ISEN 315
Spring 2011
Dr. Gary Gaukler
Review: Prototype LP Problem
• Desk manufacturer
• Regular and rolltop desks, made of wood
• Regular: 20 sqft pine, 16 sqft cedar, 10 sqft
maple
• Rolltop: 10 sqft pine, 4 sqft cedar, 15 sqft
maple
Review: Prototype LP Problem
• Profits:
– Regular = $90
– Rolltop = $115
• Wood available:
– 200 sqft pine, 128 sqft cedar, 220 sqft maple
• How much to produce of each type of desk?
Review: Prototype LP Problem
• Decision variables:
• Objective function:
• Constraints:
Review: Aggregate Planning LP
• Parameters:
– c H, c F
– cI
– cR
– cO, cU, cS
Aggregate Planning LP
• Parameters:
– nt
–K
– I0 ,W0
– Dt
Aggregate Planning LP
• Decision variables:
– Wt
– Pt
– It
– Ht, Ft
Aggregate Planning LP
• Decision variables:
– Ot
– Ut
– St
Aggregate Planning LP
Aggregate Planning LP
• Constraints:
Aggregate Planning LP
• Constraints:
Aggregate Planning LP
• Objective function:
Aggregate Planning LP
• Now: Implement and solve the problem on
p.147 in Excel
Hierarchy of Planning
• Forecast of aggregate demand over time horizon
• Aggregate Production Plan: determine aggregate
production and workforce levels over time horizon
• Master Production Schedule: Disaggregate the
aggregate plan and determine per-item production
levels
• Materials Requirements Planning: Detailed schedule
for production/replenishment activities
Inventory Control
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•
•
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Deterministic inventory control
Stochastic inventory control
MRP / Lot sizing / JIT
Supply chain management
Reasons for Holding Inventories
Relevant Costs
• Holding Costs - Costs proportional to the
quantity of inventory held.
Relevant Costs (continued)
• Ordering Cost (or Production Cost).
Can include both fixed and variable components.
slope = c
K
Relevant Costs (continued)
• Penalty or Shortage Costs. All costs that
accrue when insufficient stock is available to
meet demand.
Simple EOQ Model
• Assumptions:
1. Demand is fixed at l units per unit time.
2. Shortages are not allowed.
3. Orders are received instantaneously.
4. Order quantity is fixed at Q per cycle.
5. Cost structure:
a) Fixed and marginal order costs (K + cx)
b) Holding cost at h per unit held per unit time.
Inventory Levels for the EOQ Model
Cost Equation for the EOQ Model
The Average Annual Cost Function G(Q)
The Average Annual Cost Function G(Q)
The Optimal Q*
Properties of the EOQ Solution
Example
•
•
•
•
•
Desk production rate = 200 per month
Each desk needs 40 screws
Screws cost $0.03
Fixed delivery charges are $100 per order
25% interest rate for holding cost
• What is the optimal order size?
Example