So I have been working with this Inventory Problem and this is where I am now:

What I want to do is to determine a production schedule that will meet all demands and minimize cost.

I want to store the minimum cost and production quantity for each period and inventory level in a 2 matrices

Here is the code I have so far, I would say I am very close to being done

I am having problems finding the correct minimum cost and the corresponding Product_Quantity.

Basically I compute the cost values, compare it to the cost matrix and when I find the min cost, I record the cost and quantity associated.

Please help ASAP!!

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];%C_Cost = [% 20 16 31/2 15 27/2% 16 15 14 12 21/2% 12 10 7 13/2 6% 0 4 5 6 7];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;%Prod_Q_Min = 0;%Prod_Q_Max = 5;n=size(C_Cost,1);Min_Cost=zeros(1,n); %added matrix to keep argmin(Min_Cost)Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 4 - 0 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = C_Cost(Inv_Level+1,Inv_Level+Prod_Quantity-Demand(Period)); % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + C_Cost(Inv_Level+1,Inv_Level+Prod_Quantity-Demand(Period)); % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint if C_Cost(Period,Inv_Level+1) == cost;% Check to see if this is the minimum cost X = (cost+0.5*(Inv_Level + Prod_Quantity - Demand(Period))); % Store the Minimum cost Min_Cost(1,Inv_Level+1) = (X); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Inv_Level+1) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

I am getting the 2 matrices now but the values are not correct

Updated code attached...

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];%C_Cost = [% 20 16 31/2 15 27/2% 16 15 14 12 21/2% 12 10 7 13/2 6% 7 6 5 4 0];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;%Prod_Q_Min = 0;%Prod_Q_Max = 5;n=size(C_Cost,1);Min_Cost=zeros(1,n); %added matrix to keep argmin(Min_Cost)Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 0 - 4 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = Setup_cost + Prod_Quantity*variable_cost; % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + Setup_cost + Prod_Quantity*variable_cost; % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint if C_Cost(Period,Inv_Level+1) == cost;% Check to see if this is the minimum cost X = (cost+0.5*(Inv_Level + Prod_Quantity - Demand(Period))); % Store the Minimum cost Min_Cost(1,Inv_Level+1) = (X); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Inv_Level+1) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

Ok I've got a work around for the min cost, but I need the right production quantities.

The Correct Prod_Quantity is [1 5 0 4]

Updated Code Attached

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];%C_Cost = [% 20 16 31/2 15 27/2% 16 15 14 12 21/2% 12 10 7 13/2 6% 0 4 5 6 7];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;%Prod_Q_Min = 0;%Prod_Q_Max = 5;n=size(C_Cost,1);%Min_Cost=zeros(1,n); %added matrix to keep argmin(Min_Cost)Min_Cost = 0;Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 4 - 0 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = Setup_cost + Prod_Quantity*variable_cost; % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + Setup_cost + Prod_Quantity*variable_cost; % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint if C_Cost(Period,Inv_Level+1) == cost;% Check to see if this is the minimum cost X = (cost+0.5*(Inv_Level + Prod_Quantity - Demand(Period))); % Store the Minimum cost Min_Cost = C_Cost(1,1); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Period) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

Using my cost formula I compare the computed cost to C_Cost. When the computed cost = min(C_Cost) in that row, I want to record the Production quantity which corresponds to that minimum cost.

I have attached the code I have so far.

I need help with this ASAP!

Thanks in advance

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;n=size(C_Cost,1);Min_Cost = 0;Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 4 - 0 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = Setup_cost + Prod_Quantity*variable_cost; % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + Setup_cost + Prod_Quantity*variable_cost; % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint if min(C_Cost(Period,Inv_Level+1)) == cost;% Check to see if this is the minimum cost X = cost; % Store the Minimum cost Min_Cost = C_Cost(1,1); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Period) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

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I tried something but I am still not getting the right results...

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;n=size(C_Cost,1);Min_Cost = 0;Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 4 - 0 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = Setup_cost + Prod_Quantity*variable_cost; % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + Setup_cost + Prod_Quantity*variable_cost; % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint for i = 1:5; min_value = min(C_Cost(Period,i)); end if min_value == cost;% Check to see if this is the minimum cost %X = cost; % Store the Minimum cost Min_Cost = C_Cost(1,1); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Period) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

Let's see if I';m understanding the setup correctly:

you have a 4x5 C_cost matrix as you showed above. For each row, you compute a cost value. In addition, for each row, you have a production value.

So you have a 4x5 C_cost matrix, and if you run through the for loops in your next-to-last comment, exluding the "if min(C_Cost(Period,Inv_Level+1)) " blocke, you get a 4-element cost vector and a 4-element vector of production values (prodv).

The C_Cost matrix is what I am supposed to get when I perform my calculations.

It is only there for reference. So I calculate the cost values that are actually there in the cost matrix using the cost formulas in my code. The min of the C_Cost matrix (row) is then compared to the cost that I come up with, and when both of them are the same, then I add the production quantity to the matrix.

I am having problems with finding the correct cost value = min C_Cost part

I'm not understanding why the code snippet I gave doesn't suit, then.

min(C_Cost,[],2) wil give you a vector containing the minimum values for each row of the matrix (i.e. the first vector element is the min of the first row, etc.).
if you create a computed cost vector, min(C_Cost,[],2)==cost will tell you at what rows the minimum for that row is equal to the computed cost corrosponding to that row.

I added a Break in the last if statement, which decreases the Period loop by 1 which is what I want, but the other 2 inner loops are not being incremented properly and I am getting wrong values for the computed cost formula, which is why I am getting wrong production quantities....

Eyal-f: The snippet you provided is working fine and I have incorporated it into my code, but the code is not matching the computed cost to the min cost correctly.

Updated code attached

function [f] = Inventory_ma2rafiq(C_Cost)Demand = [1,3,2,4];Setup_cost = 3;variable_cost = 1;holding_cost = 0.5;Prod_Cap = 5;WareHouse_Cap = 4;Period_Begining = 1;Period_End = 4;Inv_Min = 0;Inv_Max = 4;n=size(C_Cost,1);Min_Cost = 0;Opt_Prod_Quantity=zeros(1,n); %added matrix to keep argmin(Min_Cost)for Period = Period_End:-1:Period_Begining; % Period Loop for 4 - 1 for Inv_Level = Inv_Min:Inv_Max; % Inventory Level Loop from 4 - 0 for Prod_Quantity = max(0,Demand(Period)-Inv_Level):min(Prod_Cap,WareHouse_Cap-Inv_Level+Demand(Period)); % Loop only with Current Month Demand met constraint and Ending Inventory cannot exceed Capacity Constraint if Period == 4 % Cost for Period 4 if Prod_Quantity == 0 cost = 0; % No Production = 0 Cost else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)); % Holding Cost + ProdCost end end if Period ~= 4 % Cost for Periods other than 4 if Prod_Quantity == 0 cost = Setup_cost + Prod_Quantity*variable_cost; % Calculate only cost from Cost Matrix else cost = Setup_cost + Prod_Quantity*variable_cost + holding_cost*(Inv_Level + Prod_Quantity - Demand(Period)) + Setup_cost + Prod_Quantity*variable_cost; % Complete Cost Formula end end %Inv_Level + Prod_Quantity - demand(Period) <=4; % Current Month Demand Constraint %Inv_Level + Prod_Quantity - demand(Period) >=0; % Ending Inventory cannot exceed Capacity Constraint %for i = 1:5; %min_value = min(C_Cost(Period,i)); %end if min(C_Cost,[],2)==cost;% Check to see if this is the minimum cost %X = cost; % Store the Minimum cost Min_Cost = C_Cost(1,1); % If we are at the minimum cost then store min_cost Opt_Prod_Quantity(1,Period) = (Prod_Quantity); % If we are at the minimum cost then store min_cost associated Prod_Quantity break end end endendMin_Cost % Output Min_Cost matrixOpt_Prod_Quantity % Output Production Quantity matrixend

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