\begin{tabular}{lrrrrrrrrrr} \hline Week & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ Gross requirements & 417 & 0 & 0 & 0 & 417 & 0 & 417 & 0 & 0 & 417 \\ \hline \end{tabular} Example 8.2 A machine shop uses the Silver-Meal heuristic to schedule production lot sizes for computer casings. Over the next five weeks the demands for the casings are r=(18,30,42,5,20). The holding cost is $2 per case per week, and the production setup cost is $80. Find the recommended lot sizing. Solution Starting in period 1: C(1)=80,C(2)=[80+(2)(30)]/2=70C(3)=[80+(2)(30)+(2)(2)(42)]/3=102.67.StopbecauseC(3)>C(2). Set y1=r1+r2=18+30=48. Starting in period 3 : C(1)=80,C(2)=[80+(2)(5)]/2=45,C(3)=[80+(2)(5)+(2)(2)(20)]/3=56.67.Stop. Set y3=r3+r4=42+5=47. Because period 5 is the final period in the horizon, we do not need to start the process again. We set y5=r5=20. Hence, the Silver-Meal heuristic results in the policy y=(48,0,47, 0 , 20). (Hint: You can streamline calculations by noting that C(j+1)=[j/(j+1)][C(j)+hrj+1].) 26. Consider the example presented in Section 8.2 of scheduling the production of the valve casing assembly. a. Suppose that the production capacity in any week is 100 valve casings. Using the algorithm presented in this section, determine the planned order release for the valve casings. b. What gross requirements schedule for the valves does the lot sizing you obtained in part (a) give? c. Suppose that the production capacity for the valves is 200 valves per week. Is the gross requirements schedule from part (b) feasible? If not, suggest a modification in the planned order release computed in part (a) that would result in a feasible gross requirements schedule for the valves