Statement of the problem:Statement of the problem:

Question$-3$: $($Dymamic Planning by Wagner$-$Whitin algonithm$)$

Consider the case of a production planning where the demand rate is not steady over

the time horizon. The demand for $6$ months is given below.

The setup cost and the inventory holding cost are given below:

Setup cost, $A=500[$Rs$]$;

Inventory holding cost

$h=4$; Rs per item per month

The state diagram is as depicted

alongside in which $D_i$ is demand, $P_i$

is production and $l_i$ is the inventory.

The starting and ending inventory

are zero:

Calculate the optimum schedule of production

plan using the dynamic programming

approach of Wagner$-$Whitin Algorithm.

Assume the initial inventory to be zero.

$($i$)$ Hence state the optimum values of

the cost function

$F(1),F(2),F(3),F(4),F(5),F(6)$

$($ii$)$ The periods when the production

machine is run according to the

optimum schedule, hence, state the

values of $P_1,P_2,P_3,P_4,P_5,$ and $P_6$ :

$($ii$)$ As per the optimum schedule what should be the values of inventory,

$I_1,I_2,l_3,I_4,I_5,$ and $I_6.$ The starting and ending inventories should be zero.

$($iv$)$ Draw a neat sketch of the state diagram with all values shown.

$F(t)=Mi{n}_{\text{s}\text{a}\text{t}}[F(s-1)+A+HC(s,t)]$

$($Marks $10)$

Question$-3$: $($Dynamic Planning by Wagner$-$Whitin algorithm$)$

Consider the case of a production planning where the demand rate is not steady over

the time horizon. The demand for $6$ months is given below:

Demand

Time $123456$

Demand $301001601208040$

The setup cost and the inventory holding cost are given below:

Setup cost, A $=500[$Rs$]$;

$12$ n

P$1$ P$2$ Pn

D$1$ D$2$ Dn

I$0$ I$1$ I$2$ In$-1$ In

Figure: State Diagram

$7$

Inventory holding cost

$=4$; $$

The state diagram is as depicted

alongside in which $$

is demand, $$

is production and $$

is the inventory.

The starting and ending inventory

are zero:

Calculate the optimum schedule of production

plan using the dynamic programming

approach of Wagner$-$Whitin Algorithm.

Assume the initial inventory to be zero.

$($i$)$ Hence state the optimum values of

the cost function

$(1),(2),(3),(4),(5),(6)$

$($ii$)$ The periods when the production

machine is run according to the

optimum schedule, hence, state the

values of $1,2,3,4,5,6$;

$($iii$)$ As per the optimum schedule what should be the values of inventory,

$1,2,3,4,5,6.$ The starting and ending inventories should be zero.

$($iv$)$ Draw a neat sketch of the state diagram with all values shown.