The demand for a certain product is 2000 units per year and the items are withdrawn at a constant rate. The ordering cost incurred each time an order is placed to replenish inventory is £50. The unit cost of purchasing the product is £470 per item, and the holding cost is £4.10 per item per year.
Apply a basic inventory model to determine the optimal size of each order and how often an order should be placed. You should follow the following steps:
(a) Formulate the mathematical problem.
(b) Determine the optimal size of each order.
(c) Determine how often an order should be placed.
Let q= numbers of unit ordered at a time
Total cost = commodity cost + ordering cost + holding cost
Commodity cost (CC)= units per year \times cost per unit
Ordering cost
Holding cost (HC) = cost of carrying average inventory
(a)
(b) For optimum size
(c) Length of production run/ or length of order
Hence order shouls be placed after 1.325 months.
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