Question

A production company A, made JITD strategic alliance with a distribution company B. The content of alliance is,  Company A executes work for company B’s inventory management and all the inventory cost caused from B is responsible on A.  The decision for inventory replenishment is made on every Saturday,  An order quantity is arrived every Sunday night after the delivery-process from A to B.  The amount of starting inventory is 50 at Week 0  Inventory holding cost: 1,000 won/week per unit  When the shortage is incurred, it is considered as Lost-sale, not as Backorder. Lost-sale cost : 2,000 won/week per unit.  Inventory replenishment happens when the inventory level is under 20(not including 20th), and the amount of inventory to be refilled is calculated as “50-current inventory level”.  Transportation cost: 50,000 won per every delivery  If the total number of satisfied demand - the total number of Lost-sale is greater than 110(not including 110th), the incentive, 20,000 won per extra unit is given to A. Following table shows weekly demand of ‘B’ company for last 8 weeks. Please answer based on the information given above. All the cost is calculated from week 1(not from week 0). Week 0 1 2 3 4 5 6 7 8 Total Weekly demand 15 20 10 15 30 20 5 35 150 Satisfied demand Inventory level at the end of Week 50 Holding cost Shortage cost The amount of Inventory to be replenished Transportation cost (1) How much inventory does company A replenish for the first time? (2) How many times does company A replenish inventory for 8 weeks? (3) How many times does company B experience inventory shortage for 8 weeks? (4) How many demands of company B were met for 8 weeks among 150? (5) How much does company A have to pay for total shortage cost for 8 weeks? (6) Company A would experience (More profit or Loss of profit), and the difference between the total expense and the total incentive would be _______________ won. [Note: Total expense of company A = holding cost+ shortage cost+ transportation cost. If the total expense is lower than the total incentive company A would receive, we consider “More profit”. Otherwise we consider it as “Loss of profit”]

Answer 1

1) For the first time company A replenish quantity is 35 units it is calculated the following way

replenishment of inventory= 50 - current inventory level

available inventory	weekly demand	current inventory level	replenishment
week 0 50	15	35 (50-15)	not required (as current inventory level is above 20)
week 1 35	20	15(35-15)	35 required as current inventory falls below 15
week 2 35 calculated as 50-15	10	25	not required

2) company A replenish the inventory 5 times in eight weeks

available inventory	weekly demand	current inventory	replenishment
week 0 50	15	35	NR
week 1 35	20	15	R (35 units)
week 2 35	10	25	NR
week 3 25	15	10	R (40 units)
week 4 40	30	10	R(40 units)
week 5 40	20	20	NR
week 6 0	5	-5	R (55 units)
week 7 55 week 8 0	35 150	20 -150	NR R

3) company B falls short of inventory 2 times in eight weeks that is week 6 and week 8

4) From week 0-8 , 7 times company B demand was fulfilled.

5) company A has to pay for shortage cost for 2 times that is week 6 = 2000*5=10000 , as 5 units were short and cost per unit short is 2000

week 8= 2000*150=300000

total 310000 company A has to pay to company B

6) total expenses are more due to shortage of inventory