047: Supply Chain Coordinations

/** 
 * Supply chain coordination problem
 * OPL model for a leaf agent, i.e. an agent that has no sub-suppliers.
 * The agent agrees delivery schedules for its products with other agents in the problem.
 * The products of this agent are the components of the receiving agents.
 */


/**
 * MODEL INPUT PARAMETERS
 */
 
// Time horizon
int numPeriods = ...; 
range horizon 1..numPeriods;

// Number of product configurations
int numProducts = ...; 
range products 1..numProducts;

// Number of components
int numComponents = ...; 
range components 1..numComponents;

// Maximum number of orders to consider for each product
int maxNumOrders[products]  = ...;

// Bill Of Materials
int bom[products,components] = ...; 

// The batch size of a product in a particularly delivery
int batchSize[products] = ...;

// The lead time/delivery time for a particular component
// I.e. the number of periods between an order being made 
// and the goods being delivered
int leadtime[products] = ...;
   
// Number of processing cycles for each configuration
int cycles[products]= ...; 

// Number of cycles required to setup a configuration
int setupCycles[products] = ...;

// Factory capacity
int capacity[horizon] = ...;  

// Starting product inventory
int openingProductInventory[products] = ...;

// Starting component inventory
int openingComponentInventory[components] = ...;

// Holding costs
int productHoldingCost[products] = ...;
int componentHoldingCost[components] = ...;

// Setup costs
int setupCosts[products] = ...;

// Expected inventory arriving for each component in the time horizon
int componentArrivals[horizon,components] = ...;

// Constants
int maxManufacture = max(t in horizon) capacity[t];
int maxOrders = max(p in products) maxNumOrders[p];


/**
 * PUBLIC VARIABLES
 * (variables constrained with other agents)
 */

// The number of orders for a each product to be delivered in each period.
var int productDeliverySchedule[products,horizon] = 0..maxOrders;



/**
 * PRIVATE VARIABLES
 * (variables not constrained with other agents)
 */

// 0/1 variable indicating whether or not a product will be built in a particular period
var int isbuilt[horizon,products]  in 0..1; 

// The number of a product built in a particular period
var int manufacture[horizon,products] in 0..maxManufacture; 



/**
 * AUXILIARY VARIABLES
 * (additional variables used to simplify the model specification)
 */


// Remaining product inventory after each period
var float+ productInventory[0..numPeriods,products]; 

// Remaining component inventory after each period
var float+ componentInventory[0..numPeriods,components]; 

// The quantity of product delivered in each period
var float+ deliveryQuantity[horizon, products]; 

// Components needed on a particular day to produce everything in manufacture
var float+ componentsUsed[horizon, components]; 

 
minimize

   // Total cost
   sum (t in horizon, p in products) (
      (productHoldingCost[p]*productInventory[t,p]) +
      (isbuilt[t,p]*setupCosts[p])
                                  ) +   
   sum (t in horizon, c in components) (
      (componentHoldingCost[c]*componentInventory[t,c])
                      )

subject to
{        
      
   // Opening product inventory
   forall(p in products) productInventory[0,p]=openingProductInventory[p];
   

   // Opening component inventory
   forall(c in components) componentInventory[0,c]=openingComponentInventory[c];


   // Calculate the number of products delivered
   forall(p in products) forall (t in 1..numPeriods-leadtime[p]) deliveryQuantity[t,p] = batchSize[p] * productDeliverySchedule[p,t+leadtime[p]];
   forall(p in products) forall (t in [numPeriods-leadtime[p]+1..numPeriods]) deliveryQuantity[t,p] = 0;   
   

   // Set the isbuilt variable correctly - should be 1 if any of that product is built on that day
   forall(t in horizon, p in products) maxManufacture * isbuilt[t,p] >= manufacture[t,p];
   

   // Capacity constraint for manufacturing decision
   // The factory's capacity for each day cannot be exceeded
   forall(t in horizon) sum(p in products) (manufacture[t,p]*cycles[p] + isbuilt[t,p]*setupCycles[p]) <= capacity[t];
   

   // The number of components needed is calculated by multiplying manufacturing decision by BOM
   forall(t in horizon, c in components) componentsUsed[t,c] = sum(p in products) manufacture[t,p]*bom[p,c];
   
      
   // Calculate the expected excess product inventory of each period
   forall(t in horizon, p in products) productInventory[t,p] = productInventory[t-1,p] + manufacture[t,p] - deliveryQuantity[t,p];     

   
   // Calculate the expected excess component inventory of each period
   forall(t in horizon, c in components) componentInventory[t,c] = componentInventory[t-1,c] + componentArrivals[t,c] - componentsUsed[t,c];   

};