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• Script Parts 1+2: Production Networks and Plant Location
• Exercise Questions

Note on this Note

I did not take lecture notes on Production Management. Below is an AI-generated summary of this chapter, and you’ll want to check out the resources above.

Strategic Network Planning

Planning Levels and Horizons

Decision-making in industrial production systems spans multiple levels:

• Strategic Planning (Long-term): Top management decisions determining the entire company’s long-term development (e.g., introducing new technologies, designing the infrastructure of the production system).
• Tactical Planning (Mid-term): Middle management decisions designing the production systems (e.g., job shop, flow shop, cellular manufacturing).
• Operative Planning (Short-term / Ad-hoc): Operative or local management decisions (e.g., demand forecasting, master production scheduling, material and capacity requirements planning, order allocation).

Supply Chain Management (SCM)

• Involves geographically dispersed suppliers, production facilities, distribution centers, and customers.
• Covers multiple stages of supply, production, and distribution.
• Characterized by the integration of supply, production, distribution, and sales activities.
• Internal Supply Chains: Entities within one company.
• External Supply Chains: Legally and organizationally independent parties.

The Classic Transportation Problem

An optimization problem to determine minimum cost transportation quantities from multiple production locations to multiple customer regions.

Vogel’s Approximation Method

A heuristic to determine an initial solution.
Idea: Minimize the maximum additional costs for not selecting the optimum supplier or destination. Uses additional costs incurred by selecting the second-best option as a priority rule.

Procedure:

1. Determine cost differences for each row and column (difference between the lowest and second-lowest cost) and identify the row/column with the maximum cost difference.
2. For the selected row/column, identify the transportation link with minimum costs. Set the transportation quantity equal to the minimum of available capacity and unfilled demand.
3. Update cost differences, capacities, and demand. If a plant’s capacity is used up or a customer’s demand is satisfied, eliminate the corresponding row or column from the tableau.
4. Repeat steps (1) to (3) until all demand is satisfied.

Transportation Model Formulation

Indices and Sets:

• $i\in I$: plants
• $j\in J$: customer zones

Parameters:

• $K_i$: capacity of plant $i$
• $D_j$: demand of customer zone $j$
• $c_{ij}$: per unit costs for production at plant $i$ and transportation to customer $j$

Decision Variables:

• $x_{ij}$: quantity transported from plant $i$ to customer zone $j$

Model Formulation:
Minimize:
${\sum }_{i\in I}{\sum }_{j\in J}{c}_{ij}\cdot x_{ij}$

Subject to:
${\sum }_{i\in I}{x}_{ij}\ge D_j\forall j\in J$
${\sum }_{j\in J}{x}_{ij}\le K_i\forall i\in I$
$x_{ij}\ge 0\forall i\in I,j\in J$

Assumptions

Single period, single product, only transportation and plant-specific production costs considered, linear cost structure, unlimited transportation capacities on links, all assignments feasible.

Selection of a Manufacturing Site

Reasons for opening new locations include increasing capacity, modernization, entering new markets, lower labor costs, and strategic issues.

Capacitated Production Plant Location Model

An extension of the classic transportation model to decide which plants to open given fixed costs.

Additional Parameters:

• $f_i$: fixed costs for set-up and operation of plant $i$
• $K_i$: potential annual capacity of plant $i$

Decision Variables:

• $y_i\in \{0,1\}$: $1$ if plant $i$ is open, $0$ otherwise
• $x_{ij}$: quantity shipped from plant $i$ to customer zone $j$ per year

Model Formulation:
Minimize:
${\sum }_{i\in I}{f}_i\cdot y_i+{\sum }_{i\in I}{\sum }_{j\in J}{c}_{ij}\cdot x_{ij}$

Subject to:
${\sum }_{i\in I}{x}_{ij}=D_j\forall j\in J$
${\sum }_{j\in J}{x}_{ij}\le K_i\cdot y_i\forall i\in I$
$x_{ij}\ge 0\forall i\in I,j\in J$
$y_i\in \{0,1\}\forall i\in I$