1. The manager at ChocolateFactoryCo has hired you as a business analyst to improve overall operations. Their primary motive is to plan the replacement policy for the chocolate-making machine. The current machine is 3-years old, and it must be replaced when it becomes 6-years old. The cost of a new machine is Rs. 80,00,000. The following table provides revenue, operation cost and salvage values of the machine,

Age Revenue (in Rs) Operating cost (in Rs) Salvage value (in Rs)

0 1600000 16000 _

1 1520000 48000 6400000

2 1480000 96000 4800000

3 1376000 120000 4000000

4 1240000 136000 2400000

5 1120000 144000 800000

6 976000 176000 400000

Determine the optimal replacement policy for the current 3-year-old machine. Assume the firm has space to only keep one machine at a time and will not keep two machines.

2. You are hired as a data analyst by a leading quick commerce firm. As an initial project, you are specifically tasked to improve the inventory ordering system of a certain popular product at their flagship store in Connaught Place, Delhi. The first thing you do is analyse the historical data of demand of the product at the given store. Based on your analysis, you predict the demand for the next 6 months as,

Month Demand

1 100

2 200

3 100

4 300

5 200

6 300

The next set of data you gather is different set of costs and prices of the product displayed in table below,

Selling price (in Rs) 1000

Ordering cost (in Rs) 500

Holding cost (in Rs) 200

Penalty cost (in Rs) 200

Maximum order amount 300

Penalty cost is incurred on demand lost and the orders can only be placed in batch of 100 units.

i. Given the demand to be known and deterministic, how much units should the firm order in the next 6 months? Use an appropriate optimization model. ii. The operations team has come up with multiple suggestions,

a. Demand in last month is predicted to be 100 instead of 300.

b. Selling price might be adjusted by 10% for the next 6 months

c. Holding cost might increase by 20%

d. Ordering cost be reduced by 30%

Apply each of their suggestions separately in the model developed in part 1.

Comment on the findings while applying every suggestion.

iii. The head of forecasting and estimation suggests you assume demand to be an uncertain parameter by assuming it to be a distribution. Solve the problem as a dynamic programming problem considering demand per month follows a probability distribution as,

Demand Probability

0 0.3

200 0.7

Compare the solutions in part 3 with part 1. Describe the policy decision-making process in both cases and discuss your findings

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