We want to be efficient in how we manage our inventories. For some items we know what we need each year, demand is constant, we can't have any shortages and our supplier's delivery times are known and constant. A key example is bandages. Our supplier gives a discount for bigger orders. For up to 50 boxes ordered, we pay 40USD per box. For 51 - 100 boxes ordered, it's 35USD per box. Above 100 boxes ordered, it's 30USD per box. Ordering costs are US$15 per order, and holding costs are US$5 per box per year. (The holding cost is the same no matter how much is purchased - no volume discount). We require 1000 cases per year. What order quantity will minimize our total cost?"

We also have some supplies where we need to keep safety stock and need to know when we should best reorder - there is variability in both the time it takes to receive the supplies and variability in our demand (both fluctuate in a normally distributed way). We don't want more than a 1% chance of running out-of-stock while replenishing. What info would we need to give you to tell us what our safety stock should be, and at what stock level we should reorder?

We need to put a plan together to define a workforce schedule for the 11 nurses at the new centre. Our aim is to minimize any excess capacity. We would for each nurse have a 5-day work week, with 2 consecutive days off. We would see the staffing requirements as 7 nurses on Monday, 5 on Tuesday, 9 on Wednesday, 10 on Thursday, 11 on Friday, 4 on Saturday and 3 on Sunday. What would an optimal weekly schedule look like for each of the 11 nurses?