A restaurant serves an average of 5,000 bottles of locally produced red wine per year….

a) A restaurant serves an average of 5,000 bottles of locally produced red wine per year. The annual holding cost for a bottle of wine is $1. It costs $10 to place an order for wine. The total number of working days per year is 360.

i) How many bottles of red wine should be ordered each time an order is placed? How many orders per yearshould be placed? What are the annual inventory and ordering costs? [6 marks]

ii) Assume that when the restaurant is out of wine it incurs a penalty of $5 as the result of lost goodwill and profit loss. Determine an optimal ordering policy for the wine with planned shortages. What is the maximum number of backorders and reorder point if lead time is 10 working days? [6 marks]

iii) Determine the safety stock level and revised reorder point if shortage is not allowed and supply lead time demand has been estimated as having a normal distribution with average value of 300 bottles and a standard deviation of 100 bottles. The company wants at least 98% service level during the supply lead time. [4 marks]

b) A consultant wants to assess the performance of four university departments in which every department provides data on two inputs: teaching and research staff, and three outputs: full-time students, part-time students and research publications. In discussing how this evaluation could be done in a meeting with representatives from these departments, the following summaries of input and output measures for a one-year period were identified:

i) Formulate the problem as LP model using data envelopment analysis approach to evaluate the performance of department D. [6 marks]

ii) Solve the LP problem using LINDO. [3 marks]

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