Question

METRO HOSPITAL You are the materials manager at Metro Hospital. Approximately one year ago, the hospital began stocking a new drug (Ziloene) that helps the healing process for wounds and sutures. It is your responsibility to forecast and order the monthly supply of Ziloene The goal is to minimize the combined cost of overstocking and understocking the drug Orders are placed and received at the beginning of the month and demand occurs throughout the month. The following demand and cost data have been compiled Costs. If more is ordered than is demanded, a monthly holding cost of $1.00 per case is incurred. If less is ordered than is demanded, a $2.00 per case lost sales cost is incurred. The drug has a short shelf life, and any overstocked product at the end of the month is worthless and no longer available to meet demand Demand. The demand for the twelve months of last year was: Last year's demand Month 2 3 45 6 789 10 12 Cases43 36 24 69 34 75 90 67 59 5 77 50 You believe this demand to be representative of Metro's normal usage pattern FIGURE 1 Plot of last year's monthly demand in cases 100 80 60 E 40 20 12 34 5 6 78 9 10 11 12 Month

task: 1. Develop a forecast for the next 12 months.

2. Develop an ordering strategy for the next 12 months.

Answer 1

For Metro Hospital, What is the overage cost? C o = $1  What is the underage cost? C u = $2  What is the critical ratio? C u /(C o +C u ) = 2/3

Since the critical ratio is 2/3 set P(In-stock) = P(Demand ≤ Q * ) = 2/3 and solve for Q * . Assume the demand has a Normal(F t ,20.88) probability distribution where F t is the forecast in period t. Standardizing: P((Demand - F t )/20.88 ≤ (Q * - F t )/20.88) = P(Z ≤ (Q * - F t )/20.88) = 0.667 where Z is a Normal random variable with mean zero and standard deviation one. From the standard normal probability distribution tables the “z-score” is z = (Q * - F t )/20.88 = 0.44 Solving for Q * : Q * = F t + 0.44 × 20.88 = F t + 9.19 For example in month 13: F 13 = 60.2 => Q * = 60.2 + 9.19 = 69.39 (rounded to 69 in the spreadsheet). For example in month 14: F 14 = 49.78 => Q * = 49.78 + 9.19 = 58.97 (rounded to 59 in the spreadsheet).