A restaurant decided to sell a new type of sushi, for which the demand is deterministic and stable with a rate of lambda units per day. The food manufacturer of this sushi charges c per unit. The restaurant expects to incur a holding cost of h per unit held per day. No shortage is allowed. The food manufactureroffered the restaurant the following shipment plan: once the order placed by the restaurantis received, thefood manufacturerwill ship the order in threeshipments (assume the lead times for the shipments are negligible).The size of the firsttwoshipmentswill be one fourthof the order, respectively. The remainder of the order will be shipped in the third shipment. The later shipment will be timed so that the restaurant can receive this latter shipment just before it runs out of the inventory. The food manufacturer charges the restaurant K for three shipments as fixed cost. Let G(Q) be the restaurant's total cost per day (including the fixed cost, holding cost, and purchase cost) when the ordersize is Q.
a) What is the average inventory in one cycle?
b) What is total cost per cycle?
c) Derive an expression for G(Q).
d) Derive the optimal order quantity for this case that can minimize the G(Q) you derive in part b).