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Models and Decision Making Quantitative Decision Making with Spreadsheet Applications 7 th ed. By Lapin and Whisler Section 1-4

Inventory Problem Total annual cost = ordering cost + holding cost + procurement cost ordering cost + holding cost + procurement costMinimize: Where A = annual number of items demanded k = cost of placing an order k = cost of placing an order h = annual cost per dollar value for holding h = annual cost per dollar value for holding items in inventory items in inventory c = unit cost of procuring an item c = unit cost of procuring an item Q = order quantity ← this is a variable Q = order quantity ← this is a variable And TC is a variable, everything else is a parameter

Constraints and Feasible Solutions Constraints place special limitations on the problem variables. Ex: Q ≤ 300 Feasible Solutions: values of Q less than or equal to 300. Infeasible Solutions: values of Q bigger than 300.

Optimal Solution Use quantitative methods to find an optimal solution. We find the optimal solution by setting the formula for the holding cost equal to the formula for the ordering cost and solving for Q. Set holding cost equal to Set holding cost equal to ordering cost ordering cost Solve for Q. This is Solve for Q. This is Wilson’s Formula Wilson’s Formula

Suppose each order costs $4 to place, the annual demand is 1000 units, it costs $.20 per year for each dollar value of items held in inventory, and these items can be procured from the supplier for $1 each. k=4A=1000h=.20c=1

Wilson’s Formula The Wilson formula is a method for determining the optimal quantity to order and the time between any two orders for a given entity. Assumption: The only costs entailed are a warehousing cost per stock keeping unit and a one-time cost every time an order is placed. Goal: Find an optimal balance between the two costs to minimize the total cost, which is known as the economic order quantity (EOQ). <

Algorithms and Model Types An algorithm is the procedure used to solve a problem. Deterministic models are models that contain known and fixed constants throughout their formulation. Stochastic models are models that involve one or more uncertain quantities and probability must be considered to find a solution.

Discussion Question Analee Mark owns a tea shop. The demand for gourmet teas is roughly constant over the year. Past data indicate that the annual demand for Assam Tea is 5200 cases per year. Ordering costs are $10/order. The procurement cost is $1.50 per case for the tea and $.50 for shipping. The holding cost (storage and theft insurance) is $.20 per dollar value of the tea held in inventory. She wants to place orders at regular time intervals for the same amount of tea each time. Analee Mark owns a tea shop. The demand for gourmet teas is roughly constant over the year. Past data indicate that the annual demand for Assam Tea is 5200 cases per year. Ordering costs are $10/order. The procurement cost is $1.50 per case for the tea and $.50 for shipping. The holding cost (storage and theft insurance) is $.20 per dollar value of the tea held in inventory. She wants to place orders at regular time intervals for the same amount of tea each time.

Discussion Question A = annual number of items demanded = 5200 = 5200 k = cost of placing an order = 10 = 10 h = annual cost per dollar value for holding items in inventory =.20 c = unit cost of procuring an item = = 2.00 = = 2.00 Q = order quantity this varies depending how frequently she orders this varies depending how frequently she orders

Discussion Question What would be the cost if she were to order the total inventory once a year? = $ 11,450 Q=5200

Discussion Question What would be the cost if she were to order the total inventory once a week? = $10,940 Q=5200/52=100