Question

The Michael Scott Paper company has two retail outlets not far from each other (let us denote them by A and B). Assume that they sell one kind of plain paper. Weekly demand in each store is identical and is given by the following forecast — demand is either 3 units or 5 units with equal likelihood. Further, assume that the demands across the two outlets are independent. The cost structure for plain paper is as follows — revenue per unit of sale is $4. The cost of purchasing is $1.6 per unit (do not worry what units we are dealing with, the costs and demand have been scaled suitably). Ignore all other costs including the holding cost of inventory and the goodwill cost of a lost sale, which for the purposes of this computation, we assume to be zero. Consider a weekly time horizon. Also assume zero salvage costs.

1) If each store makes independent stocking decisions, how much should each store stock in anticipation of demand?

2) Jim Halpert, the inventory manager of the paper company, decides to come up with a different operational structure. He realizes there is an empty warehouse close to both stores. He decides to buy and store inventory in this central warehouse and replenish instantaneously when stores have demand. What is the new optimal stocking quantity in this central warehouse? What operational strategy is Jim Halpert attempting to leverage? Given the same cost and revenue structure, will he save any costs or will the costs increase? Justify your results with computation.

Answer 1

1) We understand that the demand could be either 3 units or 5 units but profit margins will remain the same, if all the units are sold.

If we stock up 5 units and sell 3 units, each of the stores will have a bear cost of un-sold units i.e. 2 units. The profit margins will drop from 60% to 33%

Store A	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	3	12	8	4	33%
Store B	Stock		Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	3	12	8	4	33%

If we stock 3 units and observe a demand for 5 units, we will have to bear the cost of lost opportunity. Maintaining a a good cash flow is essential for businesses.

There is equal likelihood for demand to be either 3 or 5, so it is advisable to stock up store A with 3 units and store B with 5 units and vice versa. In case, if we donot sell 5 units at store B, our over all profit margin will drop by mere 10% but we will have healthy business cash flows

Store A	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	3	12	8	4	33%
Store B	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	5	20	8	12	60%
Over-all	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
10	8	32	16	16	50%

But if you are view the problem statement from profitability standpoint, then you have stock just 3 units across both the stores - Your profitability will continue to remain at 60%

Store A	Stock	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
3	12	4.8	7.2	60%
Store B	Stock	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	20	8	12	60%

2) Here we are exercising demand based inventory management model.

Store A : 3 units of stock

Store B : 3 units of stock

Warehouse Inventory : 4 units of stock (2 units for store A, 2 units for store B)

when demand exceeds 3 units in store A and store B, Jim can replinish the stock immediately and sell all 5 units. He is minimising the scope of potential opportunity cost of business. However, if demand does not exceed 3 units, there is an additional cost on business and hit on profit margins. A drop from 60% to 33%

Store A	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	3	12	8	4	33%
Store B	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
5	3	12	8	4	33%
Over-all	Stock	Sold	Revenue ($)	Cost of purchase ($)	Profit ($)	Margin %
10	6	24	16	8	33%

Since the demand and cost projections are constant, Tim not be able to save any costs by warehousing the inventory.

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