Question

1. A hyper market plans to order vacuum cleaners from three different supplies equally that has an annual demand 4500 units. There is a fixed transportation cost of 700 SAR that is incurred each time the order is placed, along with the additional fixed cost of 150 SAR for each supplier. The hyper market incurs a holding cost of 15% while the cost of each model is purchased at 200 SAR.
   1. Evaluate the frequency and lot size that the hyper market manager must order for each model if he decides to aggregate the order. Also determine the cycle inventory, average flow time, and the annual ordering and holding costs per supplier
   2. Determine the lot size that the hyper market manager has to order when the supplies are aggregated per supply with a capacity of 900 units, frequency of supplies, with the cycle inventory, average flow time, and annual ordering and holding costs per supplier.
   3. Identify the strategy that the hyper market manager has to choose to adopt economics of scale.

please I want it to be solved in details....

Answer 1

Annual demand, D = 4500 units (considering this as the combined demand of three models)

Fixed transportation cost per order, Ct = 700

Additional fixed cost per supplier per order, Cs = 150

Unit cost, c = 200

Inventory holding charge, i = 15%

Inventory holding cost per unit per year, H = i*c = 15%*200 = 30

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(a)

Aggregate ordering

Total cost per order, S = 700+150*3 = 1150

EOQ = sqrt(2DS/H)

= sqrt(2*4500*1150/30)

= 587 units

Lot size for each model = 587/3

= 196 units

Cycle inventory = Q/2

= 587/2

= 294 units (combined quantity of three models)

Average flow time = Q/D

= 587/4500

= 0.13 year

Annual ordering and holding cost = S*D/Q+H*Q/2

= 1150*4500/587+30*587/2

= 17,621

Annual ordering and holding cost per supplier = 17621/3

= 5,874

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(b) & (c)

The EOQ is 587, which is less than capacity of 900 units.

So, recommended lot size is same as determined in part (a),

Hence, answer to parts (b) and (c) are same as that of part (a)