# Quantitative Methods in Health Care Management

Resolved Question: Complete Exercises 11.1 and 11.6 on pages 285 and 288 in Quantitative Methods in Health Care Management. Use this template for your calculations and answers: Excel template for Exercises 11.1 and 11.6 Note on using the Excel templates: Use the automated Excel tables in Sheets 1 and 3 to perform calculations, and Sheets 2 and 4 to record your answers. For an explanation of the automated Excel tables, refer to Quantitative Methods, pp. 281–284. Save the template to your desktop before using. Make sure macros are enabled. Any existing numbers in green cells in the automated tables are for examples, and show where you should enter the data. You must delete or overwrite these numbers to perform the calculations. The yellow cells of templates are protected to prevent users from accidentally deleting or overwriting the formulas. There is no need to unprotect the templates. Exercise 11.1: A product used in a laboratory of the hospital costs $60 to order, and its carrying cost per item per week is one cent. Demand for the item is six hundred units weekly. The lead time is three weeks and the purchase price is $0.60. What is the economic order quantity for this item? What is the length of an order cycle? Calculate the total weekly costs? What is the investment cost for this item? If ordering costs increase by 50 percent, how would that affect Economic Order Quantity (EOQ)? What would be the reorder point for this item if no safety stocks were kept? What would be the reorder point if one thousand units were kept as safety stock? Exercise 11.6: SURGERY ASSOCIATES, a local surgery practice group, orders implants from device manufacturers. Order quantities for ten items have been determined based on the past two years of usage. Other relevant information from the practice’s inventory records is depicted in Table EX 11.6. The practice is functional for fifty-two weeks a year. Perform basic EOQ analysis for each item. Classify the implant inventory items according to the ABC analysis. Calculate the yearly inventory management cost. Determine the investment cost (per cycle) for each item. TABLE EX 11.6 Implant Item No. Yearly Demand (Unit/Year) Unit Cost Yearly Carrying Rate of Each Item Ordering Cost 1 104 2,225 12% 6.00 2 260 5,000 10% 5.00 3 728 3,550 8% 12.00 4 1,248 1,205 12% 28.00 5 104 11,100 2% 18.00 6 1,040 1,500 20% 32.00 7 780 1,900 11% 50.00 8 884 3,700 9% 12.00 9 780 6,400 2% 35.00 10 520 2,700 5% 12.00 Week 6 Exercises Assistance Exercise 11.1 b: Formula 11.6, p. 279 Once Q0 is known, the length of an order cycle (the length of a time between orders), or order frequency, can be calculated as: Length of order cycle = Q0/D Exercise 11.1 c: Formula 11.3 p. 278 If we add holding and ordering costs for every point in their respective graphs, we can determine the total annual cost (TC) associated with inventory management. Figure 11.3 shows this as the TC curve where holding and ordering inventory for a given order quantity (Q) ordered each time. The total cost can be expressed as the sum of annual holding cost and annual ordering cost: TC = Q H/2 + D S/Q Where D = demand, usually in units per year Q = order quantity, in units S = ordering cost, in dollars H = holding cost, usually in dollars per unit per year. (Note: D and H must be in the same units, such as months or years.) We see in Figure 11.3 that the total cost curve is U-shaped and that it reaches its minimum at the quantity where carrying and ordering costs are equal. The mathematical solution to find this minimum point requires differentiating TC with respect to Q. dTC /dQ = dQ H/2 + d(D/Q)S = H/2 –DS/Q2 The next step is to set the right hand side of this equation to zero . We can solve for the value of Q as: H/2- DS/Q2 = O, And rearranging the equation, we get Q2 = 2DS/H and Qo = ?(?2DS/H?^ ) That is the optimum solution for Q, given by the minimum total cost of the TC curve. We will call the point where both costs equal each other, as derived by the above equations, Qo. And that is the EOQ formula (11.5). It can be used when given annual demand, the ordering cost per order, and the annual holding cost per unit. One can also compute the minimum total cost by substituting Qo for Q in the TC formula. Exercise. 11.1 e: If ordering cost goes up then EOQ changes accordingly. Exercise. 11.1 f: Formula 11.7 p. 283 We used the EOQ model to answer the question of how much to order, but not the question of when to order. We will now look at a new model that identifies the reorder point (ROP) in terms of the quantity of an item currently in stock. The reorder point occurs when the quantity on hand drops to a predetermined amount (see Figure 11.2 and ROP level). This trigger amount usually includes the expected demand during the lead time. There are four conditions that affect the reorder point quantity: (1) the rate of forecast demand; (2) the length of lead time; (3) the extent of variability in l

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