A company based in Oman is faced with the problem of determining the optimal production plan to fulfillcustomer demand over the next N weeks at the lowest possible cost. The company has M factories, eachwith its production capacities for both regular and overtime production. Costs associated with regularproduction and overtime vary by both the factory and the week. Besides its internal production capacity,the company has the flexibility to subcontract, procuring products from S suppliers, and the purchasingcosts fluctuate from week to week. The company also manages W warehouses, each incurring a uniqueholding cost per unit per week, and these costs vary across warehouses. The objective is to minimize theoverall cost, encompassing regular and overtime production costs, subcontracting expenses, andwarehouse holding costs, all while ensuring customer demand is met.