# M451 Supply Chain Management M451 Supply Chain Management

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M451 Supply Chain Management – Inventory Sample Exam Paper Questions and Solutions
Question 1

A home appliance company produces a new line of quiet washing machines with a capacity of 200 washing machines per day. The annual demand is 25000 washing machines and it costs £250 to produce a quiet washing machine. The cost for setting up a production run to make the quiet washing machine is £300. The annual carrying cost is £0.80 per washing machine. Assume that there are 52 weeks and 365 working days in a year. Determine the following:

(a)
The optimal production run size and the maximum on-hand inventory level.

[4 Marks]

washing machine [2 marks]   The maximum on-hand inventory level:    washing machine [2 marks]
(b)
The optimal length of a production run and the optimal cycle length.

[4 Marks]

Optimal length of a production run    year [2 marks]   Optimal length of a cycle:    year [2 marks]
(c)
The optimal number of production runs per year.

[3 Marks]

Optimal number of production runs:    runs per year [3 marks]
(d)
The total annual inventory cost. [4 Marks]

[4 marks]

(e) Explain the key differences between a standard EOQ and a continuous rate EOQ. How should a company use the standard and continuous rate EOQ models in order to determine whether to produce or purchase a product?   Marks will be awarded for: Clear explanation of the differences between the two EOQ models Clear explanation of the process of calculating both EOQs for the same product under outsourcing (purchase – standard EOQ) or in-house manufacture (produce – continuous rate EOQ) and mention of calculation of, and choice of option with lowest, total cost.       [5 Marks]

Question 2

A big retail company sells assembled furniture packages for living room including a TV table, a coffee table and a sideboard to its customers. Annual demand for assembled furniture is normally distributed with mean of 2100 and standard deviation of 70. The retail company orders its furniture from its partner carpentry company. It costs £100 to place an order and the lead time is 2 weeks. The retail company estimates that each stockout causes a loss of £50 in future goodwill. The retail company pays £80 for each furniture package and sells it for £120 and any furniture which is ordered but not sold will have a lower price of £60 in retailer’s sale. The annual cost for holding a furniture package in inventory is 30% of its purchase cost. Assuming that all stockouts result in lost sales, determine the following:

(a)
How many furniture packages should be ordered?

[4 Marks]

furniture packages [4 marks]
(b)
The probability that a stockout occurs in a cycle.

[6 Marks]

Probability of stockout = [6 marks]
(c)
At what level of stock should the furniture package be re-ordered?

[7 Marks]

Use the standard normal distribution table for 0.8182, we have [7 marks]  furniture packages
(d)
How much safety stock should be kept?

[3 Marks]

Safety stock  =  furniture packages [3 Marks]

[Total marks for question = 20 Marks]

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