The above spreadsheet contains demand data for ten weeks. Please solve the following replenishment problem using Gurobi optimizer in Pyhton. Show the Linear program and the model (code). Decide how much to order each week to minimize the total cost, which includes cost of purchasing and holding cost. In this new variant of the problem, we can hold inventory at our supplier as well as our own warehouse.

Inventory held at the end of the week at the supplier and at our warehouse incurs a holding cost per unit. There is a minimum amount of inventory that must be on hand each week at the warehouse. If an order is placed in a period, the order amount must be at least the minimum order quantity (MOQ). When purchasing, there is a quantity discount, as shown in the spreadsheet.

Inventory can only be held at the supplier for a certain number of weeks. After that, the inventory is automatically shipped to the warehouse. If a shipment is made, it must be at least the minimum shipment quantity (MSQ).

5 min order ty min shipment 5 max number of weeks that inventory can be held at supplier Quantity discount schedule minimum order amount 5 20 30 price per unit $3 $1.00 $0.50 Week Order Demand amount 0 1 30 2 0 Shipment amount Minimum Holding from inventory at Inventory at inventory Holding cost per Cost of is order supplier to supplier at warehouse requireme cost per unit at goods Holding cost - Holding cost - feasible Is shipment warehouse end of week end of week nt unit supplier purchased warehouse supplier ? ? feasible? 201 15 5 4.5 2 1 $ 45$ 10$ 0 0 5 0 2 1 $ - $ 10$ 10 15 0 2 1$ 30$ 30$ 0 15 0 2 1 $ - $ 30$ 8 17 0.9 2 1$ 24$ 34 $ 0 13 0.6 2 1 $ $ 26 $ 0 0 9 9 0.6 2 1 $ $ 18$ 0 5 5 0.6 2 2 1 $ $ 10$ 0 1 0.6 2 1 $ $ 2 $ 0 0 0 0.15 2 10 $ $ $ 0 3 4 0 0 6 5 6 4 7 4 4 8 4 - 9 4 10 1 TOTAL COSTS $ 269 5 min order ty min shipment 5 max number of weeks that inventory can be held at supplier Quantity discount schedule minimum order amount 5 20 30 price per unit $3 $1.00 $0.50 Week Order Demand amount 0 1 30 2 0 Shipment amount Minimum Holding from inventory at Inventory at inventory Holding cost per Cost of is order supplier to supplier at warehouse requireme cost per unit at goods Holding cost - Holding cost - feasible Is shipment warehouse end of week end of week nt unit supplier purchased warehouse supplier ? ? feasible? 201 15 5 4.5 2 1 $ 45$ 10$ 0 0 5 0 2 1 $ - $ 10$ 10 15 0 2 1$ 30$ 30$ 0 15 0 2 1 $ - $ 30$ 8 17 0.9 2 1$ 24$ 34 $ 0 13 0.6 2 1 $ $ 26 $ 0 0 9 9 0.6 2 1 $ $ 18$ 0 5 5 0.6 2 2 1 $ $ 10$ 0 1 0.6 2 1 $ $ 2 $ 0 0 0 0.15 2 10 $ $ $ 0 3 4 0 0 6 5 6 4 7 4 4 8 4 - 9 4 10 1 TOTAL COSTS $ 269