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a)What do we mean when we say productivity is a relative measure? Choose an industry and measure productivity of the company in two different ways with supportive data.

b)Should safety stock be necessary in an MRP system with dependent demand? If so, why? If not, why do firms carry it anyway?

c)Many practitioners currently update MRP weekly or biweekly. Would it be more valuable if it were updated daily?

In a manufacturing firm, two workers are producing four products. The market demand is unlimited and takes all the products that the workers can produce. However, it is required that the number of any product sold cannot be fewer than one fifth of the maximum number of any one product sold. For example, if the maximum number of any one product sold is 100 units, the number sold of any other product cannot be fewer than 20 units. Workers 1 and 2, are not cross-trained and can work only on their own operations. The selling price, processing time and raw material (RM) costs for each product are shown in the Graph 1. And a summary of the costs and times involved is given in the Table 1. Both workers can work 5 days a week and 8 hours per day and they both are paid £(12+a) per hour.

Graph 1 Production Requirements and selling price of four products

Table 1 A summary of the production requirements and selling price of four products

The manager wishes to maximise the weekly profit to the firm.

a)Formulate an Integer Programming model for this product mix problem so that the weeklyTotal Profit of the firm is maximized (Total Profit = Total Revenue –– Raw Material Costs – Labour costs). Describe clearly each of the following parts of your mathematical model with ONE or TWO sentences: objective function, decision variables, constraints and decision variable domain.

b)Model this problem in Excel and use Solver to find the optimal solution. Provide a description of the optimal solution found in the context of the application. ONE hard copy screenshot of your Excel model should accompany your description.

c)Generate the Answer Report and Sensitivity Analysis Report by dropping the integer requirement on the decision variables in a).

i)Use the Answer Report and Sensitivity Analysis Report to find out the most limiting resource or activity to the manufacturing process, and analyse what happens if the availability of the most limiting resource changes?

If the worker 1 and work 2 are available to work up to 10 hours per day, and they need to be paid £18 per hour for any hour that they work out of the regular working hours (more than 8 hours). Would you recommend them to work overtime (Assume the availability of raw material is unlimited)? why? Note that you DO NOT need to revise and rerun the mathematical model.

Acorn Computers Ltd., a British computer manufacturer, needs to develop an aggregate production plan for the coming six months from January to June. You have been commissioned to create the aggregate plan. The following information should help:

Table 2 Information for the aggregate plan of the Acorn company

In Table 2, the demand forecast and number of working days in each month have been provided. The company requests that If the demand cannot be satisfied in the current month, it should be satisfied in the next month, and each unit of unsatisfied demand will incure a lost goodwill cost (referred to as stockout cost £20/unit in Table 2) even if it can be satisfied later. With this requirement, all demand should be satisfied in the six months. And the company requests that no more than 10% of the stock out be allowed in each month. The plant operates eight hours each day. One worker can assemble a laptop every 4 hours. The workers are paid £12.50 per hour in the first 8 hours of the day and £14.00 per hour for overtime working. Acorn currently employs 15 permenant workers. Acorn also has a team of 5 people who are willing to work as seasonal workers. The cost of hiring them on is £30 per worker, and the layoff cost is £60 per worker. The hiring and laying off workers can only take place at the beginning of each month. Overtime is limited to a maximum of 1 hour per day per worker. Component costs for each laptop is £100. Given the rapid decline in component and finished product prices, carrying inventory from one month to the next incurs a cost of £20 per laptop per month. Assume that Acorn has a starting inventory of 200 units and wants to end the year with the same inventory level. Finally, a third party has offered to produce laptops as needed at a cost of £156 per unit.

a)Formulate an Integer Programming model for this aggregate planning problem The objective is to minimize the six month Total Cost (Total Cost = material cost + stockout cost + regular-time labour cost + overtime labour cost + inventory cost+ hiring and laying off cost). Describe clearly each of the following parts of your mathematical model with ONE or TWO sentences: objective function, decision variables, constraints and decision variable domain.

b)Model this problem in Excel and use Solver to find the optimal solution. Provide a description of the optimal solution found in the context of the application. ONE hard copy screenshot of your Excel model should accompany your description.

c)How does your answer change if the third party offers a price of less than or more than £156 per unit? Write up a parametric analysis report to advise the manager. Provide alternative solutions and analyse the advantages and disadvantages of the different solutions. The report you present should be understandable by someone who has no knowledge of Linear/Integer Programming terminology. Explain why would Acorn use the third party even when the per-unit cost of the third party is higher than the average per unit cost (including inventory holding and overtime) for in-house production without a third party?

One unit of A is made of two units of B, three units of C, and two units of D. B is composed of one unit of E and two units of F. C is made of two units of F and one unit of D. E is made of two units of D. Items A, C, D, and F have one-week lead times; B and E have lead times of two weeks. Lot-for-lot (L4L) lot sizing is used for the Acorn computer and items B, C, and D; lots of size 50 and 220 are used for items E and F, respectively. Item C has an on-hand (beginning) inventory of 10; D has an on-hand inventory of 50; all other items have zero beginning inventories. We are scheduled to receive 20 units of item E in Week 2; there are no other scheduled receipts.

a)Construct simple and low-level-coded bill-of materials.

b)If 25 units of A are required in Week 8, use the low-level-coded bill-of materials to find the necessary planned order releases for all componen

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