## Solving the Lot Sizing Problem in Resolver One (Wagner-Whitin Algorithm)

I was working on a lot sizing problem today and implemented a Wagner-Whitin algorithm in Resolver One. I just want to share it with you here. Some people use a MIP solver to solve lot sizing problems while Wagner and Whitin have devised an algorithm that can be implemented quickly on a spreadsheet and there is no need to use an expensive solver. You can download the spreadsheet from this link.

In the classical lot sizing problem we have the following assumptions:

1. We have a single product (with the production quantity in period t$X_t$)
2. Discrete Time (unlike EOQ model)
3. Demand is known but varies over time (e.g., we have orders) $d_t$
4. No shortage is allowed
5. No capacity constraints
6. There is a positive setup cost that might be varying over time $K_t$
7. The unit production cost is constant
8. The objective is to minimize the total setup cost and inventory costs

Here is the formulation for the model:

1. $K_t$ setup cost in period t
2. $h_t$ inventory holding cost per unit remaining at end of period t
3. $d_t$ demand in period t
4. $M$ a large number (will be used in the MIP model)
5. $X_t$ production quantity in period t
6. $Y_t=1$ if $X_t> 0$ and is 0 otherwise
7. $l_t$ inventory remaining at the end of period t

The MIP model will be:
$Minimize$ $\sum_t K_tY_t + \sum_t h_tI_t$

$Subject\: to:$

1. $I_t=I_{t-1}+X_t-D_t$
2. $MY_t\geq X_t, \forall t$
3. $I_t\geq0, \forall t$
4. $Y_t \:is\: binary$
5. $X_t\geq0, \forall t$

Wagner and Whitin have solved this problem using the forward dynamic programming. In this spreadsheet we implement the forward dynamic programming for the lot sizing problem. The spreadsheet then suggests the time period than it is optimal to pay for the setup cost, in other time periods it is cheaper to carry an inventory.

~ by marksalen on September 3, 2009.

### 8 Responses to “Solving the Lot Sizing Problem in Resolver One (Wagner-Whitin Algorithm)”

1. i need your help Mr, for my Thesis,,cause my Thesis Title also likes your scribd in this blog.how can i call u or always chat with you.i really dont know about my problem. plez,,help me Mr.
this is my title :
Integer Program Model for Resolving Issues Lot Size
Coordinated with deterministic Dynamic Demand

can you give me some books that relation with my title ,,Mr???ples yaaaaaaaa

4. Hi there:

I am an undergraduate student at SUNY Buffalo. I wanted to open the sample spreadsheet file you have posted, but it is an .RSL file, and I can’t find information about that extension online. Which program can I use to open it?

Thanks!
Alex