A hotel uses an external laundry service to provide clean towels. The hotel gene

Question

A hotel uses an external laundry service to provide clean towels. The hotel generates 600 dirty towels a day. The laundry service picks up the dirty towels and replaces them with clean ones at regular intervals. There is a fixed charge of $81 per pickup and delivery service, in addition to the variable cost of $0.60 per towel. It costs the hotel $0.02 a day to store a dirty towel and $0.01 per day to store a clean one. How often should the hotel use the pickup-and-delivery service? Note: There are two types of inventory items in this situation; as the level of the dirty towels increases, that of clean towels decreases at an equal rate.

Explanation / Answer

We need to optimize the objective function by minimizing the cost associated with the inventory of towels.

Let

T= Total no of towels on ground

t0 = Time between deliveries

C(T) = (Holding clean+holding dirty+placing order+cleaning dirty)/time between orders

C(T) =(0.01(0.5)(T+(T-600t0))t0 +0.02(0.5)(0+600t0 )t0 +81+0.6(600t0 ))/t0

Also T/600 = t0

Setting C(T)=0 and solving for T

We get T=1800 and -1800

-1800 is rejected as not being physical in nature. hence hotel should have 1800 towwels in inventory.

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