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Logistic Assignment

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MS3121 Homework Two

Name: Tsang Lei Man     Student ID: 53399558

  1. The demand for spring water at the Shatin ParknShop is 600 litres per week. The setupcost for placing an order to replenish inventory is $25. The order is delivered by the supplier which charges Parknshop $0.10/liter for the cost of transportation. This transportation cost increases the cost of water to $1.25/liter. The water loses its freshness while stored at the Shatin ParknShop. To account for this, Parknshop charges an annual holding cost of $2.6/liter. Determine how often Parknshop should order for water and what size (how many litres) each order should be and give your answers to one decimal place. (3pt)

D = 600×52 = 31200 litres

A = $25/setup

h = $2.6/liter

Q* =  =   774.5967 = 774.6 liters/order[pic 1][pic 2][pic 3]

The number of order placed in a year =   40.2790 = 40.3 orders/year[pic 4][pic 5]

How often should order for water =  = 1.3 weeks[pic 6]

The optimal order quantity is 774.6 liters per order. Parknshop should place an order every 1.3 weeks and it should place 40.3 orders in a year.

  1. Consider a newsvendor who sells newspapers at a unit price of $6. He purchases the newspapers at unit cost of $2. Unsold papers can be returned for $1 each. The newsvendor expects a demand of 100 units with probability 15%, 200 with 20%, 300 with 30%, 400 with 20%, 500 with 10%, and 600 with 5%. Plot the cumulative distribution function of the demand, derive the critical ratio, and then determine the optimal order quantity. (3pt)

Cu = p-c = $6-$2 = $4

Co = c-s = $2-$1 = $1                                               [pic 7]

Critical Ratio =  = 0.8[pic 8]

Demand Quantity

Cumulative Probability

100

0.15

200

0.35

300

0.65

400

0.85

500

0.95

600

1

As 0.85>0.8, 400 is the optimal order quantity.

  1. Refer to the Grid Technique example in Week 9’s lecture (slide 24). Now consider the following: What if the transportation rate associated with the Jacksonville market is increased by 50% (from $1.5 to $2.25)? (4pt)

  1. Without any calculation, can you tell to what direction will the new least-cost location move?

Yes. The new least-cost location will move downward and rightward. The increased in transportation rate (Fn) of Jacksonville market will increase its product of transportation rate and volume (Fn×Dn), also the product of transportation rate, volume and coordinate values associated with the Jacksonville market (Fn×Dn×Xn & Fn×Dn×Yn) at the same percentage. Those increases make the summation value become greater. As the percentage increase in (i.e. denominator) is larger than the percentage increase in (i.e. numerator), the value decrease in Y-coordinate larger than its increase, so the Y-coordinate will become smaller and move downward. For X-coordinate, as the percentage increase in (i.e. numerator) is larger than the percentage change in  (i.e. denominator), the value increase in X-coordinate larger than its decrease, so the X-coordinate become bigger and move rightward.[pic 9][pic 10][pic 11][pic 12]

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