Problem 1: (6.2/224 Silver et.al. (1998) Book)

The demand pattern for another type of filter is:

Jan.	Feb.	Mar.	Apr.	May	June
18	31	23	95	29	37
July	Aug.	Sept.	Oct.	Nov.	Dec.
50	39	30	88	22	36

Those filters cost the company $4.75 each; ordering and carrying costs are $35 and 0.24 $/$/year respectively. The variability coefficient equals 0.33. Use the Silver Meal heuristics to determine the sizes and timing of replenishments of stock.

Variability coefficient: A parameter to determine when to use heuristics method, when demand pattern having variability exceeds some threshold value, it makes sense to change to a heuristic. It is Variability coefficient (VC). In particular, if VC <0.2, Use simple EOQ. Otherwise, Use heuristic. .

Problem 2: (6.10/224 Silver et.al. (1998) Book)

Consider a company facing a demand pattern and costs as follows:

Month	Sequential number	Requirements (units)
January	1	20
February	2	40
March	3	110
April	4	120
May	5	60
June	6	30
July	7	20
August	8	30
September	9	80
October	10	120
November	11	130
December	12	40
	Total	800

Given: Fixed ordering cost A = $25.00, carrying cost r (per month) = $0.05 (Carrying costs are very high in this industry) and unit variable cost v = $4.00.

Using a three-month decision rule, the replenishment schedule and associated costs are as follows:

Month	1	2	3	4	5	6	7	8	9	10	11	12	Total
Starting inventory	0	150	110	0	90	30	0	110	80	0	170	40
Replenishment	170	0	0	210	0	0	130	0	0	290	0	0	800
Requirements	20	40	110	120	60	30	20	30	80	120	130	40	800
Ending inventory	150	110	0	90	30	0	110	80	0	170	40	0	780

Total replenishment costs: $110.00

Total carrying costs: $156.00

Total replenishment + carrying: $256.00

a/ Construct a replenishment schedule and calculate the associated costs using the Fixed Economic Order Quantity method.

b/ Repeat using the Wagner-Whitin algorithm.

c/ Repeat using the Silver Meal heuristic.

d/ Repeat using the Least Unit cost method.

e/ Repeat using the Part-period balancing method.

f/ Repeat using the Periodic Ordering Quantity method.

Problem 4:

A component used in a manufacturing facility is ordered from an outside supplier. The component is used in a variety of finished items and therefore the demand is high. Forecast demand (in thousands) over the next 8 weeks is:

Week	1	2	3	4	5
Demand	21	33	29	15	9

Each component costs 70 cents and the inventory carrying charge rate is 0.56 cents ($0.0056) per unit per week. The fixed order cost is $300. Assume instantaneous delivery.

What is the ordering policy recommended by DP algorithm?