Optimal Lot Sizing for Time-Varying Demand .Example (continued):We continue with the four-period scheduling problem. ·y1=52,0ry1=139,y1=162,ory1=218 ·y2=0,y2=87,ory2=110,ory2=166 ·y3=0,y3=23,0ry3=78 ·y4=0,0ry4=56 .It is easy to see that every exact requirements policy is completely determined by specifying in what periods ordering should take place. 上泽充鱼大皇
Optimal Lot Sizing for Time-Varying Demand •Example (continued): We continue with the four-period scheduling problem. • y1=52, or y1=139, y1=162, or y1=218 • y 2=0, y 2 =87, or y 2 =110, or y 2 =166 • y 3=0, y 3=23, or y 3=78 • y 4=0, or y 4=56 •It is easy to see that every exact requirements policy is completely determined by specifying in what periods ordering should take place
Optimal Lot Sizing for Time-Varying Demand Example (continued):We continue with the four-period scheduling problem. if the production takes place in periodj else .This problem can be regarded as a one-way network with the number of nodes equal to exactly one more than the number of periods. .Every path through the network corresponds to a specific exact requirements policy 上游充道大睾
Optimal Lot Sizing for Time-Varying Demand •Example (continued): We continue with the four-period scheduling problem. •Define •This problem can be regarded as a one-way network with the number of nodes equal to exactly one more than the number of periods. •Every path through the network corresponds to a specific exact requirements policy. 1 if the production takes place in period 0 else j j i 1 2 3 4 5
Optimal Lot Sizing for Time-Varying Demand .Example(continued):We continue with the four-period scheduling problem. .The next is to assign a value to each arc in the network. .The value or"length"of the arc (,)called c is defined as the setup and holding cost of ordering in period i to meet the requirements through j-1. "Finally,dynamic programming is used to determine the minimum- cost production schedule,or shortest path through the network. 上游充道大睾
Optimal Lot Sizing for Time-Varying Demand •Example (continued): We continue with the four-period scheduling problem. •The next is to assign a value to each arc in the network. • The value or “length” of the arc ( i, j), called cij, is defined as the setup and holding cost of ordering in period i to meet the requirements through j-1. •Finally, dynamic programming is used to determine the minimumcost production schedule, or shortest path through the network