Giapetto's Woodcarving: The LP Model

max 3x1 + 2x2

subject to

2x1 + x2 100 (finishing hours)

x1 + x2 80 (carpentry hours)

x1 40 (demand for soldiers)

x1 0 (nonnegativity constraint)

x2 0 (nonnegativity constraint)

• Where– x1 : number of soldiers produced each week– x2 : number of trains produced each week

Formulating an LP

• Define decision variables• Objective function-max or min• Constraints-explanation/label in words next to

constraint• Non-negativity constraints

The Excel Model

  soldiers trainsTotal(objective)  

changing cells 20 60   

profit 3 2 180 

  soldiers trains used capacity

finishing 2 1 100 100 carpenter 1 1 80 80 demand     20 40          

Filled in by Excel Solver

Questions

• What is the optimal product mix?• Is producing 30 soldiers and 30 trains feasible?• Which constraints are binding?• What is the optimal profit (or optimal

objective function value)?

Process variability

• Measured by CV of inter-arrival and service times• Managing waiting– Is there a perpetual queue? If yes, add capacity– Is there a predictable queue? If yes, schedule capacity

better or manage demand– Are there stochastic queues-always! Reduce

variability through process design– If you can’t reduce waiting, manage perceived waiting

through the psychology of waiting

Queue formulaA new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.

What if service times are constant?

How many servers will I need if I want to ensure a given waiting time target?

If a customer cost of waiting and a per server staff cost is given, what is the optimal staff level?

EOQ? Costs? ROP? Inventory Turns?

• A university bookstore sells MP3 players. Sales are 6400 units per year. The bookstore buys the players at 240 TL per unit. The cost of placing an order with the supplier is 30TL. Annual holding cost rate (or equivalently interest rate) is 25%. Lead time is 5 days.

• What if I misestimated the demand by 40%?

Estimate of demand Probability

100 0.10

200 0.40

300 0.40

400 0.10

•A retail store selling apparel will order merchandise for the Christmas Season. A men’s overcoat from Hong Kong is expected to have a demand range from 100 to 400 overcoats, with probabilities that are as follows:The total cost to the store would be 60€ per overcoat, and the retail price is estimated at 110€ per overcoat. Any overcoats left over after the christmas season are expected to be sold at 40€ each. How many overcoats should thestore buy to maximize profits over the coming Christmas season? Expected sales? Expected Profit? Expected left-overs?

Continuous review: ROP? ss? Average on hand inventory?

l = 3 weeks = 1.5 units per week = 4 units per weekTarget service level,

CSL=95%

Quality

• Know what is TQM-continuous improvement• Difference between normal/common cause variability and assignable/abnormal variability

• Process improvement implies a reduction in normal variability

• Process control implies absence of assignable cause variability

Know how to

• Do a Pareto analysis• Fishbone diagram-main bone problem, 4 sub-

bones: man, material, machine, method• Draw a histogram• Interpret a control chart

Control chart

• The overall average on a process you are attempting to monitor is 50 units. The process standard deviation is 1.72. Determine upper and lower control limits for an X-bar chart if you choose a sample size of 5.