Could you please help me to solve these two questions.

 

Q.3 Consider an item with the following deterministic, time varying demand pattern:

 

Week:      1    2         3         4         5         6         7         8         9         10       11           12

Demand: 50    80       180      80       0         0         180      150      10       100      180           130

 

Suppose that the pattern terminates at week 12. Let other relevant characteristics of the item be:

1. Inventory carrying cost per week (incurred only on units carried over from one week to the next) is TL0.20/unit.
2. Fixed cost per replenishment is TL30.
3. Initial inventory and replenishment lead time both zero.

 

a)     Find the fixed economic order quantity (rounded to the nearest integer number of months of supply; that is, each time the EOQ, based on the average demand through the entire twelve months, is adjusted so that it will last for exactly an integer number of months)      

b)    A fixed time supply (an integer number of periods), based on the EOQ expressed as time supply, using the average demand rate for the 12 months.                         

 

Hint: For each case, it would be helpful to develop a table with at least the following columns: (1)Month, (2)Replenishment Quantity, (3)Starting Inventory, (4) Demand, (5) Ending Inventory

 

Q.4 The Galt Gadget Company is a manufacturer of automotive parts. For a particular line of products the demand in the next six periods (each of two months’ duration) is estimated to be

 

          Period, j           1         2         3         4         5         6

Demand, D(j)        30       60       60       60       160      50

(in shifts of output)

 

The company does not permit deliberate backlogging. However, the requirement shown for a period can be satisfied (if necessary) by production in that period. With the specified manpower schedule the production available is as follows:

 

 

 

Type of

Cost (100 x YTL)

Capacity

Period

Production

Per shift of Output

(Shifts)

1

Regular

8

46

2

Regular

8

44

 

2^nd Shift

11

22

3

Regular

8

44

 

2^nd Shift

11

44

4

Regular

8

43

 

2^nd Shift

11

43

5

Regular

8

43

 

2^nd Shift

11

43

 

3^rd Shift

17

20

6

Regular

8

42

 

2^nd Shift

11

42

 

The initial inventory (at the beginning of period 1) is 20 shifts of output. An inventory carrying charge of YTL200 per shift of output is incurred when material is carried forward from one period to the next (no charge is incurred during a period). Warehouse limitation restrict the inventory at the end of any period to be no larger than 70 shifts of output.

 

a) Determine the production plan for Galt Gadget that minimizes the total of production and carrying costs over the six-month period if an ending inventory of 15 shifts of output is desired. In particular show the actual production by period-shift and the ending inventory of each period.

 

b) From your solution, can you infer the value (in terms of reduced costs) of increasing the warehouse capacity to 72 shifts output? 75 shifts of output?