Question

Please provide all explanations, calculations, and formulas (like Inventory=Flow Time * Flow Rate) where possible. That would really help me understand how to solve those type of problems. Thank you!؜؜؜؜

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The Accounts Receivable department of Kelloggs Company, receives an average of 1,000 payments (checks) per week from retail customers like Lidl and Aldi. These checks are deposited into the bank account of the company as time permits. An inspection showed that there is an average of 600 checks waiting to be deposited at any given time. The company works 5 days a week. You can assume a stable operation of deposits.

(a) What is the average number of working days a check waits to be deposited?

(b) Assume that the checks coming in are either small or large. Small checks are for an average of €500 and large checks are for an average of €5,000. 20% of the checks coming in are large with the rest being small. Currently the deposit process makes no distinction (see part a question above) between the large and small checks. As a result 20% of the 600 checks waiting to be processed are large and 80% are small. Is it worth reallocating resources in AR so that large checks wait an average of 2 days before being deposited while small checks wait an average of 4 days before being deposited?                         
(Hint: calculate the amount of money tied up in inventory)

Answer 1

Arrival rate = 1000 /5 =200 per day = Flow rate

Avg checks in queue = 600 ( inventory)

Inventory = flow time x flow rate

Flow time = Inventory / flow rate = 600 units / 200 per day = 3 days

(b)

Number of large checks = 20x600/100 =120

Amount tied up in inventory in large checks = 120x5000 =600000

Amount tied up in inventory in form of small checks = 480x 500 = 240000

Cost of holding inventory for large checks for 3  days each n old system ( assuming that it is n% for day)

Both type of checks = n/100 x 3 x 840000 = 25200n

Cost of holding inventory under new system

Large checks = 600000x2xn/100 = 12000n

Small checks = 240000 x4xn /100 =9600n

Total = 21600n

Since the cost of holding inventory is reduced with the new system, it is favourable.