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 trains Total(objective) changing cells 20 60   soldiers trains Total(objective) changing cells 20 60 profit 3 2 180 used capacity finishing 1 100 carpenter 80 demand 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 formula A 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%?

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? Estimate of demand Probability 100 0.10 200 0.40 300 400

Continuous review: ROP? ss? Average on hand inventory? l = 3 weeks  = 1.5 units per week 2 = 4 units per week Target 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.