Suppose that the rate of customer demand for candy bars at Grocery City is constant at a rate of 200 candy bars per week. Each time that Grocery City places an order for more candy bars it must pay processing fees of $20 regardless of the size of the order. Holding costs for candy bars are $0.01 per candy bar per week. Finally, leadtime for the delivery of candy bars is 0 days. Assume that there are 52 weeks in a year.
a. Suppose that Grocery City places an order for 500 candy bars each time that its inventory of candy bars reaches 50. Draw a graph showing the number of candy bars that Grocery City has on-hand in inventory at each point in time up until the time when it places its fourth order. Label the points in time at which Grocery City places a new order. What will be Grocery City’s average inventory holding costs per unit time? What will be Grocery City’s average fixed ordering costs per unit time? Assume that Grocery City starts out with 550 candy bars on day 0.
b. Assuming that Grocery City would like to minimize the sum of its average purchasing, fixed ordering and holding costs per unit time, what is the optimal number of candy bars for Grocery City to purchase each time that it places an order and what should be its reorder point?
c. Suppose now that it takes 1.5 weeks for each order of candy bars to be delivered. When the quantity of candy bars reaches what level should Grocery City place an order for more candy bars? Assume that Grocery City orders according to the optimal order quantity from part b above.
d. [Extra Credit] Finally, suppose that Grocery City is considering consolidating the ordering and storage for four of its locations into a single warehouse. In other words, candy bars will be ordered and stored at a single warehouse and then delivered to each of the four locations. Trans- portation costs from the warehouse to each of the four stores are negligible. Each Grocery City store individually faces a constant (non-random) demand of 200 candy bars per week and has ordering costs of $20 per order and holding costs of $0.01 per candy bar per week. The single warehouse has identical ordering and holding costs as the individual stores. Is it a wise business decision to consolidate or not? Provide numerics to justify your answer.
