Short summary Operations Management
Operations Management problems in supply chain (Introduction & LP)
Operations Management (OM) is the process and scientific discipline of managing people and
resources to create products or services.
The production system
- Input: a resource required for the manufacture of a product or service
- Conversion system: a production system that converts inputs into outputs
- Output: a direct outcome or indirect outcome of a production system
Basic types of Production Processes
• Intermittent Production System: production is performed on a start-and-stop basis, such as
for the manufacture of made-to-order products
• Mass Customization: designing, producing, and delivering customized products to customers
at the cost and convenience of mass-produced items
• Continuous Production Process: a production process that runs for very longs periods without
the start-and-stop behavior
Deterministic OM: the process that are managed all behave in totally predictable way: demand is
certain, productivity is fixed, no delays, duration of process steps are fixed
Supply chain: suppliers, manufactures, distribution centers, demand markets
- Storage: where to locate and how to design the warehouse
- Transportation: which transport modalities, routing of transport
- Production: which sequence, how much do I produce
- Inventory: where to place, how much inventory, how to account for price
- Purchasing: how much, from whom do I buy, how to account for price
Three hierarchical steps:
1. Strategical level
o Network design
o Number, locations and size of warehouse
o Assignment of retail outlets to warehouses
o Major sourcing decisions
2. Tactical level
o Warehouse organization, inventory management
o Distribution channels, node routing
3. Operational level
o Real-time dispatching for rapid courier operations
o Real-time vehicle location and relocation
o Management of berthing operations in ports
Linear programming model seeks to maximize or minimize a linear function, which consists of
- Set of decision variables
- Objective function -> quantity to maximize/minimize
- Constraints -> linear inequality/equation
,Assumptions of Linear Programming model:
• The parameter values are known with certainty.
• The objective function and constraint exhibit constant returns to scale – linearity.
• There are no interactions between the decision variables – additivity.
• Variables can take on any value within a given feasible range – continuity.
General Form of Optimization Problems Linear Programming (LP) Problems
Formulating LP Models
1. Understand the problem
2. Identify the decision variables (e.g. X1, X2)
3. State objective function as linear combination of decision variables (e.g. MAX: 350X1+300X2)
4. State the constraints as linear combinations of decision variables (e.g. 1X1 + 1X2 <= 200)
5. Identify any upper/lower bounds on decision variables (e.g. X1 => 0)
Summary of Grapical Solution to LP Problems
1. Plot the boundary line of each constraint
2. Identy the feasible region (determine which side of
the line corresponds to the inequality)
o Plot level curves
o Enumerate the extreme points
Feasible region: set of values of the decision variables that satisfy the constraints
Optimal solution: feasible solution that maximize or minimize the objective function
An important property of linear programs is that the optimal solution always occurs at an extreme
point of the feasible region.
The objective function is Z. As Z is varied, one generates a family of parallel lines.
The graphical method of identifying the optimal solution is to pick one value of Z that takes us beyond
the feasible region, place a ruler on the Z line, and move the ruler parallel to the Z line toward the
feasible region. The extreme point that is hit first is the optimal solution.
Special conditions LP
- Alternative Optimal Solutions: when the Z line is parallel to one of the constraints, it does not
contact a single point first, but an entire edge
- Redundant Constraints: these constraints can be eliminated from the formulation without
affecting the solution
- Unbounded Solutions: you can make x1 and x2 as large as you like, no optimal solution
- Infeasibility: it is possible for two or more constraints to be inconsistent, no feasible solution
, Deterministic inventory management (EOQ and variants)
Examples of inventories:
• Goods
o Raw materials (e.g. oil in Pernis)
o Semi-finished products (e.g. sandwiches at Subway)
o Work in process (e.g. bread in oven)
o Finished products (e.g. supermarket)
• Resources: empty containers, trolleys, bottles
• Agricultural products
Why inventories?
- Fast delivery to customers
- Minimum purchase/order quantities
- Price speculation
- Set-up / fixed order costs
- Too limited production capacity to deal with peak demand, uncertainty
Economic Order Quantity model (EOQ)
Goal: inventory control for a single product at a single stock point in a constant environment
Q order quantity per order
K fixed costs per order
c purchasing costs per unit of product
h holding costs per unit of product per time unit h = I*c
I annual interest rate sum of interest rates/100
D customer demand per time unit
p shortage costs (not having sufficient stock on hand)
Lambda rate of demand
C maximum inventory level units
Assumptions:
• Setting: purchasing and selling goods in a deterministic and constant world.
• Purchasing: zero lead-time (time between orders the same), every quantity can be supplied
• Storage: shortages are not permitted (demand is immediately delivered)
• Sales: constant demand per time unit and demand rate is known
General approach
1. Define in words: goal, objective function, constraints
▪ Goal: minimizing total average relevant costs -> fixed order, purchasing, holding costs
▪ Restrictions: order quantity should be non-negative
2. Define decision variables
▪ When to order and how much?
▪ Predict optimal values for our decision variables
▪ Consequences:
1. It is optimal to receive an order when the last product
has been delivered to the customer.
2. Order quantity always the same, only decision variable
