Consider a manufacturing process for a handheld communication device with an $8$ week lead time. The process produces three product variants, which differ in terms of how many cameras are in the device. The product variants are named the Uni $($one camera$),$ the Duo $($two cameras$),$ and the Triple $($three cameras$).$ Except for this difference in number of cameras, each product variant is the same. In the current manufacturing process, the customization of the device occurs at the start of production; the first step of the process is to set the number of cameras in the device, and this determines whether the product will be a Uni or a Duo or a Triple.

Each product is made to stock, and the inventory is controlled with a periodic review, base stock policy. The review period is two weeks, demand is assumed to be normally distributed, and the safety factor is z $=2.$

device mean demand per week standar deviation of demand per week

uni $20050$

Duo $8030$

triple $15040$

Determine the safety stocks for each product variant, with the demand parameters given in the above table. Please round to the nearest integer.

Suppose now that the customization of the device can be delayed until $6$ weeks into the $8-$week manufacturing process. This delay in customization will reduce the amount of safety stock needed for each product. Use the cross dock approximation model to determine the safety stocks for each product variant, for this assumption of delayed differentiation.

Suppose there is a cost to implement the change in process given in $4\mathrm{.}2.$ Namely, the production cost for each unit produced increases by $$0\mathrm{.}10$ when the process is changed to postpone customization until week $6.$ The annual holding cost is the same for each type of device and is equal to $$50$ per unit. Suppose there are $50$ weeks in a year.

Should the firm make the process change to postpone when the cameras are added?

Based on Problem $4\mathrm{.}3,$ how much money is saved per year if we make the change? Please note, your answer can be negative if you find that the cost will increase. Suppose there are $50$ weeks in a year.