Question 1 (75 marks)

Your company buys and resells luxury yachts for Sydney’s rich and famous. At the start of every month, you purchase yachts without knowing the demand for the        upcoming month. Delivery of purchased yachts is immediate. The monthly demand for yachts is uncertain but based on past data is known to follow the discrete            distribution depicted in the table below:

You have an area you own in the marina with a capacity to hold at most 4 yachts. The monthly holding costs of yachts are given in the table below. These include                 maintenance, insurance and security.

Assume that you cannot hold more than 4 yachts at any given time. If by chance you have any additional yachts, they will need to dock in a public marina where there is a very high likelihood that they will be damaged or stolen. You want to avoid this        scenario at all costs.

Your goal is to be able to meet demand for yachts, however, your customers will     agree to have their demand backlogged in return for appropriate discounts and         compensation. In order to avoid loss of reputation and goodwill, you decide to        consider only policies which allow at most a shortage of 3 yachts at any given time. You estimate the shortage (per month) costs as follows:

You will not consider being short more than 3 yachts at any given time.

Purchase of yachts can be done once a month (at the start of the month). Assume that demand for yachts occurs immediately after any your order has been placed (hence,  you don’t know the demand when ordering). You can only order once a month.

Delivery of yachts is a very complex and expensive process. As a result, your supplier only considers two ordering policies: he will either delivery 4 yachts or 5 yachts in     each order. The total delivery cost per order varies depending on the number of yachts and is given in the table below:

The purchasing and selling prices of your yachts are fixed. Hence, your revenue is constant regardless ofyour ordering policy. Hence, you focus on minimizing your total costs.

Assume that you have to lock in a policy for a long-term planning horizon. Hence,  you are interested in determining how many yachts to order and how often. Your goal is clearly to minimise your average costs. A policy is defined by 2 decisions: (i) at     which level of stock to place an order; and (ii) how many yachts to order. Consider   only simple policies where the number of yachts you order is fixed (don’t              consider, for example, ordering 4 yachts when you have 0 in stock and 5 yachts when you are short of yachts).

What are the different policies you should consider? What is the preferred policy       based on expected profits? Are there certain shortcomings and/or advantages in some policies (ones that aren’t related to profit/costs)?