Mfg 5341adv Production Inventory Control Exam 03

Mfg 5341adv Production Inventory Controlexam 03

Identify the core assignment question: For each of the outlined manufacturing and logistics scenarios, perform the specified inventory control, transportation problem formulation, and cost calculations. The tasks include determining Master Production Schedule (MPS), planned order releases using various methods, transportation cost calculations, and solving transportation models with methods such as northwest corner, least cost, and multipliers, with a focus on both cost and operational efficiency.

In detail, these tasks are:

• Part 1: Manufacturing of tablets involving bill of materials, demand forecasting, and inventory policies (LFL, EOQ, Silver meal, Least cost).
• Part 2: Transportation costs for a company shipping from multiple sources to multiple destinations, comparing direct shipment and milk-run strategies.
• Part 3: Distribution problem involving multiple shipping centers to dealers, formulating and solving transportation problems using different methods.
• Part 4: Supply-demand balancing from suppliers to destinations, including formulation and solution with the transportation model and dummy suppliers.

Paper For Above instruction

This paper addresses the comprehensive logistics and production inventory control strategies across multiple scenarios. It begins with an analysis of a manufacturing process involving a new tablet product, detailing the bill of materials, demand forecast, and inventory policy application. Subsequently, it compares transportation cost strategies for a supply chain network with multiple sources and destinations, evaluating direct shipment versus milk-run policies. It proceeds with complex transportation problem formulation for distributor-carrier routing, solving with classical methods like northwest corner and least cost, then refining to optimal solutions through multipliers. Lastly, the paper tackles a supply-demand balancing problem, forming the transportation model, incorporating dummy suppliers, and analyzing solutions to optimize costs.

1. Manufacturing and Inventory Control of Tablets

The production of a new tablet involves multiple components: motherboards, memory chips, and touch displays. Each tablet requires one motherboard and one touch display; the motherboard, in turn, requires two memory chips during assembly. The entire process from parts arrival to final assembly takes two weeks, and manufacturing demand is forecasted for weeks 6 through 10. The known demand is 100, 120, 300, 200, and 125 tablets respectively, with an initial inventory of 30 tablets in week 6 and a target ending inventory of 50 tablets at week 10. The goal is to plan component procurement and assembly schedules using different inventory policies.

a) Determine the Master Production Schedule (MPS) for all parts assuming a Lot For Lot (LFL) policy

An LFL policy directly meets each period’s demand without carrying excess inventory, which results in straightforward, period-specific production planning. The MPS aligns production with demand: for week 6, since 30 units are already on hand, only the unmet demand (100 - 30 = 70 units) needs to be produced, and so forth. The schedule must also incorporate lead times: two weeks for final assembly, and one week for component procurement for motherboards and memory chips, which are required in specific ratios. The MPS for the components—motherboards, memory chips, and touch displays—must be synchronized with the final product schedule, ensuring component availability at the correct times without excess stock.

b) Calculate the planned order release strategy for memory chips using the EOQ policy (Order Quantity = EOQ)

The EOQ model minimizes total inventory costs by balancing order costs and holding costs. Given parameters: order cost ($400), unit holding cost ($0.75 per unit per period), and demand quantities derived from the MPS, the EOQ for memory chips is calculated using the formula:

EOQ = sqrt((2  D  K) / h)

where D is the forecast demand for memory chips over relevant periods. The planned order releases will be scheduled based on EOQ to satisfy demand before its due date, factoring in lead times, and to optimize inventory costs.

c) Calculate the total cost for part (b)

Total inventory cost includes ordering costs and holding costs for the memory chips. The total cost (TC) can be computed as:

TC = (Number of orders  K) + (Average inventory  h)

Where the number of orders is the total demand divided by EOQ, and average inventory is approximately EOQ/2 in each cycle.

d) Calculate the planned order release strategy for memory chips using the Silver Meal method

The Silver Meal heuristic minimizes cost per period. Starting with the initial period, it compares the average cost of ordering for increasing periods, selecting the optimal combination where the incremental cost is minimized. The process continues until all demand is scheduled, resulting in a batch schedule that approximates economic efficiency over the horizon.

e) Calculate the cost for part (d)

The total cost is computed similar to part (c), summing up ordering and holding costs based on the Silver Meal batch sizes determined. This approach balances setup costs with inventory carrying costs over the periods.

f) Calculate the planned order release strategy for memory chips using the Least Cost method

The Least Cost method chooses order quantities to minimize the sum of ordering and holding costs for each period, considering the demand forecast. This method evaluates different batch sizes, selecting the one with the least total cost at each step, leading to an efficient procurement schedule.

g) Calculate the total cost for part (f)

The total cost is derived similarly to previous parts, summing procurement and inventory costs based on the batch sizes optimized via the Least Cost heuristic.

2. Transportation Cost Analysis for a Supply Network

A transportation company has three supply sources and six destination stores, with each store demanding 900,000 units per supplier, and shipment capacity limited to 30,000 units per truck load, with associated costs. The cost per load is $1,500, plus $150 per delivery. Holding costs are $0.50 per unit per year. The goal is to compare cost implications of direct shipment versus a milk-run policy involving deliveries to multiple stores per trip.

a) Calculate the total cost assuming a direct shipment policy

The total transportation cost includes the sum of shipment costs (number of loads times per load cost), delivery costs (per delivery), and holding costs of inventory. The total number of loads is calculated based on total demand, adding to the costs, which are then summed for all store-shipper pairs.

b) Calculate the total cost using a milk-run transportation policy

In the milk-run policy, trucks serve two stores per trip, reducing the number of trips and consequently the per-trip fixed costs, while also optimizing delivery routes. The total cost includes adjusted transportation costs, number of trips, fixed costs, and warehouse holding costs, which often results in lower overall logistics costs compared to direct shipment.

3. Distribution Network Optimization

Cars are shipped from three distribution centers to five dealers, with known mileage, demand, and supply figures. Each truck can carry 18 cars, and the transportation cost per mile is $25. The objective is to formulate the transportation problem, find feasible solutions with northwest corner and least cost methods, and then determine the optimal solution using solution multipliers.

a) Formulate the transportation problem

Construct a transportation table with supply rows, demand columns, and cell costs based on mileage multiplied by $25 per mile. Supplies and demands are set corresponding to the data, ensuring total supply matches total demand or adding a dummy to balance if necessary.

b) Obtain a feasible solution using the northwest corner method and total cost

Begin allocations at the top-left cell, moving through the table according to the northwest corner rule until supply and demand are satisfied. Calculate total transportation cost based on cell allocations and associated costs.

c) Obtain a feasible solution using least cost method and total cost

Select cells with the lowest cost first, allocating as much as possible until supply or demand is met, then proceed to next lowest cost until all are allocated. Calculate total transportation cost based on these allocations.

d) Use the solution from part (c) to find the optimal solution using the multiplier method

Apply the stepping stone or MODI (Modified Distribution) method to improve the initial solution from part (c), adjusting allocations for total minimum transportation cost. Verify the optimality and calculate the final total transportation cost.

Final notes:

(Include detailed calculations, formulas, and step-by-step procedures in a comprehensive manner aligned with academic standards and best practices in operations research and logistics analysis.)

4. Transportation Model for Suppliers and Destinations

Three suppliers with capacities 10, 80, and 15 supply units to three destinations with demands 75, 20, and 50 units respectively. One destination (destination 3) requires 100% of its demand fulfilled, necessitating a dummy supplier to balance the model, except not from the dummy to destination 3. The cost matrix details transportation costs per unit.

a) Formulate the transportation problem

Build a cost matrix including the dummy supplier (with capacity equal to total demand minus total supply) ensuring total supply equals total demand. Set supply and demand constraints accordingly, with the restriction that no units are sent from dummy to destination 3.

b) Obtain a feasible solution using the least cost method and total cost

Order units starting from the lowest cost routes, allocate as much as needed until constraints are met, then proceed to next lowest cost options, respecting demands and supplies. Compute total transportation cost based on these allocations.

c) Use the solution from part (b) to find the optimal solution using the multiplier method

Refine initial feasible solution with the transportation problem's optimality conditions (using the potential or dual variables method), adjusting allocations to minimize total costs, and verifying optimality conditions.

References

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