TC = .04167(100,000) + 5,000,000,000/100,000

= $54,167

  • LOSS = 54,167 - 28,868 = $25,299
economic production quantity assumptions
Economic Production Quantity Assumptions
  • Only one item is involved 
  • Annual demand is known 
  • Usage rate is constant 
  • Usage occurs continually
  • Production occurs periodically
  • Production rate is constant
  • Lead time does not vary 
  • No quantity discounts 
operations strategy
Operations Strategy
  • Too much inventory
    • Tends to hide problems
    • Easier to live with problems than to eliminate them
    • Costly to maintain
  • Wise strategy
    • Reduce lot sizes
    • Reduce safety stock
slide11

(in millions, except per share amount)

Fiscal Year Ended

28-Jan-00

29-Jan-99

Net revenue

$25,265

$18,243

Cost of revenue

20,047

14,137

Gross margin

5,218

4,106

Operating expenses:

Selling, general and administrative

2,387

1,788

Research, development, and engineering

568

272

Total operating expenses

2,955

2,060

Operating income

2,263

2,046

Other income

188

38

Income before income taxes

2,451

2,084

Provision for income taxes

785

624

Net income

$1,666

$1,460

Earnings per common share:

Basic

$0.66

$0.58

Diluted

$0.61

$0.53

Weighted average shares outstanding:

Basic

2,536

2,531

Diluted

2,728

2,772

Retained Earnings:

Balances at beginning of period

606

607

Net income

1,666

1,460

Repurchase of common stocks

(1,012)

(1,461)

Balances at end of period

$1,260

$606

Income Statement – Dell Computer Co.

debt ratio
Debt Ratio
  • What It Measures: The extent to which a firm uses debt financing
  • How You Compute: The ratio of total debt to total assets
inventory turnover ratio
Inventory Turnover Ratio
  • What It Measures: How effectively a firm is managing its inventories.
  • How You Compute: This ratio is computed by dividing sales by inventories

Inventory turnover ratio =

slide14

Lecture

6

MGMT 650

Simulation – Chapter 13

simulation is
Simulation Is …
  • Simulation – very broad term
    • methods and applications to imitate or mimic real systems, usually via computer
  • Applies in many fields and industries
  • Simulation models complex situations
  • Models are simple to use and understand
  • Models can play “what if” experiments
  • Extensive software packages available
    • ARENA, ProModel
  • Very popular and powerful method
applications
Applications
  • Manufacturing facility
  • Bank operation
  • Airport operations (passengers, security, planes, crews, baggage, overbooking)
  • Hospital facilities (emergency room, operating room, admissions)
  • Traffic flow in a freeway system
  • Waiting lines - fast-food restaurant, supermarkets
  • Emergency-response system
  • Military
example simulating machine breakdowns
Example – Simulating Machine Breakdowns
  • The manager of a machine shop is concerned about machine breakdowns.
  • Historical data of breakdowns over the last 100 days is as follows
  • Simulate breakdowns for the manager for a 10-day period
simulation procedure
Simulation Procedure

Expected number of breakdowns = 1.9 per day

statistical analysis
Statistical Analysis

95 % confidence interval for mean breakdowns for the 10-day period is given by:

monte carlo simulation
Monte Carlo Simulation

Monte Carlo method: Probabilistic simulation technique used when a process has a random component

  • Identify a probability distribution
  • Setup intervals of random numbers to match probability distribution
  • Obtain the random numbers
  • Interpret the results
example 2 simulating a reorder policy
Example 2 – Simulating a Reorder Policy
  • The manager of a truck dealership wants to acquire some insight into how a proposed policy for reordering trucks might affect order frequency
  • Under the new policy, 2 trucks will be ordered every time the inventory of trucks is 5 or lower
  • Due to proximity between the dealership and the local office, orders can be filled overnight
  • The “historical” probability for daily demand is as follows
  • Simulate a reorder policy for the dealer for the next 10 days
  • Assume a beginning inventory of 7 trucks
in class example 3 using ms excel
In-class Example 3 using MS-Excel
  • The time between mechanics’ requests for tools in a AAMCO facility is normally distributed with a mean of 10 minutes and a standard deviation of 1 minute.
  • The time to fill requests is also normal with a mean of 9 minutes and a standard deviation of 1 minute.
  • Mechanics’ waiting time represents a cost of $2 per minute.
  • Servers represent a cost of $1 per minute.
  • Simulate arrivals for the first 9 mechanic requests and determine
    • Service time for each request
    • Waiting time for each request
    • Total cost in handling all requests
  • Assume 1 server only
simulation models are beneficial
Simulation Models Are Beneficial
  • Systematic approach to problem solving
  • Increase understanding of the problem
  • Enable “what if” questions
  • Specific objectives
  • Power of mathematics and statistics
  • Standardized format
  • Require users to organize
different kinds of simulation
Different Kinds of Simulation
  • Static vs. Dynamic
    • Does time have a role in the model?
  • Continuous-change vs. Discrete-change
    • Can the “state” change continuously or only at discrete points in time?
  • Deterministic vs. Stochastic
    • Is everything for sure or is there uncertainty?
  • Most operational models:
    • Dynamic, Discrete-change, Stochastic
advantages of simulation
Advantages of Simulation
  • Solves problems that are difficult or impossible to solve mathematically
  • Flexibility to model things as they are (even if messy and complicated)
  • Allows experimentation without risk to actual system
  • Ability to model long-term effects
  • Serves as training tool for decision makers
limitations of simulation
Limitations of Simulation
  • Does not produce optimum solution
  • Model development may be difficult
  • Computer run time may be substantial
  • Monte Carlo simulation only applicable to random systems
fitting probability distributions to existing data
Fitting Probability Distributions to Existing Data

Data Summary

Number of Data Points = 187

Min Data Value = 3.2

Max Data Value = 12.6

Sample Mean = 6.33

Sample Std Dev = 1.51

Histogram Summary

Histogram Range = 3 to 13

Number of Intervals = 13

arena input analyzer
ARENA – Input Analyzer

Distribution Summary

Distribution: Gamma

Expression: 3 + GAMM(0.775, 4.29)

Square Error: 0.003873

Chi Square Test

Number of intervals = 7

Degrees of freedom = 4

Test Statistic = 4.68

Corresponding p-value = 0.337

Kolmogorov-Smirnov Test

Test Statistic = 0.0727

Corresponding p-value > 0.15

Data Summary

Number of Data Points = 187

Min Data Value = 3.2

Max Data Value = 12.6

Sample Mean = 6.33

Sample Std Dev = 1.51

Histogram Summary

Histogram Range = 3 to 13

Number of Intervals = 13

course conclusions
Course Conclusions
  • Recognize that not every tool is the best fit for every problem
  • Pay attention to variability
    • Forecasting
    • Inventory management - Deliveries from suppliers
  • Build flexibility into models
  • Pay careful attention to technology
    • Opportunities
      • Improvement in service and response times
    • Risks
      • Costs involved
      • Difficult to integrate
      • Need for periodic updates
      • Requires training
  • Garbage in, garbage out
    • Results and recommendations you present are only as reliable as the model and its inputs
  • Most decisions involve tradeoffs
  • Not a good idea to make decisions to the exclusion of known information